quantitative three-dimensional analysis and diffusion modeling of oligonucleotide concentrations...

560 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 48, NO. 5, MAY 2001

Quantitative Three-Dimensional Analysisand Diffusion Modeling of Oligonucleotide

Concentrations after Direct Intraparenchymal BrainInfusion

Peter J. Haar, John E. Stewart, George T. Gillies, Senior Member, IEEE, Sujit S. Prabhu, and William C. Broaddus*

Abstract—We compared quantitative experimental results onthe diffusion of 35S-labeled phosphorothioate oligonucleotide(PS-ODN) after intraparenchymal infusion in rat brain, withthe distributions predicted by Fick’s second law of diffusion.Fischer 344 rats underwent identical intracerebral infusions of35S-PS-ODN. After 0, 5, 11, 23, and 47 h, groups of animalswere sacrificed and sequential brain cryosections subjected toautoradiography. The resulting experimental data were comparedto the predicted distributions, for estimation of the apparentfree diffusion coefficient, . Volumes of distribution and totalcontent of 35S-PS-ODN in the parenchyma were also computed,to monitor loss of total material. The values for were withinthe expected range for the 21-mer PS-ODN used, but a progressivedecrease in over time was noted. The model requires toremain constant and, thus, does not adequately explain the spreadof 35S-PS-ODN following infusion. The progressive slowing ofspread over time suggests that at later time points,35S-PS-ODNmay be fixed by tissue binding or cellular uptake in the brain. Lossof material via vascular and CSF clearance may also contributeto the lack of fit. Our results highlight issues to be addressed inthe modeling and experimental design of the intraparenchymalinfusion process.

Index Terms—Antisense oligodeoxynucleotide, Fick’s secondlaw, high-flow microinfusion, mathematical diffusion modeling,three-dimensional diffusion.

I. INTRODUCTION

I NVESTIGATIONAL studies of therapeutic macromolec-ular agents have increased the need for methods of

accurately targeting the distribution of these agents in thebrain and delivering them across the blood brain barrier.

Manuscript received June 27, 2000; revised January 8, 2001. This workwas supported in part by the Jeffress Memorial Trust, the Kopf Founda-tion, the National Institutes of Health (NIH) under Grants NS01766 andCA72955-01A10004, and the Cullather and Hord Funds of the MCV Founda-tion. Asterisk indicates corresponding author.

P. J. Haar, J. E. Stewart, S. S. Prabhu are with the Division of Neurosurgery,Medical College of Virginia, Virginia Commonwealth University, West Hos-pital, Richmond, VA 23298 USA.

G. T. Gillies is with the Department of Biomedical Engineering, Universityof Virginia Health Sciences Center, HSC Box 377, Charlottesville, VA 22908USA. He is also with the Division of Neurosurgery, Medical College of Virginia,Virginia Commonwealth University, West Hospital, Richmond, VA 23298 USA

*W. C. Broaddus are with the Division of Neurosurgery, Medical Col-lege of Virginia, Virginia Commonwealth University, West Hospital, 1200E. Broad Street, P.O. Box 980631, Richmond, VA 23298 USA (e-mail:[email protected]).

Publisher Item Identifier S 0018-9294(01)03395-X.

Some methods of distribution now under clinical evaluationinclude chemically induced increases in vessel permeability[1]–[3], dissolvable biodegradable implants [4], [5], im-munoisolatory encapsulations, intraventricular infusion [6] andintraparenchymal injection [7], [8]. Direct controlled-rate intra-parenchymal infusion, also termed high-flow microinfusion orconvection-enhanced infusion, offers several unique advantagesover these other delivery methods. By placing a catheter tipdirectly into the parenchyma, chemotherapeutic agents maybe delivered in known concentration to a localized volume ofbrain, thus, potentially reducing central nervous system (CNS)side effects [9]. The dynamics of direct intraparenchymalinfusion of molecules of varying sizes into rodent [10]–[14],feline [15] and primate [16] brain have been examined in anumber of studies [17]. Additionally, direct infusion as a clin-ical delivery means for cisplatin [18], nerve growth factor [19],Tf-CRM107 [20], DAB [21], and antisense oligonucleotides(ODNs) [22], [23] has demonstrated significant potential utility.These preliminary studies indicate that the distinctive clinicaladvantages of direct infusion seem to be directly suited to theadministration of ODN therapy.

