Margin determination

Abstract

A method for identifying target regions in a tissue for local drug delivery, where functional and/or structural anatomical data such as edema and/or resection cavity is captured by an imaging system, and where the anatomical data is evaluated by segmentation techniques such as region-growing-based methods with computer assistance to determine a margin around a resection cavity and/or the volume of edema, the margin and/or the volume of edema being the target tissue for local drug delivery.

Claims

1. A method of operating a medical planning and navigation system comprising an imaging device, a computer including a processor and a non-transient memory, and a human viewable display for planning an infusion of a fluid drug, the method comprising: using the processor of the computer, identifying one or more target regions in a tissue for local delivery of the fluid drug, said identifying comprising: i) obtaining, via the imaging system, at least one of functional anatomical image data, structural anatomical image data, or functional and structural anatomical image data corresponding to at least one of an edema, a resection cavity, or an edema and a resection cavity, wherein the at least one of the functional anatomical image data, the structural anatomical image data, or the functional and structural anatomical image data comprises at least one of magnetic resonance (MR) derived data, single photon emission computed tomography (SPECT) derived data, position emission tomography (PET) derived data, or ultrasound or computed tomography (CT) derived data, the at least one of the functional anatomical image data, the structural anatomical image data, or the functional and structural anatomical image data being evaluated by image processing techniques two-dimensionally with respect to distribution information contained in the at least one of the functional anatomical image data, the structural anatomical image data, or the functional and structural anatomical image data; and ii) using the processor of the computer, evaluating the at least one of the functional anatomical image data, the structural anatomical image data, or the functional and structural anatomical image data, said evaluating comprising using segmentation techniques to determine at least one of: a margin around the resection cavity, a volume of the edema, or a volume of the edema and a margin around the resection cavity, the determined at least one of the margin around the resection cavity, the volume of the edema, or the volume of the edema and the margin around the resection cavity being the identified one or more target regions for the local delivery of the fluid drug; using the processor of the computer, obtaining, from the at least one of the functional anatomical image data, the structural anatomical image data, or the functional and structural anatomical image data, a rate of change of a concentration of the fluid drug based on an anisotropic diffusion tensor of a molecule of the fluid drug; using the processor of the computer, computing a pressure profile along an associated delivery device used for the local delivery of the fluid drug, the pressure profile being computed based on a poroelastic model of backflow such that backflow of the fluid drug along an insertion track of the associated delivery device is minimized; and using the computed pressure profile as a boundary condition for obtaining by the processor of the computer a planned interstitial pressure of the fluid drug to be delivered to the one or more target regions of the tissue.

2. The method as set forth in claim 1, wherein the evaluating the at least one of the functional anatomical image data, the structural anatomical image data, or the functional and structural anatomical image data comprises: evaluating the at least one of the functional anatomical image data, the structural anatomical image data, or the functional and structural anatomical image data by one or more image processing techniques three-dimensionally with respect to distribution information contained in the at least one of the functional anatomical image data, the structural anatomical image data, or the functional and structural anatomical image data.

3. The method as set forth in claim 1, wherein the evaluating the at least one of the functional anatomical image data, the structural anatomical image data, or the functional and structural anatomical image data comprises: evaluating the at least one of the functional anatomical image data, the structural anatomical image data, or the functional and structural anatomical image data by one or more image processing techniques over a period of time with respect to distribution information contained in the at least one of the functional anatomical image data, the structural anatomical data, or the functional and structural anatomical image data; and making an adjustment in the distribution information to at least one of anatomical or structural conditions which have changed over the period of time.

4. The method as set forth in claim 1, further comprising determining a diffusion velocity of the fluid drug using Diffusion Weighted-derived Images in combination with the at least one of the MR derived data, the SPECT derived data, the PET derived data, or the Ultrasound or CT derived data.

5. The method as set forth in claim 1, further comprising determining the isotropy of flow directions in at least one of the one or more target regions or surrounding tissue by analyzing Diffusion Tensor data in combination with the at least one of the MR derived data, the SPECT derived data, the PET derived data, or the Ultrasound or CT derived data.

6. The method as set forth in claim 1, further comprising: calculating a distribution volume for the fluid drug by one or more segmentation techniques from the at least one of the functional anatomical image data, the structural anatomical image data.

