TEL AVIV UNIVERSITY The Iby and Aladar Fleischman Faculty of Engineering
The Zandman-Slaner School of Graduate Studies
THERMAL SPECIFIC BIO-IMAGING AND THERAPY
TECHNIQUE FOR DIAGNOSTIC AND TREATMENT OF
MALIGNANT TUMORS BY USING MAGNETIC
NANOPARTICLES
A thesis submitted toward the degree of
Master of Science in Biomedical Engineering
by
Iddo Michael Gescheit
October 2007
TEL AVIV UNIVERSITY The Iby and Aladar Fleischman Faculty of Engineering
The Zandman-Slaner School of Graduate Studies
THERMAL SPECIFIC BIO-IMAGING AND THERAPY
TECHNIQUE FOR DIAGNOSTIC AND TREATMENT OF
MALIGNANT TUMORS BY USING MAGNETIC
NANOPARTICLES
A thesis submitted toward the degree of
Master of Science in Biomedical Engineering
by
Iddo Michael Gescheit
This research was carried out in the Department of Biomedical Engineering under the supervision of Dr. Israel Gannot and Dr. Avraham Dayan
October 2007
i
To:
My parents Dorrit and Yehuda, who has always been there for me
My brothers Illai and Jonathan, who inspired me to complete this work
ii
Acknowledgments
I would like to take this opportunity to thank the people who helped me bring this work to
completion:
• My advisor Dr. Israel Gannot, who has been an advisor, a collaborator and a friend,
and has guided me through this work process while expanding my academic horizons
by exposing me to new areas in the bio-medical science.
• My advisor Dr. Avraham Dayan, who has guided me and supported me through all
thermal aspects of my work.
• A special thanks to Dr. Moshe Ben-David for spending countless hours talking to me
about this work and assisting in finalizing it.
• The staff at the Power Electronics Laboratory of the Electrical Engineering
Department Itai, Shelly, Bshara and especially Dr. Dror Medini for helping me with
the design and building of the electrical system.
• My dear friend Tomer Eruv, who has been there for me every day, supporting and
advising throughout this whole research process.
• Lastly, I would like to thank my family from the bottom of my heart, for their support
and caring: my mom Dorrit, my dad Yehuda, my dearest brothers Illai and Jonathan,
and Orti.
iii
Abstract
The objective of this research program is to develop a novel, non-invasive, low cost infrared
(8-12 μm spectral range) imaging technique that would improve upon current methods using
nanostructured core/shell magnetic/noble metal based imaging and therapies.
The biocompatible magnetic nanoparticles are able to produce heat under AC magnetic field.
This thermal radiation propagates along the tissue by thermal conduction reaching medium's
(tissue's) surface. The surface temperature distribution is acquired by a thermal camera and
could be analyzed to retrieve and reconstruct nanoparticles' temperature and location within
the tissue.
The aforementioned technique may function as a diagnostic tool thanks to the ability of
specific bio-conjugation of these nanoparticles to a tumor's outer surface.
Hence, by applying a magnetic field we could cause an elevation of temperature of the
selective targeted nanoparticles up to 5°C, which allows us the imaging of the tumor.
Furthermore, elevating the temperature over 65°C and up to 100°C stimulates a thermo-
ablating interaction which causes a localized irreversible damage to the cancerous site without
harming the surrounding tissue. While functioning as a diagnostic tool, this procedure may
serve as a targeted therapeutic tool under thermal feedback control as well.
iv
Contents
Acknowledgement………………………………………………………………….….i
Abstract…………………………………………………………………………….….ii
Contents……………………………………………………………………………….iii
List of Figures………………………………………………………………………....vi
List of Tables……………………………………………………………………….....ix
1 Introduction………………………………………………….…………………….….1
A. Cancer……………………………………………………………………….…1
B. Motivation………………………………………………………………..….…5
C. Cancer Imaging…………………………………………………………….…..7
1. Imaging for Cancer Diagnosis………………………………...………7
2. Current Imaging Methods…………………………………….....…….8
3. Trends in Cancer Imaging……………………………………………..9
4. The Role of Imaging…………………………………………………11
5. Thermal Imaging……………………………………………………..15
6. Treatment………………………………………………………...…..19
D. The Vision………………………………………………………………….…23
E. Bioconjugation……………………………………………………………..…26
F. References………………………………………………………………….…29
2 Heat Generation……………………………………………………………………..34
A. Introduction……………… …………………………………………………..34
B. Applications of Magnetic Nanoparticles…………………………………..….36
C. Objectives…………………………………………………………………..…38
D. Heating Mechanisms……………………………………………………….…38
v
E. Affecting Parameters……………………………………………………….…42
1. Field Parameters……………………………………………...………42
2. Material Properties……………………………………………….…..42
3. Size Dependence……………………………………………….…….45
4. Miscellaneous……………………………………………………..….48
F. References…………………………………………………………………….49
3 Thermal Analysis……………………………………………………………………52
A. Introduction…………………………………………………………………...52
B. Image Processing Approaches to IR Images………………………………….53
C. The Problem………………………………………………………………..…56
D. Method of Solution…………………………………………………………...58
1. Forward Problem and Analytical Solution…………………………...58
2. Pennes Equation…………………………………………………..….58
3. Heat Conduction Equation……………………………………...……60
E. Point Simulation……………………………………………………………....63
1. Forward Solution………………………...…………………………...63
2. Inverse Solution………………………………………………...……66
F. Spherical Simulation……………………………………………………….....74
G. References…………………………………………………………………….85
4 System Design………………………………………………………………………..88
A. Introduction………………………………………………………………...…88
B. Heat Generation……………………………………………………………....89
C. Antenna Configurations……………………………………………………....91
1. Solenoid…………………………………………………………...…91
2. C-Core………………………………………………………………..92
vi
3. Helmholtz Coil……………………………………………………….94
D. Current Generation…………………………………………………...……….96
E. Thermal Image Acquisition…………………………………………………..99
F. The Integrated System……………………………………………………..…99
G. References…………………………………………………………………...102
5 Conclusions and Future Work………………………………………………….....103
A. Conclusions……………………………………………….…………………103
B. Future Work………………………………………………………………....105
vii
List of Figures
Figure 1.1: Estimated number of new cancer cases for 2006, excluding basal and squamous
cell skin cancers and in situ carcinomas except urinary bladder. Note: State estimates are
offered as a rough guide and should be interpreted with caution. They are calculated
according to the distribution of estimated cancer deaths in 2006 by state. State estimates may
not add to US total due to rounding……………………………………………………..……..3
Figure 1.2.A: The electromagnetic spectrum and the IR region……………………......……17
Figure 1.2.B: Blackbody radiation curves showing peak wavelengths at various
temperatures…………………………………………………………………………..………17
Figure 1.3: Schematic description of the system employing a targeted imaging technique and
a closed-loop system for therapy under real-time
feedback…………………………………....25
Figure 1.4: Bioconjugation of magnetic nanopatricles by using the natural immune
system……………………………………………………………………………………..….26
Figure 1.5: Magnetic nanoparticles schematic siting along the tumor surface………………27
Figure 1.6: Histological staining: 5-day old tumor with CD-3 at magnitude ×200. A colume
layer where binding was detected can be seen on the left…………………………………....28
Figure 2.1: Relative sizes of cells and their components…………………………………….37
Figure 2.2: Relaxational losses leading to heating in an alternating magnetic field (H)…….38
Figure 2.3: Schematic illustration of the energy of a single-domain particle with uniaxial
anisotropy as a function of magnetization direction……………………………………….....40
viii
Figure 2.4: Crystal structure of Fe3O4 . Big balls denote oxygen atoms, small dark balls
denote A-site (tetrahedral) iron atoms, and small light balls denote B-site (octahedral) iron
atoms…………………………………………………………...……………………………..43
Figure 2.5.A: Fe Nanoparticles produced by Nanosonics Inc. Magnetic nanoparticles in
different particle size configured as powder………………………………………………….45
Figure 2.5.B: Fe Nanoparticles produced by Nanosonics Inc. Schematic illustration of a
single Fe-Au nanoparticles…………………………………………………………………....45
Figure 2.6: Dependence of magnetic loss power density on particle size for magnetite fine
particle (2MHz, 6. 5 kA/m)………………………………………………………………...…47
Figure 2.7: Grain size dependence of the loss power density due to Néel-relaxation for
small ellipsoidal particles of magnetite (6. 5 kA/m)………………………………………….48
Figure 3.1: The thermal problem description………………………………………..………57
Figure 3.2: Schematic description og the heat conduction problem………………………...61
Figure 3.3: Non-dimensional surface temperature over an embedded point heat source……64
Figure 3.4.A: MATLAB® simulation results: surface temperature T(0, r, Q) for various point
heat sources……………………………………………………………………………..…….65
Figure 3.4.B: Draper and Boag’s results: surface temperature T(0, r, Q) for various point heat
sources………………………………………………………………………………...………65
Figure 0.5: Surface temperature cross sectional distribution………………………….…….66
Figure 03.6: FWHM as a function of varying power (Q) for different depths
(a)…………………....68
Figure 3.7: FWHM as a function of depth for various tissues…………………………….....69
Figure 3.8: Computing source depth for a specific tissue…………………………………....70
Figure 3.9: Area below the surface temperature profile (A) as a function of the source power
(Q)……………………………………………………………………………………….……71
ix
Figure 3.10: Area (A) as a function of power (Q) for various source depths…………...……72
Figure 3.11: Exponential behavior of A(Q) slopes…………………………………………..72
Figure 3.12: Selected A(Q) curve based on the p-parameter……………………………..….73
Figure 3.13: Spherical model for thermal analysis of a tumor……………………..………..75
Figure 3.14: Spherical coordination system………………………………………………….76
Figure 3.15: Nanoparticles superficial distribution on the sphere……………………..…….76
Figure 3.16: Comparison of a point source and spherical source (R=0.01 cm). The curve of
spherical source is deliberately elevated by 1˚C in order to distinguish the two curves…..…78
Figure 3.17: Problem modeling in bispherical coordinate system………………………..….79
Figure 3.18: Validation of an auxiliary MATLAB® code simulating Small and Weihs
solution…………………………………………………………………………………….….81
Figure 3.19: Effective spherical model………………………………………………………83
Figure 3.20: Comparison of Small and Weihs solution with the spherical simulation……....83
Figure 4.1: Schematic description of the system………………………………………….....89
Figure 4.2: Schematic description of a C-core configuration………………………………..92
Figure 4.3: Schematic description of Helmholtz coils configuration………………..………95
Figure 4.4: Wave templates generated by the system…………………………………….….97
Figure 4.5: System's block scheme……………………………………………………..……98
Figure 4.6: The power generator's block scheme……………………………………….……98
Figure 4.7: Schematic description of the closed-loop system……………………………....100
Figure 4.8: Laboratory system………………………………………………………...……101
x
List of Tables
Table 1.1: Estimated new cancer cases and deaths by sex for all sites, US, 2006………….…4
Table 2.1: SAR values of samples in the applied magnetic field (80 kHz, 32.5 kA/m) and
coercivity Hc of samples………………………………………………………………...……46
Table 3.1: Point heat sources in various depths a and strength Q……………………………64
Table 3.2: Given parameters for illustrative problem………………………………………..67
Table 3.3: Comparison of real parameters and estimated parameters………………………..73
Chapter 1 Introduction
1–1
1. Introduction
1.A. Cancer
Cancer is a class of diseases or disorders characterized by uncontrolled division of cells and
the ability of these cells to spread, either by direct growth into adjacent tissue through
invasion, or by implantation into distant sites by metastasis. Transportation of cancerous cells
to distant sites is done through the bloodstream or lymphatic system. Cancer may affect
people at all ages, but risk tends to increase with age. It is one of the principal causes of death
in developed countries.
Cancer may attack any organ, e.g. liver, lung, breast etc. while the severity of disease depends
on various parameters such as the site and character of the malignancy and the
presence/absence of metastasis. Despite of the fact that modern medicine and medical
research and technology made significant progress on the last decades, still a definitive cancer
diagnosis usually requires the histologic examination of tissue by a pathologist. This tissue is
obtained by an invasive procedure as biopsy or surgery. Most cancer types can be treated and
some cured, depending on the specific type, location, and stage.
Once diagnosed, cancer treatment usually involves a combination of surgery, chemotherapy
and radiotherapy. In cases of late detection or no treatment, cancers may eventually cause
illness and death, though this is not always the case.
Chapter 1 Introduction
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The unregulated growth that characterizes cancer is caused by damage to DNA, resulting in
mutations to genes that encode for proteins controlling cell division. These mutations can be
caused by radiation, chemicals or physical agents that cause cancer, which are called
carcinogens, or by certain viruses that can insert their DNA into the human genome. As
known in the art, many forms of cancer are associated with exposure to environmental factors
such as tobacco smoke, radiation, alcohol, and certain viruses.
In order to understand the severity and prevalence of cancer, American Cancer Society
expected about 1, 399,790 new cancer cases to be diagnosed in 2006. This estimate does not
include carcinoma in situ (noninvasive cancer) or any site except urinary bladder, and does
not include basal and squamous cell skin cancer. More than 1 million cases of basal and
squamous cell skin cancers were expected to be diagnosed in 2006 (Figure 1.1).
In the same year, about 564,830 Americans were expected to die of cancer, more than 1,500
people a day. Cancer is the second most common cause of death in the US, exceeded only by
heart disease. In the US, cancer accounts for 1 of every 4 deaths. The National Institute of
Health (NIH) estimate overall costs for cancer in 2005 at $209.9 billion [1, 2]. A summary of
estimated new cancer cases and deaths for the US is shown in
Chapter 1 Introduction
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Figure 1.1 Estimated number of new cancer cases for 2006, excluding basal and squamous cell skin cancers
and in situ carcinomas except urinary bladder. Note: State estimates are offered as a rough guide
and should be interpreted with caution. They are calculated according to the distribution of
estimated cancer deaths in 2006 by state. State estimates may not add to US total due to rounding [3]
Chapter 1 Introduction
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Table 1.1 Estimated new cancer cases and deaths by sex for all sites, US, 2006*
Estimated New Cases Estimated Deaths
Both
Sexes Male Female
Both
Sexes Male Female
All sites 1,399,790 720,280 679,510 564,830 291,270 273,560
Oral cavity & pharynx 30,990 20,280 10,810 7,430 5,050 2,380
Digestive system 263,060 137,630 125,430 136,180 75,210 60,970
Respiratory system 186,370 101,900 84,470 167,050 93,820 73,230
Bones & joints 2,760 1,500 1,260 1,260 730 530
Soft tissue (including heart) 9,530 5,720 3,810 3,500 1,830 1,670
Skin (excluding basal & squamous) 68,780 38,360 30,420 10,710 6,990 3,720
Breast 214,640 1,720 212,920 41,430 460 40,970
Genital system 321,490 244,240 77,250 56,060 28,000 28,060
Unary system 102,740 70,940 31,800 26,670 17,530 9,140
Eye & orbit 2,360 1,230 1,130 230 110 120
Brain & other nervous system 18,820 10,730 8,090 12,820 7,260 5,560
Endocrine system 32,260 8,690 23,570 2,290 1,020 1,270
Lymphoma 66,670 34,870 31,800 20,330 10,770 9,560
Multiple myeloma 16,570 9,250 7,320 11,310 5,680 5,630
Leukemia 35,070 20,000 15,070 22,280 12,470 9,810
Other & unspecified
primary sites† 27,680 13,320 14,360 45,280 24,340 20,940
*Rounded to the nearest 10; estimated new cases exclude basal and squamous cell skin and in situ carcinoma except urinary
bladder. About 61,980 carcinoma in situ of the breast and 49,710 melanoma in situ were expected to be diagnosed in 2006. †More
deaths than cases suggest lack of specificity in recording underlying causes of death on death certificates. Source: Estimates of new
cases are based on incidence rates from 1979 to 2002, National Cancer Institute's Surveillance, Epidemiology, and End Results
program, nine oldest registries. Estimates of deaths are based on data from US Mortality Public Use Data Types, 1969 to 2003,
National Center for Health Statistics, Centers for Disease Control and Prevention, 2006
©2006, American Cancer Society, Inc., Surveillance Research
Chapter 1 Introduction
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Cancer can also occur solely in young children and adolescents.