ODNs have demonstrated great promise as therapeuticagents because they can be tailored to virtually any geneproduct with a known mRNA sequence [24]. Among this classof chemicals, phosphorothioate ODNs (PS-ODNs), in whicha sulfur atom replaces a nonbridging oxygen atom at eachinterbase phosphodiester linkage, have received great attentionas potential drug candidates [22], [25]. The phosphorothioateaddition to the ODN backbone confers a practical therapeuticadvantage as it prevents the ODN from being quickly degradedby cellular nucleuses. Studies indicate that PS-ODNs are about100 times more potent than their unmodified phosphodiestercounterparts [26]–[30]. Our interest in PS-ODNs centers ontheir potential application in the treatment of a variety ofpathologic processes involving the central nervous system,including primary brain tumors such as the highly malignantglioblastoma multiform. Specifically, we have sought ODNsthat are efficacious in preventing cell growth and enhancingsensitivity to other treatment modalities such as radiation andchemotherapy. Rapidly growing knowledge of the molecularpathology by which tumor cells demonstrate increased pro-liferation and resistance to treatment has identified a varietyof potential molecular targets for antisense strategies. Given

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HAAR et al.: QUANTITATIVE 3-D ANALYSIS AND DIFFUSION MODELING OF ODN CONCENTRATIONS 561

a promising target, the mRNA sequence is used to identifypromising candidate antisense sequences containing 15 to 25nucleotides [31]. The general strategy for evaluating the utilityof an antisense mechanism includes the tasks of 1) searchingfor sequence-specific nonantisense effects, 2) confirming thestability of the ODN against degradation, 3) documentingreduced protein expression for the targeted gene, and 4)determining the cellular and nuclear uptake of the antisenseODN. Subsequent studies can then determine the expectedbiologic effect of the ODN on cells in culture [32], and thensubsequently in animal tumor models.

Critical to all of this is the incorporation of a successfuldelivery technique that will function satisfactorily within theCNS. Use of antisense ODNs in the CNS has been limited inthe past by poor penetration through the blood–brain barrier(BBB) after systemic administration. More recently, we havedemonstrated the efficacy of delivering antisense ODNs directlyinto the brain parenchyma, on the brain side of the BBB [22].Coupled with improving methods of imaging tumors within thebrain, the ability to deliver ODNs into the brain parenchymawith high precision offers great promise for targeting effectiveagents to areas containing the pathology. With the availabilityof such a technique, other CNS diseases that are both focaland regional in character may also be treated with antisensetherapies. The list includes Parkinson’s disease, certain seizuredisorders, and some of the sequelae of brain injury from strokeand trauma. Potential antisense treatments for a variety of otherdiseases are also being developed by those working in this field,for instance the targeting of PS-ODNs against cellular adhesionmolecules which play important roles in inflammatory andimmune responses, among many other applications. See [33]for a review of the variousin vivo andin vitro studies.

For direct intraparenchymal infusion to become a practicalclinical tool in ODN therapy, the ODN concentration must be re-liably predictable as a function of location and time, both duringand following infusion. Considerable work has been devoted tothe creation and development of theoretical biophysical modelsof both CNS infusion and diffusion through the brain extracel-lular microenvironment (BEM) [34]–[40]. Substantial experi-mental work on the intraparenchymal diffusion process has ac-companied the theoretical effort [41]–[46]. However, no pre-vious studies have experimentally quantified the ODN concen-tration created by infusion and subsequent diffusion of ODNsthroughin vivo brain. Therefore, the aims of the present inves-tigation were twofold: to precisely quantify the ODN concen-tration following direct infusion into the brain, and to comparethose results with predictions from a theoretical model. Thisstudy will provide a mathematical characterization of the dis-tribution patterns of ODN in the CNS.

II. BACKGROUND

A useful mathematical model of infusate diffusion followingdirect intraparenchymal infusion has been developed byNicholson on the basis of Fick’s Laws, modified to account forthe complex geometrical microstructure of the brain [40]. In

such a medium, the interstitial pore space fraction,, where( ), is defined as

(1)

where is a volume of brain tissue and is the extracellularphase of . The tortuosity, , is a numerical factor that takesinto account the spatial structure of the extracellular space, andis defined operationally as the square root of the ratio of the freediffusion coefficient to the apparent diffusion coefficient

(2)

Using these parameters, the complete expression that yieldspost-infusion concentration at timeand a distance from theinfusion point source is

(3)