7. The method as set forth in claim 1, further comprising determining the at least one of the functional anatomical image data, the structural anatomical image data, or the functional and structural anatomical image data three-dimensionally using one or more segmentation techniques.

8. The method according to claim 1, wherein the identifying the one or more target regions in the tissue comprises identifying one or more target regions of brain tissue, and the method further comprising planning a location for the infusion using medical navigation.

9. The method as set forth in claim 1, further comprising determining the at least one of the functional anatomical image data, the structural anatomical image data, or the functional and structural anatomical image data two-dimensionally by one or more segmentation techniques.

10. The method as set forth in claim 9, further comprising combining a number of two dimensional data sets on the at least one of the functional anatomical image data, the structural anatomical image data, or the functional and structural anatomical image data using one or more reconstruction techniques to obtain three-dimensional information.

11. The method according to claim 1, wherein the identifying the one or more target regions in the tissue comprises identifying one or more target regions of brain tissue, and the method further comprising planning an introduction of an infusion device at a selected point using stereotactic planning.

12. The method as set forth in claim 11, further comprising combining the at least one of the functional anatomical image data, the structural anatomical image data, or the functional and structural anatomical image data with information in an expected distribution of the fluid drug for planning at least one of infusion treatment or navigation.

13. The method according to claim 12, wherein the combining the information comprises overlaying at least one of: anatomical tissue data, functional tissue data, structural tissue data or functional and structural tissue data with an expected infusion distribution of the fluid drug.

14. A device for planning an infusion of a fluid drug, the device comprising: an imaging device configured to image associated tissue and capture at least one of functional anatomical image data, structural anatomical image data, or functional and anatomical image data; a computer configured to, based on the captured functional anatomical image data, the anatomical image data, or the functional and structural anatomical image data, perform at least one of: i) evaluate the at least one of the functional anatomical image data, the structural anatomical image data, or the functional and structural anatomical image data to identify in the associated tissue at least one of advantageous or non-advantageous infusion regions of a fluid drug, wherein the at least one of the functional anatomical image data, the structural anatomical image data, or the functional and anatomical image data comprises at least one of magnetic resonance (MR) derived data, single photon emission computed tomography (SPECT) derived data, position emission tomography (PET) derived data, or ultrasound or computed tomography (CT) derived data, the at least one of the functional anatomical image data, the structural anatomical image data, or the functional and anatomical image data being evaluated by image processing techniques two-dimensionally with respect to distribution information contained in the at least one of the functional anatomical image data, the structural anatomical image data, or the functional and anatomical image data, or ii) produce and evaluate a distribution simulation of the fluid drug, the distribution simulation simulating the fluid drug being introduced at particular points relative to the associated tissue; and a computer-assisted medical planning and navigation system for assisting in positioning an associated infusion device to deliver the fluid drug to one or more target regions, the medical planning and navigation system being configured to assist in the positioning by: identifying the one or more target regions in the associated tissue for local delivery of the fluid drug, said identifying comprising: i) obtaining from the imaging device the at least one of the functional anatomical image data, the structural anatomical image data, or the functional and anatomical image data corresponding to at least one of an edema, a resection cavity, or an edema and a resection cavity; and ii) evaluating the at least one of the functional anatomical image data, the structural anatomical image data, or the functional and anatomical image data corresponding to the at least one of the edema, the resection cavity, or the edema and resection cavity, said evaluating comprising using segmentation techniques to determine at least one of: a margin around the resection cavity, a volume of the edema, or a volume of the edema and a margin around the resection cavity, the at least one of the margin around the resection cavity, the volume of the edema, or the volume of the edema and the margin around the resection cavity being the one or more target regions for the local delivery of the fluid drug; obtaining, from the at least one of the functional anatomical image data, the structural anatomical image data, or the functional and anatomical image data, a rate of change of a concentration of the fluid drug based on an anisotropic diffusion tensor of a molecule of the fluid drug; computing a pressure profile along the associated infusion device used for the local delivery of the fluid drug, the pressure profile being computed based on a poroelastic model of backflow such that backflow of the fluid drug along an insertion track of the associated infusion device is minimized; and using the computed pressure profile as a boundary condition for obtaining a planned interstitial pressure of the fluid drug to be delivered to the one or more target regions of the tissue.

