1

Mathematical Methods in Cancer and Brain

Research – New Approach,

Invention, and Practice

Takashi Suzuki

Division of Mathematical Science Department of Systems Innovation

Graduate School of Science Osaka University

School/Graduate School/Graduate School of School of Engineering Engineering ScienceScience

Osaka Osaka UniversityUniversity

SEngineering Science

2

1724 Establishment of the Kaitokudo (懐徳堂)(School of General Education)

1838 Establishment of the Tekijuku (適塾)

(School of Dutch Studies in the Edo Period)

1869 Establishment of the hospital supervised by the Ministry of Education(Presently, MEXT)

1880 Establishment of the Osaka Prefecture Medical School and the Osaka Prefecture Hospital

1896 Establishment of the Osaka Industrial School

1915 Establishment of the Osaka Prefecture University Hospital

1931 Establishment of the Osaka Imperial University

1949 Establishment of Osaka University (new system)

2004 Becoming “National University Corporation”

2007 Merger with Osaka University of Foreign Studies

History of Osaka UniversityHistory of Osaka University

・・・・Letters

・・・・Human Sciences

・・・・Law and Politics

・・・・Economics

・・・・Science

・・・・Medicine

・・・・Dentistry

・・・・Pharmaceutical Sciences

・・・・Engineering

・・・・Engineering Science

10 Graduate Schools 5 Independent Graduate Schools

・・・・Language and Culture

・・・・International Public Policy

・・・・Information Science and Technology

・・・・Frontier Biosciences

・・・・Law School

Faculties and SchoolsFaculties and Schools

11 Undergraduate Schools

・・・・Letters

・・・・Human Sciences

・・・・Foreign Studies

・・・・Law

・・・・Economics

・・・・Science

・・・・Medicine

・・・・Dentistry

・・・・Pharmaceutical Sciences

・・・・Engineering

・・・・Engineering Science

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Undergraduate 16,204

Graduate

Master Course 4,525

8,037Doctor Course 3,187

Graduate School of Law 325

Grand Total 24,241

Academic staff 2,877

Non-academic staff Permanent staff 2,3695,531

Temporary staff 3,162

Grand Total 8,408

Number of Students, Faculty and StaffNumber of Students, Faculty and Staff

Number of Students

Number of Faculty and Staff

(As of 1st May, 2008)

(As of 1st May, 2008)

Undergraduate 467

Graduate 918

Total 1,385

Latin America 48 （（（（3%））））

Europe 154 （（（（11%））））

Asia 1,070 （（（（77%））））

North America 40 （（（（3%））））Oceania 18 （（（（1%））））

Middle East 28 （（（（2%））））

Africa 27 （（（（2%））））

Total

1,3851,385（（（（100%））））

International StudentsInternational Students

(As of 1st May, 2008)

4

Asian StudentsAsian Students

(As of 1st May, 2008)

Taiw an (65)

Thailand (82)

Vietnam (84)

China(409)

Rep. of Korea(221)

Malaysia (47)

Indonesia (51)

Others (88)

Bangladesh (23)

Total

1,0701,070

Immediately after the launch of Sputnik, US enforced education, military affairs, and science to catch up with the Soviet space technology program, for education, by modernizing engineering education.

Sputnik Shock in US

Sputnik, The FirstArtificial Satellite (1957)

The engineering education at the time was carried out in each small department separately without any connection to other departments. This system could hardly cope with new technologies such as space engineering.In the education of engineering science, the basic scientific knowledge from many departments, that is multidisciplinary subjects, are taught. This new method of teaching was smoothly implemented in United States universities from the beginning of the 1960’s, and spread very quickly.

For military affairs, NASA and Mercury Project were founded in 1958.

Concept of Engineering ScienceConcept of Engineering Scienceーーーーーーーー USA USA ーーーーーーーーS

Engineering Science Courtesy of Prof. Y. Tobe (Dean)

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The Department of Engineering Science at Oxford is the only unified department in the UK which offers accredited courses in all the major branches of engineering - our students develop a broad view of the subject much appreciated by employers, but can also choose from a very wide range of specialist options.

Department of Engineering Science, Oxford University

In the Department there are no barriers between the different branches of engineering, and we are involved in a great deal of multi-disciplinary researchcollaborating with groups in other departments. This broad view of engineering, based on a scientific approach to the fundamentals, is part of the tradition that started with our foundation in 1908!

The major theme underlying our research portfolio is the application of cutting-edge science to generate new technology, using a mixture of theory and experiment. We place a strong emphasis on inter-disciplinary and collaborative work , both within engineering science and across the physical, medical and life sciences.