Here, is the concentration of the infusate andis a parameterdefined as

(4)

with being the volume of the infusate, andthe pore spacefraction defined above. This equation describes an experimentalsituation in which from a point source, infusate flows uniformlyinto the extracellular space without forming an initial cavity inthe tissue. Also, since the duration of the infusion process ismuch shorter than the subsequent time over which diffusionoccurs, diffusion during the infusion (1 h) has been taken tobe negligible. To evaluate the validity of this assumption, wehave calculated the Peclet number,, which yields the ratioof bulk-to-diffusive flow in the tissue [13]. Under the condi-tions of our study, the distance-dependent range of this quantityis , confirming that bulk flow predominatesduring the infusion process. In terms of the present study, (3)provides a prediction of the distribution of PS-ODN followingmicroinfusion. In what follows, we analyze the PS-ODN distri-bution created during ourin vivo high-flow rate microinfusion,to assess the accuracy of (3) in describing this behavior.

III. M ATERIALS AND METHODS

A. Animal Model

The autoradiogram data for thein vivo infusions used in thisanalysis was generated in a series of animal trials carried outat our institution [22]. Twenty-five Fischer 344 rats were anes-thetized using a combination of ketamine (50–80 mg/kg) andzylazine (5–10 mg/kg) intraperitoneally, and were mounted ona stereotactic frame. A burr hole was made 3.5 mm lateral and1mm posterior to bregma and a 25-gauge needle was advancedto a depth of 4.5 mm to infuse radio-labeledS-PS-ODN intothe caudate putamen of each rat.

Twenty l of 100 M solution containing 0.5 Ci ofS-PS-ODN (the sequence and details of synthesis of this

ODN are described in [22]) were infused over 1 h at a rate of


0.33 l/min. At the completion of the infusion, the needle isleft in place for 15 min, then withdrawn from the brain over aperiod of 1–2 min. The rats were sacrificed at 0, 5, 11, 23, and47 h after the conclusion of the infusion. Five rats were usedin each group and their brains were removed and snap-frozenin isopentane/dry ice and stored at80 C for cryosectioning.Cryotome sections 16m thick were cut and used for quanti-tative autoradiography. Four consecutive sections (the numberfitting on a glass slide) out of every 20 were air dried and ap-plied to Kodak Biomax MR film for 18–36 h. Cryosections of aseries of concentrations ofS-sulfate mixed in known amountsof homogenized brain were used as brain-paste standards andincluded in each autoradiogram. The resulting films were thendeveloped and processed for quantitative image analysis.

B. Image Processing

One autoradiogram out of each consecutive set of four fromone slide was positioned on a lightbox and captured with amounted digital camera (resulting pixel resolution 0.333 mm),creating an atlas of images for each rat. In this way, every imagerepresented a thickness of 320m (20 slices 16 m per slice).Each image was rotated so that the visible midline was vertical.The image in each atlas that most closely corresponded to thesite of the cannula insertion could be identified by the moreintense radioactivity deposited along the needle insertion tract(see Fig. 1). This image was then was cropped in a manner thatplaced the cannula tip at a predetermined pixel location. Then,for all of the atlases, the images adjacent to this cannula sec-tion were identified, aligned with the cannula section accordingto midline and anatomical landmarks (e.g., pial and ventricularsurfaces), and cropped to the same size. By working away fromthe central cannula section in this manner (i.e., selecting andaligning adjacent images), all of the selected images for one ratwere ultimately aligned with respect to each other and they wereall cropped to a uniform size.

Cryosections of brain paste standards were included as in-ternal standards with the slides bearing the cryosections froma single brain, and exposed simultaneously to the autoradiog-raphy film. Each of the images for the brain paste standards wasthen digitized with the same light and camera settings used todigitize the brain sections. A region of uniform intensity wasidentified within each standard image and a small square zonefrom this region was captured and saved.

C. Image Data Analysis

The concentration analysis software was developed in Cto sequentially read the entire atlas for one rat and interpret thosedata in terms of a three-dimensional (3-D) volume. The firststep in the algorithm was to average the pixel intensities of eachstandard. Because the standards represented known concentra-tions, a curve could be computed which, based on these stan-dard data, mapped concentration to any pixel intensity. With thiscurve, an algorithm was designed to analyze the concentrationof PS-ODN over spherical shells centered on the cannula tip.The algorithm was applied to the 3-D image volume for each rat

to determine the quantity of PS-ODN in each brain, the volumeof distribution of PS-ODN, and the average PS-ODN concen-tration measured radially from the cannula tip.