15. The device as set forth in claim 14, wherein the imaging device, the computer, and the medical planning and navigation system are operatively connected with each other via data connections for a constant retrievable exchange of data.

16. The method according to claim 1, wherein the using the one or more segmentation techniques comprises using one or more region-growing-based methods.

Description

FIGURE LEGENDS

(1) FIG. 1 is a schematic showing concentration profiles for pressure-driven and diffusion-driven deliveries. Compared with diffusion-driven delivery, the pressure-driven delivery results in a higher concentration extending farther from the delivery site.

(2) FIG. 2 is a diagram depicting a possible subdivision of the problem involved in CED. The distribution can be inferred from knowledge about influx, transport, and efflux parameters.

(3) FIG. 3a is a sketch illustrating an infusion catheter in tissue (not to scale). Orange elongated cells represent white matter tracts. The fluid infused from the catheter forms a small annulus around the outside of the catheter, the backflow. This cylinder is the source of the subsequent infusion, which preferentially follows the white matter tracts.

(4) FIG. 3b is a T.sub.1, -weighted MR image demonstrating the infusion of Gd-DTPA into a pig brain. The infusion pattern has an irregular shape, preferentially following the white matter tracts. The image was acquired at the end of the infusion.

(5) FIG. 3c is a T.sub.1 weighted MR image obtained 1 day after the infusion was finished, depicting the effects from the same infusion shown in panel b. The Gd-DTPA has diffused to distances far beyond the original volume shown in panel b.

(6) FIG. 4a is a schematic drawing depicting two infusion catheters in inhomogeneous tissue (not to scale). The backflow distances, represented by dark blue cylinders around the catheter tips, vary depending on the hydraulic conductivity of the adjacent tissue. The backflow length is extended in areas of low conductivity.

(7) FIG. 4b is an overlaid T.sub.2-weighted MR image demonstrating backflow distances (green areas) simulated for two different catheter trajectories (yellow lines). The simulated backflow distances vary significantly within a patient, depending on the chosen trajectory.

(8) FIG. 5 is a T.sub.1-weighted MR image demonstrating the planned catheter trajectory (bold green line). The thin lines around the planned trajectory represent guidelines designed to indicate the suitability of the trajectory in providing an infusion within the interstitial space.

(9) FIGS. 6a-6d are four T.sub.1-weighted three-dimensional spoiled gradient-recalled acquisition MR images showing the effects of an infusion of a Gd-DTPA and water solution (1:200). The slice thickness is 3 mm with no gap. The infusion catheter is visible in the first slice (a). The images reveal leakage and spread of the infused agent into the subarachnoid space.

(10) FIG. 7a is a T.sub.2-weighted MR image acquired before the start of an infusion with two catheters.

(11) FIG. 7b is a T.sub.2-weighted image of the same slice 96 hours into the infusion showing increased enhancement caused by the infused agent. The added volume leads to an elastic deformation of the brain, which is apparent by a slight mid-line shift and a shift of the resection cavity margins.

(12) FIG. 8a is a computed diffusion tensor MR image revealing a map of the trace of the hydraulic conductivity tensor. Bright areas indicate regions of high conductivity.

(13) FIG. 8b is an MR image demonstrating a map of the anisotropy of the hydraulic conductivity tensor. Bright areas indicate regions with high directionality (anisotropy) of the hydraulic conductivity.

(14) FIG. 9a is a schematic demonstrating the pressure differential between the extratumoral and the intratumoral interstitial pressures.

(15) FIG. 9b is a contrast-enhanced T.sub.1-weighted MR image showing a tumor in a dog brain. A catheter was placed through the tumor with the tip approximately 1 cm beyond the tumor mass, inside adjacent tissue.

(16) FIG. 9c is a T.sub.1-weighted MR image showing the same slice as that featured in panel b, with Gd-DTPA infused through the catheter. The image reveals that the fluid does not suffuse the tumor mass but rather distributes around one side of the catheter and the border of the tumor.