The age of peak incidence of cancer in children occurs during the first year of life. Leukemia
(usually ALL) is the most common infant malignancy (30%), followed by the central nervous
system cancers and neuroblastoma. The remainder consists of Wilms' tumor, lymphomas,
rhabdomyosarcoma (arising from muscle), retinoblastoma, osteosarcoma and Ewing's
sarcoma [4]. Female and male infants have essentially the same overall cancer incidence rates,
but white infants have substantially higher cancer rates than black infants for most cancer
types.
1.B. Motivation
As known, cancer is a very prevalence disease with no satisfying cure and/or treatment. A
disease in which many resources are invested involving various research fields such as
biology, chemistry, engineering, medicine and behavioral science.
This research amongst others is motivated by several main statistics described as follows:
Diagnosis [5]
Small primary tumors go undetected. For many cancers, an internal, aggressive, noncalcified
tumor under containing fewer than 500,000 cells (i.e., under 2mm wide) is likely to pass
undetected through most body-region scans, including CT, MRI, ultrasound, radionuclide,
and metabolic PET. At this size, a tumor has effectively undergone 19 cell doublings about
halfway through doubling toward a predicted lethal load of 1010–1012 cells and is likely to be
sufficiently repleted with gene defects so that it will undergo continued and uninterrupted
growth if not treated.
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Staging
Metastatic disease underdiagnosed. For the reasons stated above, patients with negative scans
for metastases at initial presentation routinely go on to develop, and die from, metastatic
cancer. For example, about 20% of women with breast cancer clinically confined to the breast
and lymph nodes (low and intermediate risk), and the majority of men with local margin-
positivity after prostatectomy, will go on to have a recurrence of their disease, despite initially
negative bone and body imaging scans. Even though it did not appear in the image,
undetected residual and/or metastatic cancer must have been present at the time of the initial
scanning.
Margins
Residual disease common after surgery. After surgical resection, 30% or more of patients
with breast or prostate cancer have residual disease in the surgical field [6, 7], undetected by
even realtime surgical imaging, but yet which will be found on gross and histochemical
pathology in the days or weeks after the surgery has been completed, and the patient has been
closed and sent home. Cancer recurrence rates are 2.5× higher in multivariate analysis if the
margins are positive [8, 9] and these patients are significantly more likely to die of their
disease.
Therapy
Treatment response is poorly measured. ‘Measurable disease,’ a common yardstick for
monitoring response to treatment, is absent after surgical excision of many tumors. Therefore,
the standard of care is to blindly treat with chemotherapy selected by convention using prior
retrospective studies, and to consider this treatment a success or failure only in retrospect (i.e.,
success is when a patient survives 5 years, and failure is when a relapse occurs).
Chapter 1 Introduction
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1.C. Cancer Imaging
1.C.1. Imaging for Cancer Diagnosis
Most cancers are initially recognized either because signs or symptoms appear or through
screening. Neither of these lead to a definitive diagnosis, which usually requires the opinion
of a pathologist. Roughly, cancer symptoms can be divided into three groups:
(i) Local symptoms: unusual lumps or swelling (tumor), hemorrhage (bleeding), pain and/or
ulceration. Compression of surrounding tissues may cause symptoms such as jaundice.
(ii) Symptoms of metastasis (spreading): enlarged lymph nodes, cough and hemoptysis,
hepatomegaly (enlarged liver), bone pain, fracture of affected bones and neurological
symptoms. Although advanced cancer may cause pain, it is often not the first symptom.
(iii) Systemic symptoms: weight loss, poor appetite and cachexia (wasting), excessive
sweating (night sweats), anemia and specific paraneoplastic phenomena, i.e. specific
conditions that are due to an active cancer, such as thrombosis or hormonal changes.
A cancer may be suspected for a variety of reasons, but the definitive diagnosis of most
malignancies must be confirmed by histological examination of the cancerous cells by a
pathologist. Tissue can be obtained from a biopsy or surgery. Many biopsies (such as those of
the skin, breast or liver) can be done in a doctor's office. Biopsies of other organs are
performed under anesthesia and require surgery in an operating room.
The tissue diagnosis indicates the type of cell that is proliferating, its histological grade and
other features of the tumor. Together, this information is useful to evaluate the prognosis of
this patient and choose the best treatment.
Chapter 1 Introduction
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Cytogenetics and immunohistochemistry may provide information about future behavior of
the cancer (prognosis) and best treatment, however it should be appreciated that these aspects
of cancer and others such as cell biology, cancer origin, epidemiology etc are not on the scope
of this research [5].
1.C.2. Current Imaging Methods [5]
Although significant progress has been achieved in known and conventional radiologic
modalities since the first X-rays, still typical images relies on bulk characterization of the
tissue. The resulting anatomic signal is therefore epiphenomenal, being merely an expression
of the sum of nonspecific interactions of the imaging source with the tissues structure,
physiology and/or pathology. Thus, the the visualization and characterization of tumor by
conventional modalities such as CT, MRI, or ultrasound is merely dependent in distinction of
tumor from the surrounding tissue and inherent background noise, e.g. the ability of that
tumor to differentially scatter, absorb, or emit radiation in comparison to the surrounding
tissue. One of the main drawbaks of conventional modalities is the little specificity and
sensitivity for the detection of tumor, which stems in the ability to acquire data which is at
least in part, a function of cell density, microcalcifications, and the like - effects that are not a
significant signature of cancerous tissue.
Equally important, while the lethality of many solid tumors is due to the physical crowding or
bulk effects of the tumor, the majority of diagnosis, treatment selection, treatment
monitoring, and follow-up, involves decisions in which the physical, bulk characteristics of
the tumor are, not the driving question. Rather, the questions that require answers are those of
tumor presence vs. absence, of type and grade and distribution, and of gene expression, cell
function, and receptor positivity.
Chapter 1 Introduction
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As a result, oncology in particular has gone looking for methods that dovetail with the
emphasis in medicine: gene-specific or receptor-specific therapies, minimally invasive
treatments for early-diagnosed tumors, stage-specific treatment options.
1.C.3. Trends in Cancer Imaging [5]
Recent tumor imaging has been trying to neglect nonspecific imaging, and to adopt specific
imaging employing patient-specific, disease-specific, and cell-specific. Driving this change
are four trends.
Patient-specific medicine
The trend in oncology, as in medicine in general, is away from nonspecific diagnosis and
treatment, and toward patient-specific therapy. As cell receptor status and gene expression
become used with increasing frequency to manage the oncology patient, the diagnosis and
treatment for cancer becomes dependent on identifying the molecular and genetic makeup of
the tumor (for breast cancer, this is currently a palate of PR, ER, Her2-neu positivity, and
perhaps a mitotic rate assay such as Ki-66, or others, depending upon institution), rather than
upon the anatomic and pathologic grade of the tumor.
Specific markers
New markers are becoming available at a dizzying pace as a result of biochemical advances
and the genome project [10, 11]. Gene chips and other tools are allowing such markers to
begin to be correlated with clinical stage, tumor aggressiveness, outcome, and response to
treatment, while drug discovery seeks to use these identified markers as specific targets for
new pharmaceutical agents. From an imaging point of view, such markers are important as the
Chapter 1 Introduction
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anatomic, or bulk effects, of tumors are absent at the early or minimal residual disease stages
of cancer, while genetic disturbances and receptor abnormalities remain present in small
tumor populations, and can be tumor-specific, stagespecific, and response-specific
(refer section 1.E).
Novel sensors
New sensors have allowed for new types of scanners, such as portable optical imagers for
visible and near-infrared photon detection. Examples of such new sensors include activatable
contrast agents and genetic expression elements which can be used to produce or amplify
local contrast in imaging studies. Advances in computing power, which has continued to
double the power every 18 months without increases in cost, make increasingly complex
calculation- and graphicsheavy imaging software routine, and possible in real-time or near-
real-time.
Less-invasive medicine
Last, the trend in medicine for the past 20 years has been toward reduced invasiveness. More
sensitive imaging allows diagnosis and therapy to be physically targeted to the tumor, as well
as allows less invasive monitoring of therapeutic response. Local, regionally limited surgical
procedures (such as lumpectomy, local ablation, endoscopic approaches) now permit con-
fined islands of disease, if located, to be treated quickly and effectively.
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1.C.4. The Role of Imaging [5]
Imaging will become less of a tool for initial gross staging. Instead, it will become more
frequent and integrate more effectively and seamlessly with patient management at all stages
of oncology diagnosis, treatment, and followup. Sensitive and specific imaging will allow for
a more proactive role for imaging in the following areas.
Diagnosis
At diagnosis, imaging will yield more sensitive detection of cancer, including optimally
imaging such features as receptor status, gene expression, and tumor grade now obtained only
through biopsy and analysis by pathology microscopy, immunohistochemistry, and PCR (i.e.
Polymerase Chain Reaction). The lower limit for tumor detection is improving. For example,
while the lower limit of tumor detection in human subjects is currently about 500,000 cells
(2–3mm diameter tumor), optical methods have moved the lower limit of tumor detection in
animal models down to fewer than 1,000 cells, noninvasively and specifically imaged [12].
The ability to image receptor status in vivo has been demonstrated using antigenically
targeted probes, such as those targeted to somatostatin [13]. More specific scans will also play
a role in avoiding invasive evaluations. The majority of all biopsies are negative, therefore a
reduction in invasive evaluations will be a benefit of more specific scans [14]. Despite such
improvements, there will always be some degree of a lag between the identification of new
markers via molecular biology and the ability to image those markers, and thus there will
likely continue to be a need for tissue samples to allow for testing of the latest markers for
optimal selection of therapy, as well as for banking of tissue, to allow for testing of future
markers when these become available.
Chapter 1 Introduction
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Staging
Staging will become more accurate, thus profoundly influencing patient segmentation and
treatment selection. Surgical staging procedures, such as nodal biopsy, may be able to be
reduced using imaging (or perhaps replaced entirely if tissue for pathology has already been
obtained), with imaging follow-up used to ensure accuracy of a negative scan. One step
toward this scenario – limiting the size of lymphatic staging by better imaging of the
sentinelnodes – has been achieved using radioemitter-based colloid imaging for melanoma
and breast, and this has led to a decrease in the physical extent of the surgical procedure, and
to reduced morbidity and a minimal loss of diagnostic accuracy (though with an unknown
effect of long-term outcome [15]). The next step is replacing the nonspecific radioemitter with
a specific and highly sensitive marker or reporter for tumor in the nodes. For breast cancer, if
this can be achieved, then only tumor-positive nodes would be therapeutically removed (and
sent to pathology), while the majority of women would be able to forego the therapeutic nodal
biopsy altogether.
Further, the detection of mediastinal (as opposed to axillary) nodes would be improved,
perhaps leading to elective removal of those mediastinal nodes using a minimally invasive
parasternal procedure.
Therapeutic monitoring and feedback
Early, course-correcting treatment feedback will become standard-of-care for many therapies,
especially when good alternative therapies exist. Rather than perform a bone scan months
down the road after treatment is initiated, tumor response will be evaluated with scans during
the first treatment doses. For example, MR spectroscopic imaging (MRSI) and/or PET
imaging before and after treatment to look for changes in cell metabolism consistent with a
Chapter 1 Introduction
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response has already been studied as a potential method to identify responders from non-
responders months before current methods can do so [16-19].
Sequential scans may also be able to identify the emergence of resistance during ongoing
treatment, such that the treatment may be changed before the patient presents with clinical
signs of treatment failure.
Optical imaging has detected emergence of resistance in animal models of disease within days
to weeks [12], while MRI and PET have been used to image apoptosis in animals [20], and in
some instances in humans [21]. Another aspect of therapeutic monitoring is the
measurement of chemotherapy levels in the patient’s tissues, or in the tumor itself, using
noninvasive or minimally-invasive imaging techniques [22-26]. This would allow for patient-
specific dosing, based upon the actual tumor or tissue levels in a given patient, rather than
blindly based upon body surface area or weight. Using such approaches, gene therapies can be
immediately evaluated for efficacy of gene expression, and followed on an ongoing basis for
continued expression and/or tumor effect.
Similarly, cell trafficking may be followed, again as markers of anti-tumor activity or to help
assess clinical response. Such early and ongoing treatment response feedback likely to be
cost effective. While the cost effectiveness of oncologic screening tests has been hotly
debated, such as with routine mammography [27-29], a patient under treatment can
immediately balance the imaging costs against the cost of the therapy. Newer chemotherapy
agents are significantly more expensive than the older agents; therefore an early feedback
scan to measure treatment effect would prevent further use of an expensive agent that would
otherwise ultimately be without effect. Under this view, such treatment response imaging
scans may become a required part of care. Further, the patient can then rapidly be switched to
Chapter 1 Introduction
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another, and hopefully more active chemotherapeutic agent, which is likely to have a positive
impact on overall response rates, survival time, and cost of care.
Image guidance
Image guided therapies will expand as the sensitivity of images to small regions of disease
increases. Benaron's group has been developing real-time tumor imaging systems sensitive to
the antigenic presence of residual tumor in the surgical field. Preliminary data [12] suggest
that such scans may lower the detectability limit of disease to 100µm islands. Such a tool,
deployed in the operating room, directly impacts the 30% of breast and prostate cancer
patients with residual disease in the surgical field after treatment, and could potentially allow
for reduction or even elimination of the presence of positive-margins, indicating residual
tumor, after surgical resection. Researchers have also been developing real-time sensors
embedded into the surgical tools themselves, to give feedback during the surgical process
[30]. Both of these approaches could lead to more effective treatment, and as well as enabling
more minimally invasive treatment procedures.
Follow-up
Many cancer patients are at high risk for relapse. While there are again economic issues that
have been used to argue for the limitation of access to follow-up imaging techniques, such
imaging is already standard for some cancers (such as lymphoma). Increases in the sensitivity
of follow-up scans will likely increase the benefit and applicability of such scans. For
example, six months after node-negative scans in the breast cancer patient who avoided a
nodal dissection due to negative initial, a repeat scan may be indicated to catch those patients
with early disease too small to be detected on the first pass.
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Drug discovery
Imaging is playing an increasing role in the discovery and development of new agents, both
in humans and animals. The same imaging agents that can be used for imaging targets in
humans can be used during drug discovery and development for use in imaging animals.
Thus, better animal imaging permits for better and more rapid drug discovery, as well as for
better basic research [31]. Specific systems for imaging animals have been made available for
micro (small animal) CT [32, 33], PET [34, 35], MRI, and green fluorescent protein (GFP)
imaging. In addition to these imaging systems, designer animals, with desired combinations
of knockout target genes and add-in reporter genes, are playing an increasing role in the drug
discovery process. Animals with reporter genes tied to specific imaging modalities are already
being created.