To determine the quantity of PS-ODN in each brain, the av-erage concentration was found for a series of spherical shellswith radii 0.1 mm to 6 mm, in increments of 0.1 mm. The av-erage concentration of each shell was multiplied by the volumeof the shell to determine the number of micromoles of PS-ODNin each shell, and these quantities were then summed for all 60shells. Points reflecting a concentration greater than 16M/l inthe vicinity of the cannula were assumed to represent an artifactof the infusion due to the cannula tract, and a separate tabulationfor quantity of PS-ODN was kept for these points.

The volume of the PS-ODN distribution was then determinedby first obtaining information on the background (“noise”)intensity of the images. The mean and standard deviation of thepixel intensity was determined for the background noise in eachset of images. The concentration at two standard deviationsabove the mean in each atlas averaged 1.2M for all sets.Thus, a threshold of 2M was used because this represents aconcentration in the range of significant ODN antisense effects[32].

For each spherical shell, the average concentration was mea-sured for each image set over an area excluding the cannula tract.Plots of this average concentration versus radial distance wereobtained for each rat series. Data from all of the animals in eachpost-infusion time period were averaged together to yield an av-erage plot for each time period.

Using (3), plots corresponding to these measured datawere generated for each time period with all other parametersmatching those of the experiment. The calculated coefficientof diffusion was varied in (3) until the closest match with theaverage experimental plot was obtained. By superimposing thetheoretical and experimental graphs in this manner, an apparentcoefficient of free diffusion for the PS-ODN was estimated foreach time period. Because of artifacts from the needle insertionand anatomical limitations of the rat brain, the curves werematched in the range of 1.2 mm to 3.8 mm from the needleinsertion site. A minimum fitting value of 1.2 mm was chosenbecause it was sufficiently large to exclude the region aroundthe tip of the needle where the PS-ODN was backtrackingalong the needle and fixed to the tissue [Fig. 1(a)–(f)]. Themaximum fitting value of 3.8 mm was chosen because it wasthe maximum radius that would create a sphere that would fitentirely within the brain. Thus, the tendency of the distributionvolumes to deviate from a spherical surface contour at theirmargins was not allowed to affect the interpolation ofvalues by this graphical method.

D. Statistical Analysis

Student’s two-tailed-test was used for comparing data fromgroups of animals from different time points after PS-ODN in-fusion. A -value less than 0.05 was taken as statistically signif-icant. Asterisks in Table II and Fig. 3 indicate the-values forspecific comparisons.


(a) (b)

(c) (d)

(e) (f)

Fig. 1. Representative histological section and autoradiograms from time points following infusion ofS-labeled phosphorothioate oligonucleotide (PS-ODN).The histological section in (a) represents a coronal section of rat brain at the location of infusion cannula insertion (shown diagrammatically). (b)–(f) Demonstratesrepresentative audiograms from coronal sections at the cannula insertion point taken 0, 5, 11, 23, and 47 h after the infusion, respectively.

IV. RESULTS

Fig. 1(a)–(f) illustrates a representative histological section[Fig. 1(a)] and an autoradiogram from each time point followingthe direct intraparenchymal infusion of PS-ODN. Immediately

following the infusion [Fig. 1(b)], the ODN appears as a volumewith clearly defined edges, reflecting the fact that diffusion hashad little time to distribute the oligonucleotide. The autoradio-grams for later times depict the character of the distribution ofthe infused ODN over time. Each section reveals the darkened


(a) (b)

(c) (d)

Fig. 2. Average ODN concentration profiles based on radial distance from the insertion site. After digitizing sequential autoradiogram data, aligning andreconstructing 3-D data sets for individual animals, the radial distribution of ODN from the infusion site was quantified for sequential 0.1-mm shells for adistance of 0.6 mm (diameter of 1.2 mm), as described in the text. The data for these sequential shells were then averaged for the animals at each time point.The resulting averages are shown plotted relative to radial distance from the cannula. (a) Average radial concentration profiles for 5, 11, 23, and 47h followingthe infusion, together. Note that the standard deviations for these averages ranged from 10% to 15%, but are not shown in this figure for purposes of clarity.Because the data points were determined at 0.1-mm intervals, the results are shown as a curve, rather than as individual points representing the average values.(b) Multiple theoretical curves for different values ofD at time 0. (c) and (d) Experimental data for average ODN concentration at 5 and 11 h, respectively.Plotted on each of these graphs also are the theoretical curves expected for ODN concentration with different values ofD (apparent diffusion coefficient)generating curves similar to the experimental data.

vertical band surrounding the cannula tract, indicating infusatebacktracking around the cannula, and apparent fixation of someof the PS-ODN in the tissue immediately adjacent to the can-nula tract. Early inspection of the autoradiogram data, thus, in-dicated the importance of evaluating the needle tract separatelyfrom the rest of the diffusion volume. To that end, a needle tractsegmentation algorithm was developed (see Section III). Whilethe autoradiograms from different rats appear to differ in inten-sity, note that all autoradiograms and corresponding standards

from a single rat were digitized at the same light level. Use ofthe brain paste sections as internal standards, thus, allowed di-rect comparisons of quantitative results from different animals,despite apparent differences in intensity on the autoradiograms.