Education

Research

Concept of Engineering ScienceConcept of Engineering Scienceーーーーーーーー UK UK ーーーーーーーーS

Engineering Science Courtesy of Prof. Y. Tobe

Dr. Kenjiro ShodaThe First Dean of The School of Engineering Scienceand The 7th President of Osaka Univ.

The faculty, through devotion to the fundamental developments of technology through a fusion of science and engineering , contributes to the creation of the true culture o f mankind.

Educational ObjectivesTo develop scientists and engineers with a keen interest in practical technology, and who have a firm grasp of the basic sciences. To produce graduates who will use the cutting-edge expertise to generate new technology.

Our School of Engineering ScienceOur School of Engineering Scienceーーーーーーーー Concept of Foundation in 1961 Concept of Foundation in 1961 ーーーーーーーーS

Engineering Science Courtesy of Prof. Y. Tobe

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Number of StaffProfessors (incl Research Centers)

Associate Professors (incl Research Centers)

Assistant Professors

Technical Staff

Administrative Staff

Number of StudentsUndergraduates 1st - 4th (International)

Master’s Course 1st - 2nd (International)

Doctoral Course 1st - 3rd (International)

As of May 2008

60

58

65

16

43

1947 (28)

583 (24)

166 (36)

Statistics of School/Graduate SchoolStatistics of School/Graduate Schoolof Engineering Scienceof Engineering ScienceS

Engineering Science Courtesy of Prof. Y. Tobe

Graduate School of Engineering ScienceGraduate School of Engineering ScienceSEngineering Science

Department of Materials Engineering Science

• Division of Materials Physics

• Division of Chemistry

• Division of Chemical Engineering

• Division of Frontier Materials Science Department of Mechanical Science and Bioengineering

• Division of Nonlinear Mechanics

• Division of Mechanical Engineering

• Division of BioengineeringDepartment of Systems Innovation

• Division of Advanced Electronics and Optical Science

• Division of Systems Science and Applied Informatics

• Division of Mathematical Science

• Division of Mathematical Science for Social Systems

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Division of Mathematical Science

(4 Laboratories)

Mathematical Modeling 1 (Nawa)

Mathematical Modeling 2 (Suzuki)

Statistical Science 1 (Shirahata)

Statistical Science 2 (Kano)

Suzuki Laboratory

T. Suzuki Prof. M. Okado Associate Prof. R. Takahashi Assistant Prof. T. Murakami D3 M. Sato D1S. Inazumi M2F. Kanaya M1T. Yoshioka M1S. Tasaki JSPS FellowB. Rantra Visiting Prof. K. Nakane Invited Res. Y. Adachi Invited Res. T. Saito Project Res. K. Itano Project SecretaryY. Iuchi Lab. SecretaryM. Oyama Invited Prof.

Foreign (Pos-Doc, PhD, Master, Research) Students

Muhamad, M. (D3) Lin, K. (D3) L. Othman N.B. (D2) Rouzimaimaiti, M. (D1) Nirimanguli, Y. (M2) Li, H. (M2) Baikejang, R. (M1)Chang, S. (M1)

Somachai (R)Wang (R)Feng (R)Chatzitzisis (PD)Farroni (PD)

H. Mori B4K. Morita B4T. Yamazaki B4H. Yoshioka B4Y. Kodera B4

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Numerical Methos

Inverse Problem

Nonlinear Analysis

FEM (Thesis 1981)

Gel’fand-Levitan theory(1983-1988)

Elliptic Theory(1988~)

Parabolic Theory(1996~)

Chemotaxis (2000~2007)

Nonlinear Problem(1995-6, 2003)

Free Boundary Problem(2005)

Transport Problem(2005)

Parallel Optimization(2005)

Asymptotic Analysis(1990)Global Analysis (1992)

Self-Dual Gauge Theory (1996)Turbulence Theory （1991, 1995)

Self-Organization

New Solver to Ill-Posed Problems Engineering – Medical Application 2006~

New Mathematical Methods for Nonlinear Non-equilibrium Phenomena2008~ １．Thermodynamics

２．Turbulence ３．Hamilton Structure ４．Non-local Equation５．Self-Interacting Fluid６．Chemical Reaction

Dual VariationBlowup Envelope

Research Activity

Nonlinear PDE theory Mathematical Modeling - SimulationMathematical Science– Principle and PhenomenaEngineering – Medical Application

from applications to theories encourage his/her fields mostly good at fundamental disciplinecooperation between students joining research projectsfeedback to research community

Educational Activity Under Graduate (Mathematical Science 15/grade) ）

Advanced Linear Algebra (2nd year) Mathematical Modeling (3rd year)Advanced Analysis (3rd year)