1.C.5. Thermal imaging
The first documented application of Infrared (IR) imaging in medicine was in 1956 [36],
when breast cancer patients were examined for asymmetric hot spots and vascularity in IR
images of the breasts. Since then, numerous research findings have been published [37], [38],
[39] and the 1960s witnessed the first surge of medical application of the IR technology [40],
[41], with breast cancer detection as the primary practice. However, IR imaging has not been
widely recognized in medicine nowadays, largely due to the premature use of the technology,
the superficial understanding of IR images, and its poorly controlled introduction into breast
cancer detection in the 70s [42].
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Recently, advances in a couple of related areas have pushed forward series of activities to
reappraise the role of IR imaging in medicine [42-48].
These advances, including the development of the new-generation infrared technology, smart
image processing algorithms, and the pathophysiological-based understanding of IR images,
will provide a cost-effective, non-invasive, non-destructive, and patient-friendly approach to
health monitoring and examination, as well as to assisting diagnosis [40], [49]
Thermal imaging relies on sensing the infrared radiation emitted by all objects above absolute
zero temperature. All objects emit photons as a result of transitions from a high-energy to
low-energy state. In solids, such transitions lead to a continuous distribution of energy
between different wavelengths according to the Planck equation (1901), shown as follows
[50]:
( )1
5
2
2( , )
exp 1b
Ce T
C Tλ
πλ
λ λ=
−
where λ is the wavelength, C1=hc2 and C2=hc/k; h is Planck's constant, k is Boltzmann's
constant and c is speed of light in a vacuum.
In general, IR radiation covers wavelengths that range from 0.75 µm to 1000 µm, among
which the human body emissions that are traditionally measured for diagnostic purposes only
occupy a narrow band at wavelengths of 8 µm to 12 µm (refer Figure 1.2.A) [51].
This radiation is not visible to the human eye but, in sufficient intensity, can be felt by the
human skin, one function of which is a low-sensitivity infrared array detector. The Planck
function is exponentially nonlinear in temperature.
This means that the lower- temperature objects emit order of magnitude less energy than do
higher-temperature objects (Figure 1.2.B). Therefore detection of infrared energy accurately is
a challenging task [52].
Chapter 1 Introduction
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Figure 1.2.A The electromagnetic spectrum and the IR region.
Figure 1.3.B Blackbody radiation curves showing peak wavelengths at various temperatures.
Infrared imaging is a physiological test that measures the subtle physiological changes that
might be caused by many conditions, e.g. contusions, fractures, burns, carcinomas,
lymphomas, dermatological diseases, rheumatoid arthritis, diabetes mellitus, bacterial
infections, etc.
Chapter 1 Introduction
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These conditions are commonly associated with regional vasodilation, hyperthermia,
hyperperfusion, hypermetabolism, and hypervascularization [51], [53-58] which generate
higher-temperature heat source.
Unlike imaging techniques such as X-ray radiology and CT that primarily provide
information on the anatomical structures, IR imaging provides functional information not
easily measured by other methods. Thus correct use of IR images requires in-depth
physiological knowledge for its effective interpretation [48].
However, there is still an existing nonspecificity in the process, which must be recognized and
addressed by improving the analytical tools and recognizing that, even with the most
improved tools, a fundamentally nonspecific diagnostic technique such as thermal imaging
can only be used as a powerful adjunct tool. Such recognition will avoid the controversy and
confusion often surrounding this issue. This aspect of IR imaging is discussed in chapter 2
and 3.
The use of nanoparticles in cancer imaging
The biological application of nanoparticles is a rapidly developing area of nanotechnology
that raises new possibilities in the diagnosis and treatment of human cancers.
Optical imaging techniques has strong potential for sensitive cancer diagnosis, particularly at
the early stage of cancer development involving fluorescent nanoparticle probes such as dye-
doped nanoparticles and quantum dots [59]. Nanoparticles such as supermagentic and gold
nanoshells have exciting possibilities as contrast agents for cancer detection (e.g. MRI, optical
techniques), and for monitoring the response to treatment [60], [61], [62], [63].
Magnetic nanoparticles also hold promise in the combination with thermal imaging improving
its nonspecifitiy and sensitivity as described in detail in chapters 2 and 3.
Chapter 1 Introduction
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1.C.6. Treatment
Cancer can be treated by various modalities such as surgery, chemotherapy, radiation therapy,
immunotherapy, monoclonal antibody therapy or other methods. The choice of therapy
depends upon the location and grade of the tumor and the stage of the disease, as well as the
general state of the patient (performance status). The goal of treatment is a complete removal
of the cancer without causing any damage to the surrounding healthy body tissue. However,
each modality has its own limitations. Sometimes, complete tumor removal can be
accomplished by surgery, but the propensity of cancers to invade adjacent tissue or to spread
to distant sites by microscopic metastasis often limits its effectiveness. The effectiveness of
chemotherapy is often limited by toxicity to other tissues in the body. Radiation can also
cause damage to normal tissue. Therefore both the use of both methods is limited to a certain
amount of dosage, which can not be passed.
Surgery
In theory, cancers can be cured if entirely removed by surgery, but this is usually an
impractical wishful thinking. When cancerous tumor has already metastasized to distinct sites
in the body prior to surgery, complete surgical excision is usually impossible.
Examples of surgical procedures for cancer include mastectomy for breast cancer and
prostatectomy for prostate cancer. The goal of the surgery can be either the removal of only
the tumor, or the entire organ. A single cancer cell is invisible to the naked eye but can regrow
into a new tumor, a process called recurrence. For this reason, the pathologist will examine
the surgical specimen to determine if a margin of healthy tissue is present, thus decreasing the
chance that microscopic cancer cells are left in the patient.
Chapter 1 Introduction
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In addition while removing a primary tumor, surgery has essential role in staging, e.g.
determining the extent of the disease and whether it has metastasized to regional lymph
nodes. Staging is a major determinant of prognosis and of the need for adjuvant therapy.
Occasionally, surgery is necessary to control symptoms, such as spinal cord compression or
bowel obstruction. This is referred to as palliative treatment [1], [64], [65], [66].
Chemotherapy
Chemotherapy is the phatrmaceutical treatment of cancer, i.e. therapy by using "anticancer
drugs" that are capable of destroying cancerous cells. It interferes with cell division in various
possible ways, e.g. with the duplication of DNA or the separation of newly formed
chromosomes. Most forms of chemotherapy target all rapidly dividing cells and are not
specific for cancer cells. Hence, chemotherapy has the potential to harm healthy tissue,
especially those tissues that have a high replacement rate (e.g. intestinal lining).
For instance, the treatment of some leukaemias and lymphomas requires the use of high-dose
chemotherapy, and total body irradiation (TBI). This treatment ablates the bone marrow, and
hence the body's ability to recover and repopulate the blood. For this reason, bone marrow, or
peripheral blood stem cell harvesting is carried out before the ablative part of the therapy, to
enable "rescue" after the treatment has been given. This is known as autologous
transplantation. Alternatively, bone marrow may be transplanted from a matched unrelated
donor (MUD) [67], [68], [69].
Chapter 1 Introduction
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Immunotherapy
Immunotherapy is the use of immune mechanisms against tumors. These are used in various
forms of cancer, such as breast cancer (trastuzumab/Herceptin®) and leukemia (gemtuzumab
ozogamicin/Mylotarg®). The agents are monoclonal antibodies directed against proteins that
are characteristic to the cells of the cancer in question, or cytokines that modulate the immune
system's response.
Other, more contemporary methods for generating non-specific immune response against
tumours include intravesical BCG immunotherapy for superficial bladder cancer, and use of
interferon and interleukin. Vaccines to generate non-specific immune responses are the
subject of intensive research for a number of tumours, notably malignant melanoma and renal
cell carcinoma [70].
Radiation therapy
Radiation therapy (also called radiotherapy, X-ray therapy, or irradiation) is the use of
ionizing radiation to kill cancer cells and shrink tumors. Radiation therapy can be
administered externally via external beam radiotherapy (EBRT) or internally via
brachytherapy. The effects of radiation therapy are localised and confined to the region being
treated. Radiation therapy injures or destroys cells in the area being treated (the "target
tissue") by damaging their genetic material, making it impossible for these cells to continue to
grow and divide. Although radiation damages both cancer cells and normal cells, most normal
cells can recover from the effects of radiation and function properly. The goal of radiation
therapy is to damage as many cancer cells as possible, while limiting harm to nearby healthy
tissue. Hence, it is given in many fractions, allowing healthy tissue to recover between
fractions.
Chapter 1 Introduction
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Radiation therapy may be used to treat almost every type of solid tumor, including cancers of
the brain, breast, cervix, larynx, lung, pancreas, prostate, skin, stomach, uterus, or soft tissue
sarcomas. Radiation is also used to treat leukemia and lymphoma. Radiation dose to each site
depends on a number of factors, including the radiosensitivity of each cancer type and
whether there are tissues and organs nearby that may be damaged by radiation. Thus, as with
every form of treatment, radiation therapy is not without its side effects [71], [72], [73].
Hormonal suppression
The growth of some cancers can be inhibited by providing or blocking certain hormones.
Common examples of hormone-sensitive tumors include certain types of breast and prostate
cancers. Removing or blocking estrogen or testosterone is often an important additional
treatment [74].
Hyprethermia
Hyperthermia is virtually causing damage to tissue by preferably eleveating the local
temperature. Several investigators have found that a major factor in cell killing at 42°C is the
irreversible damage to cancer cell respiration [75], [76]. While the exact mechanisms of heat
destruction remain poorly understood, coincident alterations appear to take place in nucleic
acid and protein synthesis that include a reduction of activity in many vital enzyme systems
[77],[78]. Hyperthermia may be carried out by various techniques such as low frequency
current fields, ferromagnetic coupling, microwaves, radiofrequency waves, magnetic
induction etc [79]. The use of hyperthermia in combination with nanoparticles is to be
discussed in detail hereinafter.
Chapter 1 Introduction
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As depicted above, the majority of treatment modalities is not capable of distinguishing
between malignant cells and healthy tissue and does not provide the physician with adequate
precision and specificity while removing cancerous cells. Moreover, there is no real-time
control referring the physiological margins distinguishing the malignant and benign tissue.
The implicatinons of the latter are for example in surgery, if the surgeon does not remove all
the malignant cells, the progression or recurrence of the disease is almost without doubt. On
the other hand, if the surgeon removes more than necessary, the "extra" tissue being removed
is a healthy tissue and may be vital for the organ life cycle or patient's life.
1.D. The vision
The suggested system is schematically illustrated in
Figure 1.4 and is briefly described below:
The process begins in the insertion of the magnetic nanoparticles into the patient's body either
locally to a suspected tissue or systematically to the blood stream by IV injection. When the
nanoparticles arrive in short proximity to the tumor, the process of bioconjugation occurs (see
section 1.E). Eventually, the tumor's outer surface is bind with nanoparticles by virtue of a
strong chemical bonds configured as antigen-antibody complex. Since the biocompatible
magnetic nanoparticles are able to produce heat under AC magnetic field, the region of
interest (ROI) is placed under a suitable field. This emitted thermal radiation propagates along
the tissue by thermal conduction reaching medium's (tissue's) surface. The surface
temperature distribution is acquired by a thermal camera and could be analyzed to retrieve
and reconstruct nanoparticles' temperature and location within the tissue. In future minimal
invasive applications the IR radiation can be "guided" from internal compartments of the body
Chapter 1 Introduction
1–24
to the outside by waveguides and dedicated optical fibers, e.g. thermal imaging bundles
shown by Gannot and Ben-David [80-83].
The aforementioned technique may function as a diagnostic tool thanks to the ability of
specific bio-conjugation of these nanoparticles to a tumor's outer surface.
Hence, by applying a magnetic field we could cause an elevation of temperature of the
selective targeted nanoparticles up to 5°C, which allows us the imaging of the tumor.
Furthermore, elevating the temperature over 65°C and up to 100°C stimulates a thermo-
ablating interaction which causes a localized irreversible damage to the cancerous site almost
without harming the surrounding tissue. This procedure may serve as a targeted therapeutic
tool under thermal feedback control carried out by software such as LabView® software
which allows us on one hand, to maintain a sufficient heat generation, producing a readable
signal, and on the other hand the avoidance of an over-heating damage which endanger the
surrounding tissue. This is valid in both diagnostic and therapeutic purposes where the main
differences are in the targeted temperatures.
Thus, the treatment can be done immediately after imaging the tumor only by elevating the
temperature, with a continuous feedback imaging of the ROI, since those selective specific
targeted mediators are doing both tasks.
Chapter 1 Introduction
1–25
Figure 1.4 Schematic description of the system employing a targeted imaging technique and a closed-
loop system for therapy under real-time feedback.
Nanoparticles Injection
Bio-Conjugation
AC Magnetic Field
IR CameraTherapy
under IR Imaging
Analysis
Diagnosis
End of Process
Nanoparticles Injection
Bio-Conjugation
AC Magnetic Field
IR CameraTherapy
under IR Imaging
Analysis
Diagnosis
End of Process
Nanoparticles Injection
Bio-Conjugation
AC Magnetic Field
IR CameraTherapy
under IR Imaging
Analysis
Diagnosis
End of Process
Chapter 1 Introduction
1–26
1.E. Bioconjugation
An important issue lying on the basis of this work is the fact that the magnetic nanoparticles
are localized specifically and functions as madiators situated on the periphery of the tumor. In
order to target the tumor and deliver the nanoparticles reliably and specifically, the suggested
transportation leans on human's immune system. The malignant tumor tends to present
specific antigens on its outer surface. These antigens are able to communicate with
corresponding agents of the immune system (e.g. antibodies) to establish antigen-antibody
complexes which are characterized in strong chemical bonds. For instance, we can bind the
magnetic nanoparticles' surface to the antibodies via adhering polymers (e.g. PEG) so that
antibodies transport them towards the tumor being delivered by immune agents (T cell), and
conjugate them to the tumor retaining them along the tumor's outer surface
(Figure 1.5and Figure 1.6).
Figure 1.5 Bioconjugation of magnetic nanopatricles by using the natural immune system
Antibody Magnetic
Nanoparticles Labeled
Antibody
Specific
LocalizationLabeled
Antibody
T cell
Chapter 1 Introduction
1–27
Figure 1.6 Magnetic nanoparticles schematic siting along the tumor surface
This bioconjugation is analogous to that made with fluorophores in research conducted by
Fibich et al. [84] and Gannot et al [85]. That optical imaging technique is based on ‘‘Anti-
CD3’’ antibodies conjugated to a fluorescent marker (FITC or IRD38) [86], injected to the
tumor area, and specifically bind to receptors on T cells (‘‘sites’’). These T cells reach the
tumor area as part of the natural immune system reaction of the object to a cancerous tumor
[87]. They are shown in Figure 1.7 - histological staining of a 5-day-old tumor with CD-3 at
magnitude ×200. A volume layer where binding was detected can be seen on the left [84].
This specific, minimal invasive and almost natural technique of targeting the tumor, lays the
fundamentals for both novel diagnostic and therapeutic techniques targeted solely to the
malignant cells without harming the surrounding healthy tissue.
Labeled
Antibody
T cellSurface
Marker
Tumor
Chapter 1 Introduction
1–28
Figure 1.7 Histological staining: 5-day old tumor with CD-3 at magnitude
×200. A colume layer where binding was detected can be seen on the
left (reprinted from ref. [84]).