Fig. 2 presents various experimental and theoretical plots ofthe average concentrations versus distance from the cannula tip,and illustrates how these plots were compared to derive coeffi-cients of free diffusion for each time-period. Fig. 2(a) shows acomposite of the experimental results from each of the time-pe-


TABLE IINTERPOLATEDCOEFFICIENTS OFDIFFUSION DETERMINED BY COMPARING

EXPERIMENTAL DATA TO FICK’S SECOND LAW

riods. Each curve represents the average concentration distribu-tions for all of the rats in a time period. Because the concen-tration for each rat was determined by averaging concentrationover a spherical shell, each point on the plots in Fig. 2(a) (shownas curves due to the close spacing of the 0.1-mm intervals be-tween points) therefore represents the mean of the averages.Fig. 2(b) presents an array of theoretical curves determined byFick’s Second Law for the interstitial space of the brain. Eachcurve was generated assuming a different coefficient of free dif-fusion for the oligonucleotide and using values from the litera-ture ( 0.21, 1.6) for volume fraction and tortuosity.A separate array similar to that shown in Fig. 2(b) was gener-ated for each time period. As described in the Methods section,each experimental curve in A was superimposed on the corre-sponding theoretical array and the closest theoretical match inthe radial region of 1.2 mm to 3.8 mm was chosen to determinea coefficient of free diffusion.

Fig. 2(c) and (d) illustrates the fits of the 5- and 11-h theo-retical curves to the corresponding experimental data sets, anddemonstrate significant deviation of the experimental data fromthe most closely matched theoretical curves. The results of thesecomparisons are summarized in Table I where the interpolateddiffusion coefficients are listed for each respective time period.The coefficient for the initial time period (“0”) is not listed be-cause, as mentioned above, the derivation of Fick’s Second Lawused for the mathematical modeling assumes that diffusion isnegligible at this point. For the distributions occurring at 5 h fol-lowing the infusions, the diffusion coefficient for the PS-ODNwas estimated to be 1.2 10 cm /s. This value decreasessteadily for data taken longer after the infusion. After 47 h, thedistributions yield a diffusion coefficient of 2.5 10 cm /s.

The algorithm used to analyze concentric spherical shellscentered on the cannula tip was easily modified to calculatethe volume of distribution. Fig. 3 graphically illustrates theincrease in diffusion volume over time. A significant increasein volume of distribution occurs over the time of the study,though the large standard deviation resulting from interanimalvariability prevents further conclusions as to the slope of thecurve represented.

The same method of analyzing spherical shells proved to beuseful in tabulating the total quantity, in moles, of PS-ODN in-fused into each brain. Each point in a spherical shell was clas-sified into one of three categories: as an element in the diffu-sion space, as an element in the needle tract, or as an elementof background noise. By determining the average concentrationand spherical shell fraction of each of these categories, an ac-counting of the oligonucleotide content could be performed forthe entire brain. This accounting is presented in Table II, wherethe quantity in micromoles for the diffusion space and for theneedle tract are presented for each time period after the infu-

Fig. 3. Change in volume of distribution over time following infusion. Thevolumes of distribution of PS-ODN at various time points after completing theinfusion were calculated by quantitative autoradiography as described in theMethods sections. The values shown represent means and standard deviations ofthe volumes of distribution for the animals in each group. Statistically significantdifferences relative to the 0 time point by Studentst-test are indicated by anasterisk (p < 0:05).

TABLE IIQUANTITATIVE ANALYSIS OF PS-ODN RECOVERIES ANDVOLUMES OF

DISTRIBUTION AFTER DIRECT INTRAPARENCYMAL INFUSION (MEANS�

STANDARD DEVIATIONS)

sion. It will be noted that the infused ODN is well accounted forby this method at the 0-time point, [(10218)% recovery], andthat the recovery of material decreases to (7434)% at 5 h and(57 7)% by 47 h. Thus, in addition to the spread of materialthrough the brain after the infusion is completed, processes ofclearing the ODN from the brain are also at work.