Reports Lecture Notes (HP)Comments by Students

Graduate

Mathematics for Nonlinear Phenomena

PhD (1－2/year）Master (3－4/year）Foreign (Thai, China, Malaysia)PD (Greece, Italy)

Applied Analysis-Mathematical Methods in Natural Science, second edition Imperial College Press - World Scientific 2010

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Mathematical Methods for Cancer Cell BiologyHiroshima, 2011. 6. 8- 6.9

JST – Crest Project Mathematical Medicine

Oct. 2009 - March. 2015

International Research Staff Exchange SchemeCall: FP7-PEOPLE-2009-IRSES

PEOPLEMARIE CURIE ACTIONS

Euro (Italy-Greece) → JapanNov 2009-Aug 2013

Some Projects

East Asia Conference on PDE1st 2000. September, Kyoto 8th 2011. December, Pohang (Korea)

Data Medical Statistics, Photo Image, Nutrition Statistics, Epidemiology

Diagnosis – Control Surgery Navigation, Image Analysis, Inverse Source Problem (EEG,MEG,MRI,PET), Morphogenesis Analysis, Medication Simulation

Inside-Bio Mathematical Model Circulation, Neural Network, Muscle Dynamics, Blood Stream, Bio- Rhythm, Electroencephalogram, Tumor Growth, Morphogenesis, Compartment Model

Inter-Bio Mathematical ModelVirus, Immune, Age, Population, Bacillus

Complex System Heredity, Revolution, Ecosystem, Protein Interaction, Bio-Informatics, Best Strategy Game

J-SIAMMathematical Medicine Research Group 2004.4

ChemistryMechanics Fluid DynamicsElectro-Magnetic Theory

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Mathematical Methods in Cancer and Brain Research New Approach, Invention, and Practice

Abstract

Mathematical medicine is a new research field which is a collaboration between medical and mathematical sciences and several new creative studies have emerged from it. I talk on two topics involved by our project, cancer tissue exploration using homology, and brain activity research based on new source identification theory.

1. Cancer and Homology (12)

2. Source Identification for Brain Activity (14)

1. 1. 1. 1. Cancer and Homology

� The Worst Death Cause Morbidity 1/2, Death Rate 1/3

� Cancer Type

Carcinoma ： epithelial cell （８０％～）

Sarcoma ： bone, cartilage, fat, muscle, blood vessel cell

Leukemia ： hematopoiesis cell

� ９０％ cancer patients die by metastasis

Cancer 30%

Heart Compliant

16%

Brain Blood Vessel

Compliant11%

Top 3 of Death Cause (Japan, 2009)

1/28

11

Benign Tumor and Malignant TumorBenign Tumor and Malignant TumorBenign Tumor and Malignant TumorBenign Tumor and Malignant Tumor

■ Adenoma ： glandular system (benign)

■ Adeno-carcinoma ：invasion to surrounding tissues (malignant)

■ Stroma：tissue surrounding tumor, ex-cellular matrix, blood cell, glandular cell

2/28

Hematogenous Metastasis Hematogenous Metastasis Hematogenous Metastasis Hematogenous Metastasis

Figure 20-17 Molecular Biology of the Cell (© Garl and Science 2008)

cell deformationECM degradation

in-traverse

extra-traverse

basement membrane

epithelial cell

stroma

blood vessel

3/28

12

angiogenesismalignant

Invasion to Extra Cell Matrix

chemical substances, foods, X-rays, ultra-violet, radial rays, virus

gene mutation

Normal

clonalgrowth

Invasion to Blood Bessel

Metastasis to Organs

Cancer Events and Biological Hierarchy

organs

tissues

cells

organelles

proteins

DNA

Primarycarcinoma

Top down

Bottom up

4/28

Detect malignant tumor tissues

5/28

13

Topology or geometry?

6/28

fundamental group

Digitization of topology

Klein bottle, non- orientable

Homotopy?

7/28

Free abelian group observed in S^1 action to the manifold

14

connected component

genus (hole, handle)

Homology

8/28

Role of triangulation in homology – cancelation of artificial boundaries

9/28

15

object

→ simplicial division

→ simplicial complex

→ homology group

0-simplex

1-simplex

2-simplex

q-simplex q-chain group

boundary operator

10/28

11/28

automatic computation

photo data → 2D-object (figures) → Betti number

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11172 5243 7742 5782 4116 3479 2744 8.44 2.89 6.58 4.37 1.68 3.74 1.93