Chapter 1 Introduction
1–29
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Chapter 1 Introduction
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Chapter 2 Heat Generation
2–34
2. Heat Generation
2.A. Introduction
Nanobiotechnology, defined as biomedical applications of nano-sized systems, is a rapidly
developing area within nanotechnology. Nanomaterials, which measure 1–1000 nm, allow
unique interaction with biological systems at the molecular level. They can also facilitate
important advances in detection, diagnosis, and treatment of human cancers and have led to a
new discipline of nano-oncology [1, 2]. Nanoparticles are being actively developed for tumor
imaging in vivo, biomolecular profiling of cancer biomarkers, and targeted drug delivery.
These nanotechnology-based techniques can be applied widely in the management of different
malignant diseases [3]. Nanoparticles coupled with cancer specific targeting ligands can be
used to image tumors and detect peripheral metastases [4].There are various nano-mediators
being investigated in the cancer imaging and therapy fields. Semiconductor fluorescent
nanocrystals, such as quantum dots, have been conjugated to antibodies, allowing for
simultaneous labeling and accurate quantification of target proteins in a tumor [4-6]. The use
of gold-containing nanoparticles (i.e., Raman probes) [7] may allow the simultaneous
detection and quantification of several proteins on small tumor samples, which will ultimately
allow the tailoring of specific anticancer treatment to an individual patient’s specific tumor
protein profile [8]. Nanotechnological approaches (e.g. nanocantilevers and nanoprobes) are
being actively investigated in cancer imaging [9]. Metal nanoshells are a novel type of
composite spherical nanoparticle consisting of a dielectric core covered by a thin metallic
shell which is typically gold. Nanoshells possess highly favorable optical and chemical and
physical properties for biomedical imaging and therapeutic applications.
Chapter 2 Heat Generation
2–35
By varying the relative dimensions of the core and the shell, the optical resonance of these
nanoparticles can be precisely and systematically varied over a broad region ranging from the
near-UV to the mid-infrared. These nanoshells may be used as contrast agents for optical
coherence tomography (OCT), and the use of absorbing nanoshells in NIR thermal therapy of
tumors [10, 11]. Additional example is the Au/Ag nanocages which have been developed and
investigated for the purpose of optical coherence tomography (OCT) contrast agents
maintaining an optical resonance peak in the near-IR range (800 – 1200 nm) [12]. Alternative
optical imaging applications are based on the combination of contrast agents and polarization
[13].
Since the light-tissue interactions field is usually characterized by low signal and high energy
losses (low Signal to Noise ratio) due to the fact that human tissue is a turbid media (i.e. high
absorption and scattering), one should consider other exciting methods such as example
magnetic, micro-, radio- or ultrasonic waves.
Magnetic nanoparticles that have a metal core show promising results for simultaneous
imaging and targeting of cancer implemented with MRI [14, 15] or alternating magnetic fields
as depicted below.
Chapter 2 Heat Generation
2–36
2.B. Applications of magnetic nanoparticles
Magnetic nanoparticles offer some attractive possibilities in biomedicine. First, they could be
manufactured in different sizes ranging from a few nanometers up to tens of nanometers,
which places them at dimensions that are smaller than or comparable to those of a cell (10-
100 µm), a virus (20-450 nm), a protein (5-50 nm) or a gene (2 nm wide and 10-100 nm long)
(Figure 2.1). This means that they can 'get close' to a biological entity of interest. Indeed, they
can be coated with biological molecules to make them interact with or bind to a biological
entity, thereby providing a controllable means of 'tagging' or addressing it.
Second, the nanoparticles are magnetic, which means that they obey Bio-Savart's law, and can
be manipulated by an external magnetic field gradient. This 'action at a distance', combined
with the intrinsic penetrability of magnetic fields in human tissue, opens up many applications
involving the transport and/or immobilization of magnetic nanoparticles, or of magnetically
tagged biological entities. In this way they can be made to deliver a package, such as an
anticancer drug, or a cohort of radionuclide atoms, to a targeted region of the body, such as a
tumor.
Third, the magnetic nanoparticles can be made to resonantly respond to a time-varying
magnetic field, with advantageous results related to the transfer of energy from the exciting
field to the nanoparticle. For example, the particle can be made to heat up, which leads to
their use as hyperthermia agents, delivering toxic amounts of thermal energy to targeted
bodies such as tumors; or as chemotherapy and radiotherapy enhancement agents, where a
moderate degree of tissue warming results in more effective malignant cell destruction. These
and many other potential applications are made available in biomedicine as a result of the
special physical properties of magnetic nanoparticles [16].
Chapter 2 Heat Generation
2–37
Among the leading applications of magnetic nanoparticles are magnetic separation, drug
delivery, hyperthermia treatments and MRI contrast agents [16-18], however since the scope
of this research work focuses on the generation of heat via these particles, other applications
will not be discussed in detail.
Figure 2.1 Relative sizes of cells and their components
As disclosed in chapter 1, one of the functions we seek to accomplish in this research is
thermal therapy by generating heat using nanoparticles. The use of iron oxides in tumor
heating was first proposed by Gilchrist et al [19] and there are currently two different
approaches. The first is called magnetic hyperthermia and involves the generation of
temperatures up to 45-47 ˚C by the particles. This treatment is currently adopted in
conjunction with chemotherapy or radiotherapy, as it also renders the cells more sensitive
[20]. The second technique is called magnetic thermoablation, and uses temperature of 43-
55˚C that have strong cytotoxic effects on both tumor and normal cells [21, 22]. The reason
for using higher temperatures is due to the fact that about 50% of tumors regress temporarily
after hyperthermic treatment with temperatures of up to 44˚C, therefore researchers prefer to
use temperatures up to 55˚C [22]. The problem of deleterious effects on normal cells is
reduced by intratumoral injection of the particles [23].
Chapter 2 Heat Generation
2–38
2.C. Objectives
As previously mentioned, the objectives of this research is to cause local elevation in
temperature on the surface of a tumor where the magnetic nanoparticles are located, without
causing any damage to the healthy surrounding tissue. Generation of heat in a non-invasive
and human-friendly technique in the form of magnetic fields is most desired.
2.D. Heating mechanisms
There exist at least three different mechanisms by which magnetic materials can generate heat
in an alternating field [18]:
(i) Generation of eddy currents in bulk magnetic materials,
(ii) Hysteresis losses in bulk and multi-domain magnetic materials,
(iii) Relaxation losses in ‘superparamagnetic’ single-domain magnetic materials.
We wish to focus on single-domain particles in which mechanism (i) and (ii) contribute very
little to the heating of these particles (if at all) [24], while the significant mechanism in
contribution with heating is the relaxation mechanism (iii) [25, 26].
Relaxation losses in single-domain magnetic nanoparticles fall into two modes: (a) rotational
(Brownian) mode and (b) Néel mode [25, 27]. The principle of heat generation due to each
individual mode is shown in Figure 2.2.
Figure 2.2 Relaxational losses leading to heating in an alternating magnetic field (H).
Chapter 2 Heat Generation
2–39
In the Néel mode (Figure 2.2.A), the magnetic moment (dotted arrow) originally locked along
the crystal easy axis (solid arrow) rotates away from the crystal axis towards the external field
(H). The Néel mechanism is analogous to the hysteresis loss in multi-domain magnetic
particles whereby there is an ‘internal friction’ due to the movement of the magnetic moment
in an external field that results in heat generation.
In the Brownian mode (Figure 2.2.B), the whole particle oscillates towards the field with the
moment locked along the crystal axis under the effect of a thermal force against a viscous
drag in a suspending medium. This mechanism essentially represents the mechanical friction
component in a given suspending medium [23].
Each of the relaxation modes that lead to heat generation is characterized by a time constant.
Nτ is the Néel time constant given by
0 exp BN
B
E
k Tτ τ
=
(Equation 2.1)
where B u
E K V= is analogous to an activation energy that has to be overcome by the thermal
energy B
k T to overcome the inherent magnetic anisotropy energy.
The energy barrier EB is represented by the constant Ku, which is a material property and is
the anisotropy constant, multiplied by V, which is the volume of the magnetic nanoparticle.
The thermal energy is represented by the constant B
k named by Stephan Boltzmann
multiplied by the absolute temperature T. The constant 0τ is of the order of 10−9 seconds [25].
Chapter 2 Heat Generation
2–40
For the spherical particles with an uniaxial anisotropy the energy is:
2sin
uE K V θ= (Equation 2.2)
where Ku is the anisotropy constant and θ the angle between the easy axis and the
magnetization. The energy barrier (EB = Emax-Emin=KuV) separates the two minima at θ=0 and
θ=π corresponding to a magnetization parallel and antiparallel to the easy axis (Figure 2.3).
For small particles at 300 K the energy barrier becomes comparable to the thermal energy.
Thus the magnetization will fluctuate between the two energy minima. This results in a
superparamentic relaxation. This fluctuation of magnetization due to the thermal activation
between two easy-axis orientations is called superparamagnetism.
Figure 2.3 Schematic illustration of the energy of a single-domain particle with uniaxial
anisotropy as a function of magnetization direction.
Since the Néel-type superparamagnetic relaxation time is temperature dependent we should
denote a special temperature TB - the blocking temperature. Below TB the free movement of
the spins is blocked by anisotropy, while above TB the thermal energy will disrupt the bonding
of the total amount of the particles and the system turns superparamagnetic. The types of
magnetic nanoparticles in the scope of this research are characterized by blocking temperature
estimated by dozens of Kelvin. Hence, we may confidently assume superparamagnetism
throughout this paper.
Chapter 2 Heat Generation
2–41
The Brownian time constant is represented by Bτ is given by
3
HB
B
V
k T
ητ = (Equation 2.3)
where VH is the hydrodynamic volume of the magnetic nanoparticle which is the effective
volume (including that of the nanoparticle and coating or surfactant attached to the
nanoparticle), η is the viscosity of the liquid carrier and B
k T is the thermal energy.
The resultant power generation is a strong function of the effective time constant (and the
field parameters and is given by
( )2
0 0 0 2
2
1 2SPM
fP H f
f
π τπµ χ
π τ=
+ (Equation 2.4)
where H0 and f are the amplitude and frequency of the applied alternating magnetic field
respectively, 0χ is the magnetic susceptibility, 0µ is the permeability of free space and τ is
the effective time constant given by1 1
N B
ττ τ
= + [18, 25].
Chapter 2 Heat Generation
2–42
2.E. Affecting parameters
There are numerous parameters affecting the heat generation, which is produced by magnetic
nanoparticles excited by a magnetic field. Given below a few examples for some crucial
parameters one should take into consideration when heating with magnetic nanoparticles.
2.E.1. Field parameters
According to Equation 2.4, it is obvious that field strength and frequency are controllable
parameters that directly affect the power produced by the nanoparticles when alternative
magnetic field is applied. It should be appreciated that the proportional of field parameter is
not straightforward to the generated power but more complex, and depends on additional
parameters such as the nanoparticles' material properties [28].
2.E.2. Material Properties
Iron oxides
An interesting class of magnetic materials are iron oxides such as Fe3O4, γ-Fe2O3 and
MO·Fe2O3 (where M is Mn, Co, Ni, Cu) [29], because they display ferrimagnetism.
Magnetite (Fe3O4), meghemite (γ-Fe2O3) and hematite (α-Fe2O3) are the most common iron
oxides and they are discussed below.
Chapter 2 Heat Generation
2–43
Magnetite (Fe O · Fe2O3) is the oldest known magnetic material [29]. At room temperature,
bulk magnetite crystallizes in the inverse spinel structure as is shown in Figure 2.4. it should
be noticed that in a spinel structure the Fe3+ ions are located on the B sites, while the divalent
ions M2+ on the A sites. The oxygen atoms form the close-packed face-centered-cubic (fcc)
lattice with the iron atoms occupying interstitial sites [30]. Each cubic spinel contains eight
oxygen (fcc) cells. The so-called A sites are characterized by tetrahedral oxygen coordination
around the Fe ions and B sites which have octahedral oxygen coordination. The A sites are
occupied by Fe3+ and the B sites are occupied by equal numbers of Fe2+ and Fe3+. Below 851
K magnetite is ferromagnetic with A-site moments aligned antiparallel to the B-sites.
Magnetite undergoes a first-order phase transition at 120 K (Verwey transition), with a
change of crystal structure, latent heat and decrease of the dc conductivity. The distribution of
Fe3+ and Fe2+ in B sites changes from a dynamic disorder to a long range order with an
orthorhombic symmetry below 120 K. At room temperature, Fe3O4 very easily undergoes a
transformation to meghemite [31].
Figure 2.4 Crystal structure of Fe3O4 . Big balls denote oxygen atoms, small dark balls denote
A-site (tetrahedral) iron atoms, and small light balls denote B-site (octahedral) iron
atoms. (reprint ref. [30] )
Chapter 2 Heat Generation
2–44
Two additional used Iron Oxides in this field of research are the Meghemite
(γ-Fe2O3) [32] and Hematite (α-Fe2O3), which are not currently investigated in this research.
Meghemite has a good chemical stability and can be prepared involving low prices and cheap
technology. It was found that small γ-Fe2O3 nanoparticles exhibit a strong exchange
interaction and a magnetic training effect. Recently, a low temperature spin-glass transition
was found at T = 42 K [33]. In the dry state, γ-Fe2O3 transforms to α-Fe2O3 (hematite) at
temperatures ranging from 370 – 600 ˚C [31]. Hematite is the most stable iron oxide [31].
Iron-Gold nanoshells
The magnetic nanoshells were designed and characterized by Nanosonic Inc. to generate heat
in response to external magnetic field (Figure 2.5.A). The nanoshells are comprised of an iron
core with diameter of 8 nm coated with a layer of gold. The gold coatings are made in order to
prevent oxidation, hence demagnetization; ultrathin noble metal coatings of Au (~2 nm) were
prepared to provide long-term stability and biocompatibility for the Fe core.
The Fe core was over-coated with a series of block copolymer stabilizers that are compatible
with analgesics to prevent flocculation in the arterial system in vivo (see Figure 2.5.B).
In addition, the block copolymers assist in preventing agglomeration.
Other materials are also being investigated including Platinium compounds, Vanadium
Oxides, Cobalt, Nikel, Lanthanum and Manganase [34], [35].
Chapter 2 Heat Generation
2–45
Figure 2.5 Fe Nanoparticles produced by Nanosonics Inc. (A) Magnetic nanoparticles in different
particle size configured as powder. (B) Schematic illustration of a single Fe-Au nanoparticle
2.E.3. Size dependence
The size of the nanoparticles is a fundamental characteristic in this field. Ma et al. [36]
investigated the specific absorption rate (SAR) values of aqueous suspensions of magnetite
particles with different diameters varying from 7.5 to 416 nm by measuring the time-
independent temperature curves in an external altering magnetic field
(80 kHz, 32.5 kA/m). Results indicate that the SAR values of magnetite particles are strongly
size dependent. For magnetite larger than 46 nm, the SAR values increase as the particle size
decreases where hysteresis loss is the main contribution mechanism. For magnetite particles
of 7.5 and 13 nm which are superparamagnetic, hysteresis loss decreases to zero and, instead,
relaxation loss (Néel loss and Brownian rotation loss) dominate.
A B
Chapter 2 Heat Generation
2–46
The dividing line between the two cases depicted above is given by the ferromagnetic
exchange length ex
d A K≅ using the material parameters of magnetite
( 4 3 111.35 10 , 10K J m A J m−= × = ), the exchange length is estimated as 27ex
d nm≅ .
Therefore, when the particle size is larger than ex
d , the hysteresis loss increases as the
particle size decreases. However, once the particle size is less than ex
d , hysteresis loss will
vanish and the main contribution will be of relaxation losses. This is shown in Table 2.1 by
Ma et. al [36]:
Table 2.1 SAR values of samples in the applied magnetic field (80 kHz, 32.5 kA/m) and
coercivity Hc of samples, Ma et al., 2004.