V. DISCUSSION

Direct controlled-rate intraparenchymal infusion offers ameans of delivering relatively well-known concentrationsof macromolecules into specific locations within the CNS.Previous experimental studies of distributions created bymicroinfusion have been limited to rough estimates describingdiffusion diameters between one and three centimeters [11],[16], [17]. With sufficient modeling of the dynamics of theinfusion process, this system of delivery could be a tool of greataccuracy and predictability and, thus, a clinically useful meansof delivering medications that require precision targeting and


accurately obtained concentrations, such as ODNs. To this end,several biophysical models have been developed to describemathematically the transport of infusate throughout the extra-cellular phase, as driven by direct intraparenchymal infusion[17], [35], [37], [40], [47], [48]. We have used the modelderived by Nicholson [40] that mathematically describes thediffusion of infusate through the brain parenchyma followingdirect intraparenchymal infusion.

The mathematical models of diffusion contain two importantparameters: volume fraction and tortuosity. These describe themedium through which the infusate diffuses. Volume fractionis simply the ratio of extracellular volume to total volumein a region in the brain. Tortuosity is a less clearly definedprobabilistic entity that accounts for the complex pathwaysthrough which the molecules move and for dead end poresthat hinder macroscopic diffusion. Both of these parametershave been well-studied throughout different regions of rodentbrain [49], [50]. This study adopted a volume fraction of 0.21,a value supported by our own studies on the distribution ofPS-ODN in rat brain immediately after infusion [22], and atortuosity of 1.6 [40], which are values determined for rodentgray matter. Nicholson’s model was chosen as a theoreticalbasis of comparison because we observed a correspondencebetween a preliminary two-dimensional analysis of the cannulasections and the Fick’s laws model, and because Fick’s lawshave been successfully used to describe diffusion of small ionsthrough the brain [20], [22].

The values obtained for the coefficient of diffusion at eachdifferent time interval decline from 1.3 10 cm /s to 0.2510 cm /s from 5 h to 47 h post-infusion. Since the coefficientof diffusion is an intrinsic property of a molecule that cannotchange over time, these data reflect an inadequacy of the modi-fied Fick’s law model to fully describe the behavior of PS-ODNin brain tissue. With increasing post-infusion time, the apparentcoefficient of diffusion decreases, indicating that the PS-ODNwas spreading through the tissue at a decreasing rate. Althoughthe studies performed here cannot provide insight into the rea-sons for this discrepancy, the slowing of diffusion is believedto be some combination of cellular uptake and protein bindingof PS-ODN. Cellular uptake of PS-ODN has been clearly ob-served in the CNS, particularly by astrocytic cells [33], [51].Indeed, uptake of PS-ODN by cells of the brain would repre-sent a positive feature of these studies, in view of the fact thatpoor uptake of ODNs has been touted as a potential drawback ofthe antisense oligonucleotide approach as a therapeutic strategy.Further, Stein and Krieg [52] note a potential problem of studiesinvolving the polyanionic property of PS-ODNs; several studieshave revealed that oligonucleotides bind with cellular proteins.Increased binding over time could result in a decreasing ap-parent coefficient of diffusion because the larger ODN/proteincomplex would be expected to diffuse at a slower or negligiblerate in contrast to unencumbered ODN.

In general, the data obtained for the coefficients of diffu-sion fall within the expected values of 0.7 10 cm /s to1.3 10 cm /s [53]–[55] (and Nicholson, personal corre-spondence). Results below the lower end of this range suggest afactor other than diffusion is affecting the distribution of thesemolecules.

The accounting analysis performed for the PS-ODN supportsthis hypothesis also. The quantity of PS-ODN is observed todecrease with increasing time, corresponding to our studiesthat demonstrated subarachnoid CSF fluid clearance [22]. Inaddition, necropsy studies have demonstrated the appearanceof small but significant quantities of S-labeled material inthe blood and liver of animals infused in a similar fashionduring the time-frame of these studies (unpublished data). Thissystemic distribution of oligonucleotide-derived material mayvery well account for the 25% to 50% loss of material from thebrain that we have demonstrated in the studies reported here.However, as time increases, Table II demonstrates that the rateof PS-ODN clearance tapers dramatically, which would onlyoccur if some factor were restricting the free movement of theoligodeoxynucleotides.