8918 5733 5635 5194 1862 6370 2989 4.04 3.77 2.45 2.47 0.55 4.81 4.69

2695 4508 5243 1862 6321 3626 3626 0.76 1.31 1.53 0.46 3.39 1.3 5.69490 1764 1715 882 3381 3528 2303 0.07 0.44 0.78 0.17 1.33 1.11 0.78

931 2548 931 2254 2597 980 1274 0.17 0.6 0.18 0.78 1.56 0.26 0.37

1029 1225 686 1127 392 1372 882 0.21 0.27 0.17 0.27 0.07 0.49 0.21

882 931 2646 1323 1421 1029 343 0.15 0.25 0.47 0.54 0.38 0.33 0.09

Data analysis Data analysis Data analysis Data analysis

/ high speed, high accuracy, no fail negative / high speed, high accuracy, no fail negative / high speed, high accuracy, no fail negative / high speed, high accuracy, no fail negative

/ malignancy check / malignancy check / malignancy check / malignancy check

/ flexible to photo data / flexible to photo data / flexible to photo data / flexible to photo data

IPC application IPC application IPC application IPC application

Practical use Practical use Practical use Practical use

Collaboration with clinical medicine Collaboration with clinical medicine Collaboration with clinical medicine Collaboration with clinical medicine

photo data → threshold values →figures → Betti numbers

12/28

Mathematical tools really applicable to clinical medicine which helps doctor’s task

2. Source Identification and Brain Activity

→ Time series data of many channels

Neural activities → electric current

→ magnetic field

SQUID (Super Conducting Quantum Interface Device)

13/28

17

Source Identification

14/28

Stimulation Electric current

Magnetic field SQUID

Source identification

Magneto-encephalogram

MEG dipole analysis

15/28

18

Standard theory (direct problem)

16/28

Standard theory (inverse problem)

number of dipoles must be prescribed

17/28

over-determined problem

19

Nervus medianus

Visual

unknown number of dipoles?

18/28

Too many unknowns induce too many solutions19/28

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Dipole analysis

time series clusteringa priori information

non-prescribed number of dipoles time sliced datanon-uniqueness

over-determinedprescribed number least square approximationmust exclude local minimum

element number analysis using signal oscillation constant element number

under-determined clustered elements

parallel optimization

Hausdroff measure

cooperate game Divide dipoles to elements

Clustered elements recover dipoles 20/28

Numerical experimentWhy are dipoles identified in spite of non-uniqueness?21/28

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Parallel optimization

Iterative sequence with high-accuracy freezes in under-determined system

Hence iterative sequence having reached there leaves there with the probability 1

22/28

Parallel optimization

outside freezing zone … approachinginside freezing zone … melting

Melting makes frozen sequenence move

Approaching improves accuracy with the probability 1/2

→ how and where?

23/28

22

How? … singular decomposition of matrix

24/28

0-d Hausdorff measure

RepeatRepeatRepeatRepeat

Co-operative game

Where?...Binding ~Principal policy of melting in source identification

A concentrates narrow spots!

25/28

23

Program integrating sub-routines

Approaching

Freezing zone

Melting

Parallel optimization .. Keep accuracy by freezing zone and matrix singular decoposition

coveringbiting

binding

Underdetermined quantization biasing

sparking

clustering

26/28

1- time sliced real data analysis

Aural evoked current measured by 128chnnels

27/28

24

nervus medianus time series data analysis using 32×32 channels

moving, separating, annihilating, binding dipoles

28/28

ENIDM(Element Number Increasing – Decreasing Method)

10 dipole identification

New Solver ENIDM

・increasing number of elements ・determine number using instability concerning moments ・decreasing process to adjust the number ・high speed/many source identification ・robust against noise

・basic research of brain activity ・diagnosis of epilepsy ・spinal evoked magnetic field

PPPP rrrriiiimmmm aaaa rrrryyyy

CCCC uuuu rrrrrrrreeeennnntttt

RRRR eeee ttttuuuu rrrrnnnn

CCCC uuuu rrrrrrrreeeennnntttt

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Spinal cord

Magneto-spinography

Medelling

Magnetic source

Summary

1. Mathematical medicine is a new field provided with many targets where several approaches and formulations are possible

2. Among others cancer control and brain activity analysis are important issues. Chemical reaction and electro-magnetic theories may formulate some aspects of them

3. Two mathematical methods to clinical medicine are presented, homology based cancer tissue diagnosis and dipole MEG analysis from under-determined setting

Future Plan: Mathematical Modeling in Cancer Cell Biology

Part 1. PDE’s integrate medical insights – cancer events and biological hierarchy, top down modeling, system of chemotaxis, hybrid simulation

Part 2. Pathway network study opens new cell biology – protein signal, basement membrane degradation, bottom up modeling, key path search