Samples
Particle Diameter
(nm)
SAR Values
(W/[g of Fe])
Coercivity
Hc (Oe)
A 7.5 15.6 6.4
B 13 39.4 20.9
C 46 75.6 101.9
D 81 63.7 88.9
E 282 32.5 62.4
F 416 28.9 53.9
Chapter 2 Heat Generation
2–47
This phenomena was also investigated by Hergt et al. [24]. Based on their research it is shown
in Figure 2.6 that in the critical particles size region where hysteresis losses vanish (dotted
line), Néel losses (full line) grow as a new loss mechanism which, roughly speaking, extends
the loss region toward even smaller particle sizes [24].
SAR optimization is currently under investigation and, concerning its dependence on
magnetic core size, calculation should allow the optimization of particle diameter with respect
to frequency [17], as shown by Hergt et al [24] in Figure 2.7. This figure shows the particle
size dependence of the loss power density due to Néel relaxation calculated for three values
of frequencies while all parameters were chosen according to the goal of their application for
hyperthermia [24].
Figure 2.6 Dependence of magnetic loss power density on particle size for magnetite fine
particle (2MHz, 6. 5 kA/m) (Reprinted from ref. [24]).
Chapter 2 Heat Generation
2–48
Figure 2.7 Grain size dependence of the loss power density due to Néel-relaxation for
small ellipsoidal particles of magnetite (6. 5 kA/m) (Reprinted from ref. [24]).
2.E.4. Miscellaneous
The aforementioned parameters discussed in section 2.E. are merely few examples for a larger
collection of affecting parameters. Some of them have been investigated and some are
probably yet unknown. Amongst them is the concentration of the nanoparticle inserted into
the body [18]. The concentration should be large enough to effectively produce heat, but yet
in amount that won't be toxic for the human body. The coating of nanoparticles (e.g.
derivatives of dextran, polyethylene glycol (PEG), polyethylene oxide (PEO) and poloxamers
and polyoxamines) and suspending medium also affect the heat generation [18], [23], [37].
The period of time of excitation filed application and profile (e.g. continuous, pulsatile)
deeply affect the SAR which is proportional to the power dissipated [38].
Another affecting parameter under investigation is the presence of nanoparticles'
agglomeration in comparison with the heat generated in single or dispersed nanoparticles
[39].
Chapter 2 Heat Generation
2–49
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Nanoparticles for Localized Hyperthermia. Journal of Applied Physics 2006, 99. 39. Pawel K, David GC, Arun B, Charles RS, Taton TA: Limits of Localized Heating by
Electromagnetically Excited Nanoparticles. Journal of Applied Physics 2006, 100:054305.
Chapter 3 Thermal Analysis
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3. Thermal Analysis
3.A. Introduction
Following the heating of the bioconjugated nanoparticles as described previously in chapter 2,
we now may consider our challenge as a heat transfer problem. The heat source, namely the
tumor, and in particular the tumor's surface, is actively heated by external and controlled
magnetic fields. Based on the 2-dimensional thermal image acquired from the tissue surface,
we seek to derive two fundamental characteristics: the depth of the tumor and the temperature
of the tumor and its surroundings. Knowing the temperature in real-time is crucial in order to
avoid any damage to all tissues in the diagnostic mode on one hand, and on the other hand,
operating in therapeutic mode, we expect to damage only the malignant tissue leaving the
healthy surrounding tissue with minimal damage.
Chapter 3 Thermal Analysis
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3.B. Image processing approaches to IR images [1]
The application of computerized image processing methods in diagnosis, i.e. computer-aided
diagnosis (CAD) has been playing an important role in the analysis of IR images, since the
analysis task often requires high concentration and accuracy, memory and tremendous
analytic ability, factors that are influenced by human "limitations" such as fatigue, being
careless, limited human visual system etc. On top of all these factors, a shortage of qualified
radiologists also put an urgent demand on the development of CAD technologies.
Currently, research on smart image processing algorithms for IR images tends to improve the
detection accuracy from three perspectives: smart image enhancement and restoration
algorithms, asymmetry analysis of the thermogram including automatic segmentation
approaches, and feature extraction and classification. Following is a brief review of these
three perspectives of IR image algorithms.
Smart Image Enhancement and Restoration Algorithms
One of the solutions for low resolution of thermograms was proposed by Synder et al. [2] who
developed an algorithm to increase the effective resolution by 2:1 ratio while at the same time
removing the noise and preserving edges in the image. This algorithm is based on a
minimization strategy known as mean field annealing, which takes into account processes of
blur, noise, and image correlations, to make an optimal estimate of the missing pixels.
The Minimally Invasive Optical Biopsy System developed at MIT [3] uses infrared light in
conjunction with an intravenously injected dye and special computer software to create a
clear, high contrast image.
Chapter 3 Thermal Analysis
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Kaczmarek and Nowakowski [4] proposed the use of active dynamic thermography (ADT),
commonly adopted in nondestructive testing of materials, to further enhance the image
quality.
Asymmetry Analysis
Comparing between contra-lateral images is a procedure carried out routinely by radiologists.
One of the popular methods especially for breast cancer detection is to make comparisons
between contralateral images. When the images are relatively symmetrical, small asymmetries
may indicate a suspicious region. In thermal infrared imaging, asymmetry analysis normally
needs human intervention because of the difficulties in automatic segmentation.
In order to provide a more objective diagnostic result, there is a need to design an automatic
approach to asymmetry analysis in thermograms. It includes automatic segmentation and
supervised pattern classification [5].
When images are relatively symmetrical, small asymmetries may indicate a suspicious region.
Generally, these small asymmetries are not easily detectable and require an automatic
approach to eliminate human factors. There have been a few papers addressing techniques for
asymmetry analysis of mammograms [6], [7], [8].
Head et al. [9], [10] recently analyzed the asymmetric abnormalities in IR images. Qi et al.
[11] developed an automatic approach to asymmetry analysis in IR images. It includes
automatic segmentation and pattern classification. Mabuchi et al. [12] designed a
computerized thermographic system, which would produce images of the distribution of
temperature differences between the affected side and the contra-lateral healthy side.
Chapter 3 Thermal Analysis
3–55
Feature Extraction and Classification
Upon segmentation, different features can be extracted from the segments. Asymmetric
abnormalities can then be identified based on mature pattern classification techniques. In this
process, feature extraction is crucial to the success of computer-aided diagnosis. For example,
Kuruganti et al. [13] shows that the high-order statistics (e.g. variance, skewness, and
kurtosis) and joint entropy are the most effective features to measure the asymmetry, while
low- order statistics (e.g. mean) and entropy do not assist asymmetry detection. Additional
research works were conducted by Jakubowska et al. [14] also addressed the importance of
using statistical parameters (1st and 2nd order) in extracting thermal signatures for asymmetry
analysis
Chapter 3 Thermal Analysis
3–56
3.C. The problem
This problem, in virtue, may be classified as an inverse problem whose its solution is non-
trivial since being referred as an ill-posed problem involving complicated and complex methods of
solution. Hadamard coined the term ill-posed in the sense that the conditions of existence and
uniqueness of solution are not necessarily satisfied and the solution may be unstable to perturbations
in input data [15]. Inverse problems have practical implications in thermal transport systems which
involve conduction, convection and radiation. Inverse problems of heat-conduction, or IHCPs, can be
subdivided into three categories: boundary problems, retrospective problems, and identification
problems [16]. The most popular of all inverse problems is the boundary heat-flux reconstruction in a
conducting solid given temperature measurements at various points within the solid. Its popularity
stems in the fact that its applications extend in many areas of engineering, including thermal
processing of materials, thermal monitoring in nuclear engineering, and crystal growth and
solidification processes [16, 17]. Various methodologies have been proposed and successfully been
implemented for the solution of the IHCP mentioned above [16-18]. Several of these techniques
involve restatement of the ill-posed inverse problem as a conditionally well-posed functional
optimization problem, addressed by using appropriate techniques including Tikhonov regularization
[19]. In this dissertation, we will not provide any review of deterministic inverse methods
for the IHCP since such methods are very well-documented elsewhere in the literature
[16-18, 20-22]. An alternative approach is the use of stochastic inverse modeling and uncertainty
analysis techniques for continuum systems which have been developed considerably in the last two
decades. Powerful techniques like the extended perturbation method [23, 24], the improved Neumann
expansion method [25], and generalized polynomial chaos techniques [26-30] have been proposed and
successfully used to analyze uncertainty propagation in various continuum systems, or for example,
two new methods for addressing the IHCP in a fully stochastic setting introduced by Zabaras [31].
The solution techniques are not suitable to our problem since in our case, temperature is acquired non-
invasively and therefore we cannot rely on temperature value inside the solid medium (i.e. tissue) but
Chapter 3 Thermal Analysis
3–57
solely on its surface. Moreover, since we are using a thermal camera, we are acquiring only IR
radiation emitted from tissue's surface.
To clarify and determine the model of the problem, please refer to Figure 3.1.
SURROUNDINGS
Yq
Xq
IR Camera
2D Thermal Image
IR Camera
2D Thermal Image
TISSUEQ
Tq
Figure 3.1 The thermal problem description
The tumor and nanoparticles, being a general heat source, are embedded in a medium, namely a tissue.
The heat source's location is noted by the coordinates (Xq, Yq) and Q is the power being generated.
Assuming that by smart positioning of the IR camera, the number of unknown parameter may be
reduced to (i) the depth of the heat source and (ii) the generated power.
The given parameters are tissue characteristics, ambient characteristics and the IR data embodied in
the thermal image.
Chapter 3 Thermal Analysis
3–58
3.D. Method of solution
3.D.1. Forward Problem and Analytical Solution
Since dealing with the solution of the inverse problem may be mathematically complicated
and cumbersome, a time consumer and flaws in reliability, it seems advisable to address this
problem analytically. The solution of the forward heat transfer problem is well-posed and
shows good results. Based on these straightforward solutions I believe it is possible to
implement the aforementioned to the opposite direction of solution (i.e. solving the inverse
problem) by taking advantage of computerized simulations and experimental set-ups.
3.D.2. Pennes Equation
The first comprehensive bio-heat equation was developed by Pennes in 1948 [32]. The
equation is controversial and over the years it has come under criticism, from, e.g. [33], [34]
and has been defended by others. Despite the controversy and the criticism most of the
mathematical analysis carried out in bio-heat transfer has and is being done using this
equation [35].
Following the revision made by E. H Wissler [36], Pennes' principal theoretical contribution
was that the rate of heat transfer between blood and tissue is proportional to the product of the
volumetric perfusion rate and the difference between the arterial blood temperature and the
local tissue temperature.
Chapter 3 Thermal Analysis
3–59
The relation is expressed as follows:
( ) ( )1b b b ah V C T Tρ κ= − − (Equation 3.1)
where hb is the rate of heat transfer per unit volume of tissue, V is the perfusion rate per unit
volume of tissue, ρb is the density of blood, Cb is the specific heat of blood, κ is a factor that
accounts for incomplete thermal equilibrium between blood and tissue, Ta is the temperature
of arterial blood, and T is the local tissue temperature. Pennes assumed that 0 1κ≤ ≤ , although
he set 0κ = when he computed his theoretical curves, as have most subsequent investigators.
Following Pennes’ suggestion, the thermal energy balance for perfused tissue is expressed in
the following form
2m b
TC k T h ht
ρ ∂= ∇ + +
∂ (Equation 3.2)
where ρ and C refer to tissue, k is the thermal conductivity of tissue, and hm is the rate of
metabolic heat production per unit volume of tissue.
Chapter 3 Thermal Analysis
3–60
3.D.3. Heat Conduction Equation
Assumptions
Since the solution of Pennes equation Eq. 3.2 is not trivial, the problem can be degenerated
for simplicity, relying on the following assumptions:
Let us assume a homogeneous and isotropic medium (i.e. tissue) with constant characteristics
(i.e. k, ρ and C are constant). Metabolism (i.e. hm=0) and perfusion (i.e. hb=0) are neglected.
These assumptions are valid especially when dealing with an adipose or muscle tissues.
The approach of dealing with the problem is to pursue an analytical solution while assuming
symmetry in a cylindrical coordination system.
An additional assumption is that there are no temporal changes in temperature (i.e. steady
state, 0Tt
∂=
∂).
As a fundamental problem, let us assume a point heat source, modeling a very small tumor.
Trying to best model the boundary conditions of the real problem, Newtonian boundary
conditions are adopted as shown in Eq. 3.3 hereinafter, where E is a constant, called the
"surface conductance", which is made up of radiative, convective and evaporative
components: rad conv evapE E E E= + + .
Thus the problem is set (described in Figure 3.2) in cylindrical coordination system:
2
2
1 0T Try r r r∂ ∂ ∂⎡ ⎤+ =⎢ ⎥∂ ∂ ∂⎣ ⎦
(Equation 3.3)
Chapter 3 Thermal Analysis
3–61
with the boundary conditions:
0 :
0 : 0 : y
Ty K ETy
T rT
∂∀ = =
∂∀ → →∞∀ → →∞
Point Source
Following Draper and Boag [37], the analytical steady-state solution of the three-dimensional
thermal conductivity equation due to an embedded continuous point source as depicted above,
is given by:
r
y
aQ
Ta
Tsy=0
K
E
Figure 3.2 Schematic description og the heat conduction problem.
Chapter 3 Thermal Analysis
3–62
[ ]
( ) ( )
( ) ( )
1 12 22 22 2
0
0
( , ) (0, ) (0, )
1 1 4
exp
2
aET y r T T T yK
QK y a r y a r
y a J rQ dE K
π
λ λ λλ
π λ
∞
= ∞ + ∞ −
⎡ ⎤⎢ ⎥
+ −⎢ ⎥⎡ ⎤ ⎡ ⎤⎢ ⎥− + + +⎣ ⎦ ⎣ ⎦⎣ ⎦
− +⎡ ⎤⎣ ⎦++∫
(Equation 3.4)
This exact solution was developed for a point source relying on the exact solution for a buried
line source developed by Awbery [38] in 1929.
The first term of the solution establishes the absolute value of the temperature in relation to a
point at great distance from the origin of the coordinate system. The second term stems from
the fact that the ambient temperature (Ta) is less than the undisturbed skin temperature
T (0, ∞) and that the thermal gradient in the body at points far from the source is linear, which
should be a good approximation for a region limited to a couple of centimeters (even if the
skin surface is slightly curved as in the case of the female breast). Q is the energy radiating
(Watts) from the point source situated at a distance a below the surface and J0 is the zero
order Bessel function. E and K are the resulting ‘surface conductance’ and the mean thermal
conductivity, respectively.
In thermal imaging studies (IR imaging) the temperature distribution on the skin surface is
measured, which simplifies the solution of Eq. 3.4 by the substitution of y = 0. The resulting
expression reads
( ) ( )0
0
exp(0, ) (0, )
2y a J rQT r T dE K
λ λ λλ
π λ
∞ − +⎡ ⎤⎣ ⎦= ∞ ++∫ (Equation 3.5)
Chapter 3 Thermal Analysis
3–63
When applying this equation, the interest is normally focused on a description of the surface
temperature distribution not very far from the origin of the coordinate system or immediately
above the embedded tumor.
3.E. Point Simulation
3.E.1. Forward Solution
The problem depicted above has been simulated by a MATLAB® code.
The simulation describes a semi-infinite medium which represents the previously described
tissue.