Calculations of average volumes of distribution for PS-ODNdemonstrated a progressive increase over time, but interpreta-tion of these data are hampered by significant interanimal vari-ability. We believe this results primarily from limitations on thedistances over which diffusion can occur in the rat brain, butmay also in part be due to other factors affecting the distributionof PS-ODN that may vary from animal to animal. Nevertheless,it should be noted that the increase in volume of distribution at47 h shown in Fig. 3 is several-fold less than is predicted bythe model derived from Fick’s second law for a molecule witha in the range described above. We believe this further sup-ports the hypothesis that the PS-ODN is impeded in its diffusionat the later time points.

While this study clarifies the behavior of PS-ODNs followingdirect controlled-rate intraparenchymal infusion, some limita-tions of the experiment should be noted. The infused region ofbrain was treated as a homogeneous medium even though it is acombination of gray matter, white matter and CSF-filled space.This assumption is significant because studies have shown thatinfusate flows faster along white matter tracts than through graymatter [56]. Furthermore, diffusion through a heterogeneousmedium will not produce a spherical distribution of PS-ODN, aspredicted by the model. It is interesting to note, however, that atmany time-points, the distribution of PS-ODN is roughly spher-ical [Fig. 1(c)–(f)]. The model we have employed also does notaccount for potential loss of material via vascular or CSF clear-ance, or for effects of binding, cellular uptake or degradation.We believe that clearance may well play a role in the lack ofconcordance of our results with those predicted by the model,and consider this to be an important direction for further experi-mental modeling, as others have done for different experimentalsystems [57]–[60]. The biology of modified ODNs is such thatbinding and cellular uptake are expected to be less important,but this assumption will require further experimental evalua-tion. Our previous results with this model indicate that degrada-tion of the ODN is minimal [22]. Furthermore, this study mightbear only limited relevance to the delivery of PS-ODNs to braintumor because tumor tissue differs from normal brain tissuein several respects. Theoretical and subsequent experimentalstudies indicate that tumors have elevated interstitial pressure[61], which could significantly affect the rate of transport bydiffusion. Also, it is believed that tumors are less dense thannormal brain tissue (i.e., the value ofis higher than that in


normal brain tissue), and direct infusion into the parenchymaof a tumor may open channels which facilitate fluid flow [36],[62]. Similarly, our current analysis has assumed thatremainsfixed throughout the period following infusion, an assumptionthat would be false if significant edema were to develop or sub-side during the time period. We would also note that a small butsignificant portion of the material is confined to the needle tractinitially, and this material then tends to clear. More complexmodels of the distribution of infused agents in the brain may alsoneed to account for this process. Thus, the current study is in-tended to be groundwork for more detailed studies to clarify thebehavior of PS-ODN infusion and diffusion through the CNS.

Reliable prediction of the flow pattern on the basis of an ad-equately validated model for it would have substantial clinicalvalue, and this is one of the principal goals that is sought inthe synthesis of treatment planning systems for infusion ther-apies. Noninvasive confirmation of the volume of distributionand of the spatial and temporal dosage characteristics of theinfusate would complete the information needed by the clini-cian to draw conclusions about the progress of the therapeuticprocess. For instance, the infusion into the brain of the PS-ODNcould then potentially be controlled such that the volume of dis-tribution was essentially limited to the target peritumoral tissuesin a post-resection zone of a brain tumor, thus optimizing thechances for successful inhibition of further proliferation of themalignant cells within that zone. Diffusion weighted imagingor other forms of functional magnetic resonance imaging willlikely play useful roles in establishing the boundaries of thevolume of distribution in interventional procedures of this type,as will real-time scintigraphy and related nuclear medicine tech-niques in those cases where radio-labeled species are infusedinto the patient. In this way, toxicity effects in the surroundinghealthy tissues might be minimized while an efficacious doseof the infusate is delivered in contoured volumes, where and asneeded.

The dynamics of infusion and subsequent diffusion in exper-imental in vivo settings are relatively unexplored. This lack ofexperimental activity is likely due to the fact that there has pre-viously been no accurate means of quantifying infusate concen-tration distributions throughout the 3-D structure of the brain.Section-derived 3-D analysis of diffusion following direct in-traparenchymal infusion yields several insights not availablethrough other less inclusive methods of analysis. By partitioningthe data volume into concentric spherical shells, we were ableto accurately characterize, in three dimensions, total infusionvolume, total moles of PS-ODN recovered, and average con-centration at a given distance from the site of infusion.