The tissue is assumed to be homogeneous and symmetrical. Its thermal properties are time
and space independent. A point heat source representing the tumor, is embedded within the
medium, in a distance a beneath the medium's surface (y=0) generating power of Q Watts.
The simulation gets the following input parameters: y, assigned as zero for surface level, a as
the heat source depth, E the 'surface conductance' constant, K the medium's conductivity
constant, Q the power generated by the heat source, Ts the undisturbed surface temperature, Ta
the ambiance temperature and the radial axis dimensions including resolution.
Figure 3.3 shows a non-dimensional surface temperature. The non-dimensional variables
( )* *, ,Bi rφ were computed by utilizing Buckingham's-PI- theorem where the non-dimensional
surface temperature is presented by( )* sK T T a
Qφ
−= and the radial axis by * rr
a= .
The characteristic curve depends on the Biot modulus EBi aK
= ⋅ .
Chapter 3 Thermal Analysis
3–64
Figure 3.3 Non-dimensional surface temperature over an embedded point heat source
Validation
Validation of the simulation is carried out by comparing simulation results to the one
published by Draper and Boag [37]. Figure 3.4.A shows the surface temperature T(0, r, Q)
for point sources at various depths a and of strength Q produced by the simulation as detailed
in Table 3.1:
Table 3.1 Point heat sources in various depths a and strength Q
A [cm] Q [mW]
0.2 6.15
0.5 17.6
1 41.5
2 104
4 285
6 534
Chapter 3 Thermal Analysis
3–65
These parameters were chosen to produce maximum temperature of 1˚C. The compared
results of Draper and Boag [37] are shown in Figure 3..B:
Figure 3.4.A MATLAB® simulation results: surface temperature T(0, r, Q) for various point heat sources
Figure 3.4.B Draper and Boag's results: surface temperature T(0, r, Q) for various point heat sources
Chapter 3 Thermal Analysis
3–66
3.E.2. Inverse Solution
Based on the simulation that solves the relevant thermal forward problem (given the tissue
and ambient parameters: resulting ‘surface conductance’ E, mean thermal conductivity K and
ambient temperatures) a simple and fast method of computing the ill-posed inverse problem
yielding with the depth and power of the tumor is suggested. The method models a point heat
source in a simple semi analytical algorithm. The algorithm is based on the cross-sectional
temperature profile derived from the surface temperature, i.e. the thermal image acquired by
an IR camera.
Figure 3.5 Surface temperature cross sectional distribution
w
Chapter 3 Thermal Analysis
3–67
To better understand the algorithm let us look at the following example in which the surface
temperature of a point heat source is produced, given the following parameters:
Table 3.2 Given parameters for illustrative problem
Parameter Value
Depth (a) 1.2 [cm]
Power (Q) 0.1 [Watt]
Thermal conductivity (K) 34 10 WKcm C
− ⎡ ⎤= × ⎢ ⎥⋅⎣ ⎦o
Surface conductance (E) 212.5 WEm C⎡ ⎤= ⎢ ⎥⋅⎣ ⎦o
Ambient temperature (Ta) 25 [˚C]
Surface temperature (Ts) 32 [˚C]
The surface temperature cross-sectional distribution shown in Figure 3. may be fitted to a
Lorentzian function in 2-dimensional Cartesian coordination system as follows:
( ) ( )0 2 2
0
24
A wy yx x wπ
= + ⋅− +
(Equation 3.6)
where y0 and x0 are the vertical and horizontal offsets, respectively, w is the width at half
height, i.e. full width half maximum (FWHM), and A is the area lying under the curve.
This non-linear curve fitting based on the Levenberg-Marquardt algorithm provides two
essential parameters which can be extracted out of the Lorentzian temperature profile:
(i) Full Width Half Maximum (FWHM)
Chapter 3 Thermal Analysis
3–68
(ii) Area lying under the curve (A).
In this example the derived values are 3.005 [cm] and 8.896 [cm2] respectively (R2=0.9998).
The advantage of using the FWHM parameter is based on two behaviors discovered by Feasey
et. al. [39]. Following their research, the FWHM was found to be constant for a given source
depth, i.e. the temperature distribution across the area of the hot spot is a function only of the
depth, and is independent of surface cooling and heat output of the source.
More particularly, in correspondence with Draper and Boag's paper [40], Davison confirms
experimentally (in vitro) that a linear relation exists between FWHM and depth [41]. This
behavior has been validated too by our simulation as shown in Figure 3.6 and Figure 3.7.
Fig. 3.6 shows constant behavior of the FWHM parameter as a function of varying power (Q)
for different depths (a). Fig. 3.7 shows linear behavior of FWHM as a function of depth for
various tissues.
Figure 3.6 FWHM as a function of varying power (Q) for different depths (a)
Chapter 3 Thermal Analysis
3–69
Figure 3.7 FWHM as a function of depth for various tissues
Each tissue represented by the quotient E/K has its own corresponding unique linear curve.
Thus, given the FWHM which is derived from the surface temperature profile allows the
direct computation of the point source depth (Figure 3.7).
Chapter 3 Thermal Analysis
3–70
Figure 3.8 Computing source depth for a specific tissue
In this example, given the tissue represented by E and K in Table 3.2 it is possible to select
the relevant linear curve (Figure 3.8) and to extract the heat source depth:
$0.42896 1.25 [ ]
2.0534FWHMa cm−
= = (Equation 3.7)
After computing the source depth, the source power may be computed. The computation is
based on the linear relation between the curve area (A) and source power (Q). The simulation
results show that for a specific E/K quotient, each depth has its own unique linear curve A(Q).
Figure 3.9 shows this behavior for the example.
Chapter 3 Thermal Analysis
3–71
The slopes of these A(Q) curves (see Figure 3.10) can be well fitted as a sum of two decaying
exponents as source depth deepens. This exponential behavior is shown in Figure 3.11.
Estimating the source power (Q), should be carried out by substituting the already computed
source depth a in the exponential expression fitted in Figure 3.11 in order to derive the right
slope (p):
$ $ $1.691 0.17571.25 [ ] 87.25 95.58 87.272a aa cm p e e− ⋅ − ⋅= ⇒ = + = (Equation 3.8)
This slope parameter facilitates the selection of the appropriate linear curve of A(Q)
(see Figure 3.12), calculating the power Q straightforwardly, since the approximated value of
the area (A) is already known from the primary Lorentzian curve fitting:
[ ]2 8.8968.896 Q 0.187.272
AA cm Wattp
⎡ ⎤= ⇒ = = =⎣ ⎦ (Equation 3.9)
Figure 3.9 Area below the surface temperature profile (A) as a function of the source power (Q)
Chapter 3 Thermal Analysis
3–72
Figure 3.10 Area (A) as a function of power (Q) for various source depths
Figure 3.11 Exponential behavior of A(Q) slopes
p=125.01
p=96.172
p=80.491
p=70.189
p=62.749
p=57.053
p=125.01
p=96.172
p=80.491
p=70.189
p=62.749
p=57.053
Chapter 3 Thermal Analysis
3–73
Figure 3.12 Selected A(Q) curve based on the p-parameter
In conclusion, the estimation of the depth and power of heat source in comparison with the
real parameters is shown in Table 3.3:
Table 3.3 Comparison of real parameters and estimated parameters
Parameter Real Value Estimated Value Variation
Depth (a) 1.2 [cm] 1.25 [cm] 4.167 %
Power (Q) 0.1 [Watt] 0.1 [Watt] 0 %
The variation between real values and estimated values shown in Table 3.3 may occur
primarily in the forward solution calculations. Due to the fact that the computation is carried
out discretely, the spatial resolution in the radial direction is an influencing factor. To improve
and eliminate this factor, the resolution may be reduced or suitable interpolation and/or
smoothing may be applied.
Chapter 3 Thermal Analysis
3–74
Moreover, since the calculation of the infinite integral( ) ( )0
0
exp y a J rd
E Kλ λ λ
λλ
∞ − +⎡ ⎤⎣ ⎦+∫ , which
comprises the most of Eq. 3.5, is impossible to be carried out analytically, the method and
accuracy of its computation are significant in the final results.
Additional and influential factors may occur during the inverse procedure that mostly consists
of curve fitting operations. Various methods and functions for curve fittings can present
variations in the final results.
3.F. Spherical Simulation
Following the solution assuming a point heat source as shown in section 3.D., the problem
may be broadened and a spherical heat source can be assumed. This model is based
analogously on a study conducted by Gannot et. al. [42] that deals with the detection and
localization of tumors in tissue by virtue of fluorophore conjugated specific antibodies as
tumor surface markers. In particular, their study focuses on the understanding and
quantification of the pharmacokinetics of fluorophore conjugated antibodies in the vicinity of
a tumor.
Hence, in our model we have located the binding sites of nanoparticles in a volume layer
around the tumor surface as shown in Figure 3.13. The application of external AC magnetic
field induces the heating of nanoparticles' outer layer creating roughly two spherical
temperature regions: the tumor region (marked in yellow) and a higher temperature region
comprised of the magnetic nanoparticles (marked as red).
Chapter 3 Thermal Analysis
3–75
For simplicity, we assume an average uniform temperature representing each region: Ttumor
and Tnp, respectively. Since the outer region (red) shows significantly higher temperature
(assumed ~ΔT ≥ Tnp - Ttumor ≥ 5˚C), we may refer to the nanoparticles layer only, while
neglecting the tumor's temperature, i.e. a spherical shell with a constant and uniform
temperature field of Tnp. We still assume an infitisimal width of nanoparticles' layer.
Figure 3.13 Spherical model for thermal analysis of a tumor
The simulation modeling a spherical shell heat source is based on the use of fundamental
solution for a point heat source shown in section 3.D. A spherical shell characterized by a
radius R and an effective power Q is embedded while its center is located in depth a beneath
the surface. The shell's surface is represented by the superposition of discrete point sources
scattered in a predetermined spatial resolution. The point sources' spreading is determined
according to a spherical coordination system ( ), ,z θ φ (see Figure 3.14). Since each point
source is representing a different fraction of the spherical surface, it owns a corresponding
effective power source (Figure 3.15). This is taken into account by multiplying the
fundamental surface field temperature Tz with its corresponding weight (Wi) as shown
hereinafter.
Tnp
Tumor
Bound magnetic nanoparticles
Tumor
Ttumor
Chapter 3 Thermal Analysis
3–76
The Tz vector is the temperature field at the surface (y=0) produced by a single point source
located in depth z. It is designated as a fundamental parameter since it is being calculated for a
unit of power source, i.e. 1 Watt.
Figure 3.14 Spherical coordination system
Figure 3.15 Nanoparticles superficial distribution on the sphere
Chapter 3 Thermal Analysis
3–77
The weights are calculated using the following expression shown below:
spherei i
sphere
QW S
S= ⋅ (Equation 3.10)
where
iW is the corresponding weight,
sphereQ is the total power generated by the entire sphere,
sphereS is the total surface of the sphere,
iS is the fractional surface represented by a certain point source,
Hence, each point source surface field temperature (Tpoint) is calculated by the expression
point i zT W T= ⋅ (Equation 3.11)
In our model the nanoparticles' shell is characterized by an infitisimal width dimension.
Computing a shell with a different width dimension, may be simply carried out by the
superposition of various shells with different radiuses.
Validation
The validation of the simulation modeling a spherical shell source is much more complex than
a point heat source; hence, we chose to execute it in two different approaches.
The first approach is trivial. We compare a spherical shell with a radius R 0 and a point
source. Results are shown in Figure 3.16 and present an expected behavior of the two curves.
Chapter 3 Thermal Analysis
3–78
However this validating approach hasn't convinced us completely. Therefore, we seek to
compare our simulation results to a close-enough analytical solution. The comparable solution
proposed by Small and Weihs [43] introduces an exact solution in series form for the steady
temperature distribution in a semi-infinite solid medium bounded internally by a spherical
inclusion of uniform temperature. Heat transfer at the interface is via convection. Their
analysis is performed in an orthogonal coordinate system tailored to the specific problem, i.e.
bispherical coordinate system ( ), ,η θ ψ allowing simpler boundary conditions and the
achievement of an exact solution (Figure 3.17).
Figure 3.16 Comparison of a point source and spherical source (R=0.01 cm). The curve of
spherical source is deliberately elevated by 1˚C in order to distinguish the two curves
Chapter 3 Thermal Analysis
3–79
Figure 3.17 Problem modeling in bispherical coordinate system
(Small and Weihs, reprinted of ref. [43] )
Following mathematical transformation, the problem, including boundary conditions, is
described as follows:
( )
2 0: 1: 0 1
0 : cosh 0
aa
qhk
φη φ
η φφη η ξ φη
∇ =∀ = − =∀− ≤ ≤ ≤
∂∀ = − + =
∂
(Equation 3.12)
φ is the nondimensional temperature excess, a defines the spherical surface and cosξ θ= .
The physical parameters of the problem are the heat transfer coefficient (h), thermal
conductivity of the medium (k) and the distance between limiting points
( 2 22 2q D R= − , D – distance from sphere center to interface, R – sphere radius).
Chapter 3 Thermal Analysis
3–80
The solution suggested by Small and Weihs [43] for the nondimensional temperature
distribution in the solid medium is depicted as:
( ) ( ) ( )( )
12
0
sinh tanh cosh, cosh cosh2
cosh
n
n man
B m ma mP me
ma
η ηφ η ξ η ξ ξ η
∞
−=
+ ⋅⎡ ⎤⎢ ⎥= − ⎢ ⎥+⎢ ⎥⎣ ⎦
∑ (Equation 3.13)
where Pn is the Legendre polynomial of order n and m is constant depend of n.
Bn may be found by several techniques described in detail in their work. In spite of being
exact and complete, the analytical derivation of Bn is extremely cumbersome to apply due to
the lengthy algebraic expressions. Therefore, we chose an approximated numerical method in
computing the Bn coefficients.
The surface temperature field which is in interest for our needs is achieved by substituting
0η = in Eq. 3.13. Naturally, the implementation of the solution depicted in detail above
requires strong computational means.
So before exploiting it as a validation tool, we are committed to ensure the validity of this
solution itself. Figure 3.18 shows the validation of this solution versus Small and Weihs
results demonstrating the surface distribution for various D/R and Bi = 1 (Biot Modulus).
Chapter 3 Thermal Analysis
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Figure 3.18.A Simulating Small and Weihs solution
Figure 3.18.B Solution suggested by Small and Weihs (1977), (Reprinted ref. [43])
Figure 3.18 Validation of an auxiliary MATLAB® code simulating Small and Weihs solution
Chapter 3 Thermal Analysis
3–82
Now that we were convinced with the credibility of our validating simulation, we are able to
validate our spherical model (via 2nd approach). Nevertheless, we face one main hurdle when
using this comparison. While Small and Weihs's model deals with constant temperature at the
sphere surface, our case involves a spherical shell with variable temperature as a function of
depth.
Dealing with this hurdle, we compared the two models under the constrains D>>R and h>>k.
Then, we found an effective spherical shell for our model presenting constant temperature,
with new effective parameters D* and R* as shown schematically in Figure 3.19.
Now we are allowed to compare it with the solution suggested by Small and Weihs.
An example is shown in Figure 3.20 where 3230 ; 4.2 10W WE K
m C cm C−⎡ ⎤ ⎡ ⎤= = ×⎢ ⎥ ⎢ ⎥⋅ ⋅⎣ ⎦ ⎣ ⎦o o
.
The red curve represents an "analytical" solution computed based on Small and Weihs's
solution. It is being compared to the blue curve representing the spherical simulation results.