VI. CONCLUSION

Novel 3-D computational analysis of rat autoradiogramvolumes indicates that direct controlled-rate intraparenchymalinfusion represents a highly promising means of delivering

S-PS-ODN to localized volumes of brain. By comparingthese experimental data to a mathematical model of diffusionthrough a porous medium, distribution could be determinedas a function of time and radial distance from the cannula tip.This mathematical analysis also revealed that simple diffusion

fails to fully describe the distribution patterns created by mi-croinfusion. Because the rate of diffusion slows with increasingtime, these data conform to the results of other studies in whichODNs are subject to cellular uptake and/or protein binding.The use of a large volume of infusate relative to brain volumegenerates results that violate the requirements of sphericalsymmetry in a homogenous medium employed by the model.This approach is appropriate as an initial step toward modelingthe infusion process as would be required by a comprehensiveinfusion treatment planning system.

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Peter J. Haar is from Richmond, VA. He re-ceived the s B.Sc. degree in physics and cognitiveneurosciences from the University of Virginia,Charlottesville, in 1999. During his time as a studentthere, he also worked at Virginia CommonwealthUniversity’s Medical College of Virginia, in Rich-mond, VA, carrying out quantitative mathematicalanalyzes of the data fromin vivo infusion studies.He is presently a student in the M.D./Ph.D. degreeprogram at the Medical College of Virginia.

His research interests include the development ofinfusion and diffusion algorithms, computational techniques as applied to neu-rosurgical therapies, andin vivomodels of convection enhanced delivery of ther-apeutic agents within the brain.

John E. Stewart was born in Glens Falls, NY. Hereceived the B.S. and M.S. degrees in mechanical en-gineering from Old Dominion University, Norfolk,VA. In 2000, he received the M.D. and Ph.D. degreesin biomedical engineering from Virginia Common-wealth University’s Medical College of Virginia.

He worked at NASA’s Langley Research Centerin Hampton, VA, for three years as a member ofthe Geometry Laboratory. He currently serves as aHouse Officer at the Medical College of VirginiaHospitals, Richmond, VA in the Department of

Internal Medicine. In 2001, he will begin a residency in Diagnostic Radiologyat the Mayo Clinic, Rochester, MN. His research interests include AnatomicVisualization, implementation of internet-ready medical image and 3-Dvisualization systems and in computer-aided diagnosis.

George T. Gillies (S’78–M’79–SM’90) was bornin Rugby, ND. He received the B.Sc. degree inphysics from North Dakota State University, Fargo,in 1974. He received the M.Sc. and Ph.D. degrees inengineering physics from the University of Virginia,Charlottesville, in 1976 and 1980, respectively.

His experience includes positions as a Measure-ment Scientist with the International Bureau ofWeights and Measures in Paris, France, and workwith various industrial employers in the UnitedStates. He is presently a Research Professor of

Mechanical and Biomedical Engineering at the University of Virginia, anda Clinical Associate Professor of Neurosurgery at the Medical College ofVirginia, with research interests in medical physics, gravitational physics, androtating machinery.

Sujit S. Prabhu was born in Ahmadi, Kuwait. He re-ceived the M.D. degree from the Government Med-ical College, Bellary, India, in 1984 and thereafterbegan his training in General Surgery in England.

He joined the Neuro-oncology Group at theMedical College of Virginia in Richmond, VA,in 1993 and began a Residency in Neurosurgerythere in 1996. His research interests include thedevelopment of antisense oligonucleotide therapiesfor brain tumors, drug delivery via positive pressureinfusion, and the study of tumor cell movement

within the brainDr. Prabhu is a Fellow of the Royal College of Surgeons of Edinburgh.

William C. Broaddus is originally from Virginia.He received the B.A. degree in biochemistry fromCornell University, Ithaca, NY, in 1975. He receivedthe Ph.D. degree in pharmacology and the M.D. de-gree from Case Western University, Cleveland, OH,in 1982 and 1984, respectively.

He then joined the University of Virginia’sDepartment of Neurosurgery as a Resident in 1984and fulfilled a year of Chief Residency in 1991.His training included a year as senior Registrarof Neurological Surgery at Derriford Hospital,

Plymouth, U.K., in 1989. He went on to become the Hord Associate Professorof Neurosurgery at Virginia Commonwealth University’s Medical Collegeof Virginia, Richmond where his research interests include the developmentof gene-therapy techniques for the treatment of brain tumors, investigationsof spinal mechanics and dynamics, novel stereotactic surgery systems, andimage-guided intraoperative techniques.

quantitative three-dimensional analysis and diffusion modeling of oligonucleotide concentrations...

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