Based on the results mentioned above we validated our spherical simulation which is capable
of simulating the surface temperature generated by an embedded spherical shelled heat
source.
Chapter 3 Thermal Analysis
3–83
Figure 3.19 Effective spherical model
Figure 3.20 Comparison of Small and Weihs solution with the spherical simulation
The results shown above validate of the simulation of an embedded spherical shelled heat
source, by solving the forward problem.
r
y
R
r
y
R
Ta
Ta
D, R D*, R*
a>>R
E>>K
D
Chapter 3 Thermal Analysis
3–84
These results may lay the basis for a future inverse model of a spherical source based on the
forward problem's solution, analogously presented with regard to a point heat source.
Since a problem which includes a spherical source obtains an additional parameter (i.e. radius
of the sphere), its solution is much more complex and compels the discovery of supplemental
mathematical relations.
Chapter 3 Thermal Analysis
3–85
3.G. References
1. Qi H, Diakides NA: Thermography (Invited). In Encyclopedia of Medical Devices and Instrumentation. 2nd Ed. edition. Edited by Webster JG: John Wiley & Sons; 2006
2. Snyder WE, Qi H, Elliott RL, Head JF, Wang CX: Increasing the Effective Resolution of Thermal Infrared Images. Engineering in Medicine and Biology Magazine, IEEE 2000, 19:63.
3. Braunstein M, Chan RW, Levine RY: Simulation of Dye-Enhanced Near-IR Transillumination Imaging of Tumors. In.; 1997: 735.
4. Kaczmarek M, Nowakowski A: Analysis of Transient Thermal Processes for Improved Visualization of Breast Cancer Using IR Imaging. In.; 2003: 1113.
5. Qi H, Kuruganti PT, Snyder WE: Detecting Breast Cancer from Thermal Infrared Images by Asymmetry Analysis (chapter 27). In Medical devices and systems. Taylor & Fracis Group; 2006
6. Walter FG, Bin Z, Yuan-Hsiang C, Xiao Hui W, Glenn SM: Generalized Procrustean Image Deformation for Subtraction of Mammograms. In. Edited by Kenneth MH. SPIE; 1999: 1562-1573.
7. Fang-Fang Y, Maryellen LG, Kunio D, Carl JV, Robert AS: Computerized Detection of Masses in Digital Mammograms: Automated Alignment of Breast Images and its Effect on Bilateral-Subtraction Technique. Medical Physics 1994, 21:445-452.
8. Zheng B, Chang YH, Gur D: Computerized Detection of Masses from Digitized Mammograms: Comparison of Single-Image Segmentation and Bilateral-Image Subtraction. Acad Radiol 1995, 2:1056-1061.
9. Jonathan FH, Charles AL, Robert LE: Computerized Image Analysis of Digitized Infrared Images of Breasts from a Scanning Infrared Imaging System. In. Edited by Bjorn FA, Marija S. SPIE; 1998: 290-294.
10. Lipari CA, Head JF: Advanced Infrared Image Processing for Breast Cancer Risk Assessment. In.; 1997: 673.
11. Hairong Q, Head JF: Asymmetry Analysis Using Automatic Segmentation and Classification for Breast Cancer Detection in Thermograms. In.; 2001: 2866.
12. Mabuchi K, Chinzei T, Fujimasa I, Haeno S, Motomura K, Abe Y, Yonezawa T: Evaluating Asymmetrical Thermal Distributions Through Image Processing. Engineering in Medicine and Biology Magazine, IEEE 1998, 17:47.
13. Kuruganti PT, Hairong Q: Asymmetry Analysis in Breast Cancer Detection Using Thermal Infrared Images. In.; 2002: 1155.
14. Jakubowska T, Wiecek B, Wysocki M, Drews-Peszynski C: Thermal Signatures for Breast Cancer Screening Comparative Study. In.; 2003: 1117.
15. Hadamard J: Lectures on Cauchy's Problem in Linear Differential Equations. New Haven, CT: Yale University Press; 1923.
16. Alifanov OM: Inverse Heat Transfer Problems. Berlin: Springer-Verlag; 1994. 17. Beck JV, Blackwell B, Clair CS: Inverse Heat Conduction: Ill-Posed Problems. New
York: Wiley; 1985. 18. Murio DA: The Mollification Method and the Numerical Solution of Ill-Posed
Problem. New York: Wiley; 1993. 19. Tikhonov AN: Solution of Ill-Posed Problems. Washington, DC: Hlasted; 1977. 20. Beck JV, Bleckwell B: Inverse problems. In Handbook of Numerical Heat Transfer.
Edited by Minkowycz WJ, Sparrow EM, Schneider GE, Pletcher RH. New York: Wiley; 1988
Chapter 3 Thermal Analysis
3–86
21. (Editor) KAW: Inverse Engineering Handbook. Boca Raton, FL: CRC Press; 2002. 22. Ozisik MN, Orlande HRB: Inverse Heat Transfer: Fundamentals and Applications.
New York: Taylor & Francis; 2000. 23. Hisada T, Nakagiri S: Stochastic Finite Element Method Developed for Structure,
Safety and Reliability. In 3rd International Conference on Structure, Safety and Reliability; New York. Wiley; 1989: 395-408.
24. Hisada T, Nakagiri S: Role of Stochastic Finite Element Methods in Structural Safety and Reliability. In 4th International Conference on Structure, Safety and Reliability. 1985: 385-394.
25. Shinozuka M, Deodatis G: Response Variability of Stochastic Finite Element Systems. Journal of Engineering Mechanics 1988, 114:499-519.
26. Xiu D, Lucor D, Su C-H, Karniadakis GE: Stochastic Modeling of Flow-Structure Interactions Using Generalized Polynomial Chaos. Journal of Fluids Engineering 2002, 124:51-59.
27. Jardak M, Su C-H, Karniadakis GE: Spectral Polynomial Chaos Solutions of the Stochastic Advection Equation. Journal of Scientific Computation 2002, 17:319-338.
28. Xiu D, Karniadakis GE: Modeling Uncertainty in Flow Simulations via Generalized Polynomial Chaos. Journal of Computational Physics 2003, 187:137-167.
29. Narayanan VAB, Zabaras N: Stochastic Inverse Heat Conduction Using a Spectral Approach. International Journal for Numerical Methods in Engineering 2004, 60:1569-1593.
30. Narayanan VAB, Zabaras N: Variational Multiscale Stabilized FEM Formulations for Transport Equation: Stochastic Advection-Diffusion and Incompressible Stochastic Navier-Stokes Equations. Journal of Computational Physics 2005, 202:94-133.
31. Zabaras N: Inverse Problems in Heat Transfer, Chapter 17. In Handbook of Numerical Heat Transfer. 2nd Ed. edition. Edited by Minkowycz WJ, Sparrow EM, Murthy JY: John Wiley & Sons; 2004
32. Pennes HH: Analysis of Tissue and Arterial Blood Temperatures in the Resting Human Forearm. J Appl Physiol 1998, 85:5-34.
33. Wulff W: Energy Conservation Equation for Living Tissue. IEEE Transactions On Biomedical Engineering 1974, BM21:494-495.
34. Weinbaum S, Jiji LM: A New Simplified Bioheat Equation for the Effect Of Blood-Flow on Local Average Tissue Temperature. Journal of Biomechanical Engineering-Transactions of the ASME 1985, 107:131-139.
35. Rubinsky B: Numerical Bio-Heat Transfer. In Handbook of Numerical Heat Transfer. 2nd Ed. Edited by Minkowycz WJ, Sparrow EM, Murthy JY: Whily & Sons; 2006
36. Wissler EH: Pennes' 1948 Paper Revisited. J Appl Physiol 1998, 85:35-41. 37. Draper JW, Boag JW: Calculation of Skin Temperature Distributions in
Thermography. Physics In Medicine And Biology 1971, 16:201-&. 38. Awbery JH: Heat Flow when the Boundary Condition is Newtonians's Law.
Philosophical Magazine 1929, S. 7:1143-1153. 39. Feasey CM, Davison M, James WB: Effects of Natural and Forced Cooling on
Thermographic Patterns of Tumors. Physics in Medicine and Biology 1971, 16:213-&.
40. Draper JW, Boag JW: Skin Temperature Distributions over Veins and Tumors. Physics in Medicine And Biology 1971, 16:645-&.
Chapter 3 Thermal Analysis
3–87
41. Davison M: Skin Temperature Distributions over veins and tumors. Physics in Medicine and Biology 1972, 17:309-310.
42. Fibich G, Hammer A, Gannot G, Gandjbakhche A, Gannot I: Modeling and Simulations of the Pharmacokinetics of Fluorophore Conjugated Antibodies in Tumor Vicinity for the Optimization of Fluorescence-Based Optical Imaging. Lasers in Surgery and Medicine 2005, 37:155-160.
43. Small RD, Weihs D: Thermal Traces of a Buried Heat Source. Journal of Heat Transfer-Transactions of the ASME 1977, 99:47-52.
Chapter 4 The System
4–88
4. The System
4.A. Introduction
The design of a system implementing an early detection of malignant cell, i.e. cancerous
tumor and essential treatment, is expected to fulfill several fundamental requirements to be
applicable. This novel method should be non-invasive or at least minimally invasive since the
nanoparticles should be inserted into the human body (e.g. injected into the blood circulation).
The system should be cost-effective, accurate, reliable and capable of being implemented as a
bed-side device, unlike other modalities such as MRI and CT. The application of a closed-
loop system allows the detection and treatment procedures to be performed in a single device
and enabling a real-time treatment based on an imaging feedback. The lack of a feedback is a
drawback of many modalities known in the art. A description of the suggested system is
depicted hereinafter.
Figure 4.1 illustrates the main building blocks of the suggested system comprised of means
for:
(i) Heat generation
(ii) Thermal image acquisition
(iii) Thermal image Analysis (see Chapter 3)
Chapter 4 The System
4–89
Figure 4.1 Schematic description of the system
4.B. Heat Generation
Heat generation is conceptually comprised of two parts:
(i) Magnetic nanoparticles (for “heat emission”)
(ii) Magnetic field (for nanoparticles’ excitation)
Heat generation is established by the application of an alternative magnetic field on the
magnetic nanoparticles which are already located within the tissue, bioconjugated to the
tumor's surface. The magnetic nanoparticles (heating mechanism and affecting parameters)
were discussed broadly in chapter 2. This section focuses on the generation of appropriate
magnetic fields, which is not a trivial task considering the requirements we introduce in this
work.
Chapter 4 The System
4–90
The magnetic field is generated by a magnetic system usually comprised of:
(i) Antenna (e.g. coils)
(ii) AC current generator
The design of the magnetic system is implemented bottom-to-up, i.e. after choosing the
desirable field parameters (e.g. field strength, frequency), we are capable of designing the
system itself (e.g. coils, circuitry). Determination of the desirable parameters is not trivial
since the system is characterized by a large number of degrees-of-freedom.
Previous research works investigated various fields: Kalambur et al (2005) used a 1kW
generator and 4 turn RF coil to produce field strength of 0 14 kAH m⎡ ⎤= ⎣ ⎦ and frequency
[ ] 175f kHz= ; Giri et al (2005) examined the fields [ ]( )10 45 ,300kA kHzm⎡ ⎤− ⎣ ⎦ ;
Ma et al used a 15kW RF generator to produce the field [ ]( )32.5 ,80kA kHzm⎡ ⎤⎣ ⎦ ; Hergt et al
(2004) shows losses under the AC field [ ]( )11 ,410kA kHzm⎡ ⎤⎣ ⎦ ; Pankhurst et al (2003)
investigated nanoparticles under the extensive field region of [ ]( )0 15 ,0.05-1.2kA MHzm⎡ ⎤− ⎣ ⎦
and Kim et al examined the influence of fields of [ ]( )110 ,0.1-15A MHzm⎡ ⎤⎣ ⎦ .
The two principle parameters of the externally applied magnetic field, i.e. the frequency and
strength, are limited by deleterious physiological responses to high frequency magnetic fields
[1, 2]: stimulation of peripheral and skeletal muscles, possible cardiac stimulation and
arrhythmia, and non-specific inductive heating of tissue. Generally, the useable range of
frequencies and amplitudes is considered to be f = 0.05 – 1.2 MHz and H = 0 – 15 kA/m.
Chapter 4 The System
4–91
Experimental data on exposure to much higher frequency fields comes from groups such as
Oleson et al [3] who developed a hyperthermia system based on inductive of tissue, and
Atkinson et al [4] who developed a treatment system based on eddy current heating of
implantable metal thermoseeds. Atkinson et al. concluded that exposure to fields where the
product H · f does not exceed 4.85 × 108 kA/(m·s)-1 is safe and tolerable [5].
Hence, following the physiological constraints shown above and based on previous research
results such as those mentioned above, the desirable averaged working point was chosen to
be [ ]0 10 ; 100kAH f kHzm⎡ ⎤≈ ≈⎣ ⎦ .
4.C. Antenna Configurations
4.C.1. Solenoid
Trying to meet with the fundamental objectives of the suggested system, particularly cost-
effectiveness and bed side capability, we seek an alternative technology for the commonly-
used giant and expensive RF generators of several kilo-Watts and up, since they cost about
10k-100k of dollars and are not comfortable to locate near the patient’s bed or at the clinic.
Most of research works in this field are using a single RF coil with a few turns, e.g. 3-4 turns,
as shown in section 4.B.
A major drawback of the coil configuration is that there is no accessibility for any imaging
element, such as an IR camera. If we had desired to use that kind of solenoid coil, it would
have been had to be characterized with a very large diameter, and the camera would have
been exposed to the AC field. Hence, this configuration is not applicable and does not apply
to our needs.
Chapter 4 The System
4–92
4.C.2. C-Core
Another suggested alternative which have been considered is the C-core configuration.
The use of a C-shaped ferrite core wounded with a conducting wire is common in the field of
transformers. While air gaps in the field of transformers and power electronics are of the
order of a few millimeters or less, we seek to obtain an air gap of about 5 centimeters
enabling us to place there the tissue sample and to allow imaging device accessibility.
Figure 4.2 Schematic description of a C-core configuration
Figure 4.2 shows schematically the C-core configuration. In our theoretical calculations we
assumed that the core is made of some sort of an iron (e.g. silicon-iron for losses reduction).
Chapter 4 The System
4–93
From Maxwell's equation we can write:
∫∫ ⋅=⋅sc
dsJdlH (Equation 4.1)
Assuming a coil with N turns and current i, we get a discrete form of Eq. 4.1:
which in our case can be written as:
(Equation 4.2)
where:
Hc, lc are the core magnetic field strength and length respectively.
Hg, lg are the air gap magnetic field strength and length respectively.
Substitution of the relation BHμ
= in Eq. 4.2 yields in:
0
gcc g
BB l l Niμ μ
+ = (Equation 4.3)
Since we may assume that , B= c g c gB B BAφ φ φ φ= = ⇒ = = ,
we can write: 0 0
g gc c
c g
l ll lNi NiA A A
φφ φμ μ μ μ
⎛ ⎞⎛ ⎞ ⎡ ⎤+ = ⇒ + =⎜ ⎟⎜ ⎟ ⎢ ⎥⎜ ⎟⎝ ⎠ ⎣ ⎦⎝ ⎠
(Equation 4.4)
where φ is the magnetic flux.
For simplicity, we may assume that the core permeability (µr) is much larger than air
permeability (µ0), i.e. µr >> µ0
Chapter 4 The System
4–94
hence: [ ]0 weberg
NiAlμφ = (Equation 4.5)
Following Eq. 4.5, it is noticeable that we should try to have as much as large area A (trying
to avoid fringe effects), and as much as small lg, trying to achieve a larger magnetic flux.
The core material should be picked according to its saturation value of flux density (since we
wish it wouldn't be saturated, we plan working on the linear region, satLiBNA
= where µr and
Bsat are properties of the material).
Unfortunately, the C-core alternative is an impractical solution. Since we would like it to be a
bed-side device with a sufficiently large lg (e.g. 5 cm) which enables the positioning of an
organ for example therebetween, it is necessary to provide a large power source, which cannot
be portable. The C-core configuration also limits us to a predetermined length lg, which
cannot be adjusted upon user’s discretion. An example for an attempt to implement a system
for the purpose of treatment solely is depicted in the work of Jordan et al [6].
4.C.3. Helmholtz Coil
An alternative preferred method relies on a Helmholtz coil configuration. A Helmholtz coil is
a parallel pair of identical coils (e.g. circular coils) which are spaced one radius apart and
wound so that the electrical current flows through both coils in the same direction, as shown
in Figure 4.3. The fundamental premise of this configuration is that it produces a uniform
(homogeneous) magnetic field between the coils with the primary field component parallel to
the axes of the two coils and its amplitude which behaves according to the approximated
formulation given below [7] (This formula relates to an ideal set of Helmholtz coils):
Chapter 4 The System
4–95
( )
20
3 3 32 22 2 2 2 2
2 2 2 2
1 1
2 22 1 1x
NibBx ax x axb ab a b a
μ
⎡ ⎤⎢ ⎥⎢ ⎥
= × +⎢ ⎥⎛ ⎞ ⎛ ⎞+ −+ ⎢ ⎥+ +⎜ ⎟ ⎜ ⎟⎢ ⎥+ +⎝ ⎠ ⎝ ⎠⎣ ⎦
(Equation 4.6)
where:
Bx – the magnetic field, in [Teslas], at any point on the axis of the Helmholtz coil. The
direction of the field is perpendicular to the plane of the loops.
i - the current in the wire, in [Amperes].
N – number of turns per coil.
b – the radius of the current loops, in [meters].
a – the distance, on axis, from the center of the Helmholtz coil, in [meters].
Figure 4.3 Schematic description of Helmholtz coils configuration
Chapter 4 The System
4–96
Additional advantages of the Helmholtz configuration are that (1) it enables an open
workspace for sample (tissue) handling and imaging device accessibility, i.e. an easy and safe
path for placing the IR camera, and (2) it enables the change of the distance between the two
coils, i.e. adjustable workspace (unlike the C-core configuration, for example).
For simplicity, the design is based on the magnetic flux density applied on the center between
the two coils where x=0, then Eq. 4.6 is reduced the expression:
0
32
0|
45x
LNIBR
μ=
⎛ ⎞= ⋅⎜ ⎟⎝ ⎠
(Equation 4.7)
4.D. Current Generation
We would like to induce a simple alternative current (AC) in the pair of Helmholtz coils, e.g.
triangular wave, for simplicity. Since the derivative of the current over the coils is
proportional to the voltage, we should generate a square-shaped wave (see Figure 4.4).
Fortunately, designing a generator which produces a symmetrical squared wave over the coils
may be relatively cost-effective and energy conservative. This design also allows the
maximization of components' efficiency.
The voltage over coils should be high enough to facilitate current elevation from minimum to
maximum during a single half-cycle:
maxmax
2 42
LL S
IdIV L L I L fTdt⋅
= ⋅ = ⋅ = ⋅ ⋅ ⋅ (Equation 4.8)
Chapter 4 The System
4–97
The chosen wires comprising the coils are made of common insulated copper wires (Ø1[mm])
and the coils themselves are characterized by a radius of R=0.05[m] while each coil has 85
turns (N=85). The magnetic induction of each coil was measured and found to be L=2.4[mH].
Figure 4.4 Wave templates generated by the system
t
B(t)
Bmax
-Bmax T
t
IL(t)
IL ,max
- IL ,max T
t
VL(t)
VL
- VL ,max T
Chapter 4 The System
4–98
In order to produce a desired high voltage over the coils, the system design includes power
transformer for voltage elevation, as shown on the system's block scheme in Figure 4.5.
Figure 4.5 System's block scheme
The power transformer has turns ratio of 1:n, and therefore:
; bL b L
IV n V I n= ⋅ = (Equation 4.9)
The power supply of the system is composed of an oscillator (PMW controller) with a tunable
frequency, boost transformer and a push-pull full bridge inverter (H-bridge), as shown in
Figure 4.6. The full bridge is mainly composed of four FETs to allow the alternate current.
Figure 4.6 The power generator's block scheme
Power Supply
Vb
Power
Transformer
1: n
Helmholtz
Coils
N, L, R
Ib IL
Vb ± VL ±
PWM Controller
VPWM
Boost
Transformer
Full Bridge
Ib IFB
Vb ± VFB ±
Chapter 4 The System
4–99
4.E. Thermal Image Acquisition
The thermal imaging is carried out by an IR camera (FLIR A40), which detect the infrared
emission which is emitted from the examined object’s surface (e.g. phantom).
The IR camera is positioned perpendicularly above the object, which is situated within the
magnetic field induced between the two coils. When the magnetic field is applied the
nanoparticles generate heat which can be detected by the IR camera.
4.F. The Integrated System
Integrating the main building blocks of the required system mentioned above comprises the
system as shown in Figure 4.7. The system should preferably include a closed-loop
feedback to allow the adjustment of the field parameters (generated by the coils) according to
the temperature readings (acquired via the IR camera).
Chapter 4 The System
4–100
Figure 4.7 Schematic description of the closed-loop system
Obviously, interruption by the user (e.g. physicist) is possible, such as for example the tuning
of magnetic field when changing its mode of operation (e.g. achieving therapy requires a
substantial increase of the temperature within the treated tissue).
Yet, the current laboratory system that has been designed and built as shown in Figure 4.8 is
not capable of generating the required magnetic field due to technological issues. Still, it
requires more than 300 Volts to theoretically generate 5 mT only. This may also require
dedicated cooled coils and the incorporation of safety means. Moreover, a closed loop
feedback has not been implemented yet.
Chapter 4 The System
4–101
Thermal Camera FLIR
Coils
Power Transformer
Power Supply
Full-Bridge
Thermal Camera FLIR
Coils
Power Transformer
Power Supply
Full-Bridge
Figure 4.8 Laboratory system
Chapter 4 The System
4–102
4.G. References
1. Oleson J R, Cetas T C, Corry P M: Hyperthermia by Magnetic Induction: Experimental and Theoretical Results for Coaxial Coil Pairs. Radiat. Res.1983, 95:175-186.
2. Reilly J P: Principle of Nerve and Heart Excitation by Time-Varying Magnetic
Fields. Ann. New York Acad. Sci. 1992, 649:96-117. 3. Oleson J R, Heusinkveld R S, Manning M R: Hyperthermia by Magnetic Induction:
II. Clinical Experience with Concentric Electrodes. Int. J. Radiat. Oncol. Biol. Phys. 1983, 9:549-556.
4. Atkinson W J, Oleson J R, Heusinkveld R S, Manning M R: Hyperthermia by
Magnetic Induction: II. Clinical Experience with Concentric Electrodes. Int. J. Radiat. Oncol. Biol. Phys. 1983, 9:549-556.
5. Pankhurst Q A, Connolly J, Jones S K, Dobson J: Applications of Magnetic
Nanoparticles in Biomedicine. J. Phys. D: Appl. Phys. 2003, 36:167-181. 6. Jordan A, Scholz R, Maier-Hauff K, Johannsen M, Wust P, Nadobny J, Schirra H,
Schmidt H, Deger S, Loening S, Lanksch W, Felix R: Presentation of a New Magnetic Field Therapy System for the Treatment of Human Solid Tumors with Magnetic Fluid Hyperthermia. Journal of Magnetism and Magnetic Materials 2001, 225:118-126.
7. Lerner L S: Physics for Scientists and Engineers. Jones and Bartlett, 1997.
Chapter 5 Conclusions and Future Work
5–103
5. Conclusions and Future Work
5.A. Conclusions
This research deals with a system for the detection of malignant tumors and for the treatment
of those tumors. The physical principle is the generation of heat for both diagnosis and
therapy. The heat generation and its amplification above the body’s normal temperature level
are achieved by biocompatible magnetic nanoparticles that are bioconjugated to the tumor and
their stimulation by a suitable external magnetic field.
This procedure is specifically targeted to the tumor since it relies on the capability of the
immune system and its detectability, i.e. the body knows best to locate the malignant cells.
Hence, the bioconjugation of the nanoparticles to the antigen-antibody complex is probably
the most accurate method to reach the real malignancies.
The thermal model that was developed as a part of this research enables the derivation of two
crucial parameters: the depth of a heat source and its local temperature. This algorithm is
based on a single 2D thermal image of the medium surface solely. Thus, there is no need for
multiple angles, images and/or invasive measurements of temperature. The algorithm which
relies on solving the forward thermal problem is simple, does not require extensive resources
and does not require special involvement from the side of the patient and/or physicist.
On top of the in-silico validation that has been conducted, still there is a need for an in-vitro
validation and ex-vivo and/or in vivo examination of this model.
Moreover, the whole concept for enabling the unique system is presented. A preferable
configuration for the generation of the AC magnetic field is proposed and its characteristics
should be still evaluated.
Chapter 5 Conclusions and Future Work
5–104
In conclusion, this research work may serve as a novel fundamental concept for having both
diagnosis and therapy in a single device, where the transfer between both modes is merely a
simple change of field parameters. The minimally-invasive method is selective and has the
potential of being very accurate, reliable and friendly both to the operator (e.g. physician) and
to the patient. It incorporates various field of research and I believe and hope that it can be
developed into a bedside, cost effective and applicable device that may assist in a better and
improved detection and treatment of one of the prevalence diseases that the medical industry
currently has to deal with.
Chapter 5 Conclusions and Future Work
5–105
5.B. Future Work
This research shows a fundamental design of the system which is meant to pursue thermal
diagnosis and therapy in one single device which is still not bulky and can operate near the
patient’s bed, be accurate, reliable and cost effective. The concept and modularly design that
were described in this research work is the basis for such a system. The system comprises
several main modules: heat generation (including nanoparticles and the external field
generation), thermal imaging, analysis and feedback. This multi-disciplinary system
incorporates various scientific and technological fields. Furthermore, each module may be
investigated and improved independently with no direct relation to the other modules.
Producing the required external magnetic field should be designed to generate a higher
magnetic field, preferably with adjusted parameters, e.g. magnitude, frequency, distance
between the coils. One of the goals in my view is to increase the efficiency of this module
and to enable the use of standard voltage and current of a domestic electrical infrastructure.
The analysis module is based on the acquired raw thermal image and includes the processing
for improving the data quality and derivation of desired parameters. This module may be
approached by various methods implementing different mathematical models, computational
algorithms etc. It is desirable to try and derive additional parameters (other than tumor’s
depth and tumor’s temperature) such as for example 3D geometrical boundaries of the tumor.
The current model is a basic model that relies on ideal assumptions (e.g. homogeneous tissue,
steady state). Furthermore, the inverse model assumes a point source which is merely an
ideal approximation for much more complicated scenarios that involve undefined tumor
boundaries, noise signals, physiological, anatomical abnormalities etc.
Chapter 5 Conclusions and Future Work
5–106
The closed-loop feedback that allows control on the external magnetic field’s parameters (e.g.
magnitude and frequency) can be automatically adjusted based on the thermal imaging to
maintain appropriate contrast and to achieve control on the heat expansion within the tissue in
real-time in order not to harm surrounding healthy tissue. This can be carried out by a for
example LabView® dedicated program.
The first stage to be investigated is naturally in-vitro, i.e. examining the behavior of the
nanoparticles within a tissue-mimicking material. It is not trivial to choose this phantom
material since it has to fulfill two qualities: to imitate the thermal characteristics of a tissue
and on the same time to imitate the magnetic characteristics of a tissue, preferably on a
specific frequencies range. This may be important for testing the tissue behavior under the
alternative external magnetic field. For instance, the tissue will probably heat up only from
the magnetic field effect, a factor which should be taken into consideration and be eliminated
during thermal analysis. Such materials may compose derivatives of agar, carrageenan or
special plastics such as A150.
Obviously, examining this method in-vivo requires also progress in the biological field of
bioconjugation and the discovery of new and more specific signals for detection of malignant
cells such as for example novel cancer specific-antigens.
תקציר
תקציר
, אשר תהה חדשנית )IR( אדומה- ארמטרת מחקר זה הינה לפתח טכניקת דימות תרמית המבוססת על קרינה אינפ
- ננויתרונותיהם של ותשפר את השיטות הקיימות והמוכרות לנו כיום תוך ניצול , לא פולשנית ובעלת עלות נמוכה
הינם בעלי יכולת ייצור של ) קומפטביליים- ביו(ל שאינם מזיקים לגוף האדם "החלקיקים הנ. חלקיקים מגנטיים
מגיע לפני השטח של הריקמה ונפלט , מתקדם בריקמההנוצר החום . חום תחת השפעתו של שדה מגנטי משתנה
ניתוח טמפרטורת פני השטח של הריקמה מאפשר גזירה של .י עדשה של מצלמה תרמית"ע תהנרכש IRכקרינת
.בסביבתםהמתהווה ה המקומית הרל הטמפרטומיקום החלקיקים בעומק הריקמה וש
.ספציפי של החלקיקים לפני השטח של הגידולביולוגי טכניקה זו יכולה לשמש ככלי אבחוני הודות לצימוד
מעלות ( 5°C בלמשללהעלות את הטמפרטורה של החלקיקים המצומדים יתןנ, תחת שדה מגנטי מתאים, כך
העלאת הטמפרטורה באיזור הגידול . של הגידול ללא גרימת נזק לריקמהתרמי דבר המאפשר דימות , )צלזיוס
גורמת להרס מקומי ובלתי הפיך לאתר הממאיר ללא פגיעה , 100°Cועד 65°Cבין למשל ,באופן משמעותי
ככלי טיפולי ממוקד בגידולים אף תהליך זה יכול להוות עבורנו , בנוסף לדימות התרמי .רקמות השפירות השכנותב
.אירים הנעשה תחת בקרה תרמיתממ
אביב -אוניברסיטת תל ש איבי ואלדר פליישמן"הפקולטה להנדסה ע
סליינר -ש זנדמן "בית הספר לתארים מתקדמים ע
תרמיים ממוקדים לאבחון וטיפול בגידולים וריפוישיטה לדימות
חלקיקים מגנטיים- י שימוש בננו"ממאירים ע
רפואית-בהנדסה ביו" המוסמך אוניברסיט"חיבור זה הוגש כעבודת גמר לקראת התואר
ידי-לע
עידו מיכאל גשייט
רפואית-העבודה נעשתה במחלקה להנדסה ביו
ר אברהם דיין"ר ישראל גנות וד"בהנחיית ד
ח"מרחשוון התשס
אביב -אוניברסיטת תל ש איבי ואלדר פליישמן"הפקולטה להנדסה ע
סליינר -ש זנדמן "בית הספר לתארים מתקדמים ע
תרמיים ממוקדים לאבחון וטיפול בגידולים וריפוישיטה לדימות
חלקיקים מגנטיים- י שימוש בננו"ממאירים ע
רפואית-בהנדסה ביו" מוסמך אוניברסיטה"חיבור זה הוגש כעבודת גמר לקראת התואר
ידי-לע
עידו מיכאל גשייט
ח"מרחשוון התשס