(17) FIG. 10 is a digital camera shot depicting infusion of blue dye from an eight-port ventricular catheter inserted into an agarose gel preparation. Flow originated only from the most proximal port, rendering the remaining ports useless for drug delivery.

(18) FIG. 11 is a photograph depicting the different types of catheters tested in the gel experiments. Scale on the left side of the image is 1 mm.

(19) FIG. 12a is a digital camera shot depicting the volume of distribution for Catheter 1 at 10 minutes into infusion.

(20) FIG. 12b is a digital camera shot depicting the volume of distribution for Catheter 1, 40 minutes into the infusion.

(21) FIG. 12c is a graph of a pressure profile over time (pressure scale in mm Hg), showing a regular, slightly ellipsoid distribution, which is achieved due to the short backflow distance in conjunction with maintaining the structural integrity of the surrounding gel. The gel trial does not reveal issues that would limit the usability of the catheter for CED.

(22) FIG. 13a is a digital camera shot depicting the volume of distribution for Catheter 2, 10 minutes into the infusion.

(23) FIG. 13b is a digital camera shot revealing the volume of distribution for Catheter 2 at 40 minutes into the infusion.

(24) FIG. 13c is a graph depicting a pressure profile over time (pressure scale in mm Hg), revealing a long backflow distance and a helical description of the gel structure, both indicating the limited suitability of this catheter for use in CED.

(25) FIG. 14 is a screenshot of the iPlan! flow application (version 2) showing the planned trajectories for five catheters and the results of simulated infusion from these positions.

(26) FIG. 15. A, Software dialogue box indicating a potentially poorly placed catheter trajectory at risk for failing to produce intraparenchymal distribution of the infusate. B, Volume of distribution (V.sub.d) outlines for Catheter 3 in Patient 105 showing volume match between the SPECT and simulation. The V.sub.d of .sup.123I-human serum albumin (HSA) measured by SPECT is shown in white. The orange area shows the area of overlap (V.sub.d match) between the simulation (SIM) and SPECT at the 50% isodose level. The green area shows the region where the SPECT Vd was larger than the simulation. The V.sub.d match between SPECT and simulation in this patient was 74%. C, Maximum in-plane deviation for Catheter 1 in Patient 106. The geometric distribution of .sup.123I-HSA at the 50% isodose level as measured by SPECT is shown in white and is overlaid with result from the simulation (blue line). The maximum in-plane deviation which in this patient is 6.3 mm.

(27) FIG. 16. T2-weight MR images showing catheter trajectory (green) in 3D reconstruction, two perpendicular cross sectional views, and an in-line view for Catheter 3 in Patient 108. The catheter crosses a sulcus 1.2 mm from its tip (yellow arrows).

(28) FIG. 17. T2-weighted MRI showing in-plane view of Catheter 1 in Patient 102. The catheter trajectory is shown in red. The image displays a thin linear hyperintensity (yellow arrows) corresponding to the trajectory of a previous catheter tract. The contour of the .sup.123I-HSA distribution from the red catheter is shown at the 50% isodose level (yellow line).

(29) FIG. 18. T1-weighted MR images in various planes and 3D reconstruction showing mock distribution simulation. The distribution of the infusate at an effective concentration of 20% of the infused concentration is shown (blue shading) for 5 catheters (trajectories shown in yellow). Note that even 5 catheters in this patient would fail to provide an infusion volume that adequately covers the 2 cm margin surrounding this inferior temporal lobe resection cavity. The various contours represent the infusion at discrete time points (from inside out, 6, 12, 48, and 96 hours).

(30) FIG. 19 is an FE mesh and boundary conditions used to model pressure-controlled infusion into tissue. The infusion cavity boundary conditions are applied at r=a (a.sub.0=0.18 mm). The other radius of the tissue boundary is sufficiently distant that pore pressure is assumed negligible (r=20a.sub.0).

(31) FIGS. 20a-20d are a validation analysis comparing transient FE and analytical solutions for infusion into tissue. FIG. 20a is a volume-averaged radial fluid velocity, ?.sub.r=?.sup.f?.sup.f, FIG. 20b illustrates pore pressure, ?; FIG. 20c illustrates radial displacement, ? and FIG. 20d illustrates dilation, e, with distance from the infusion cavity boundary. Model simulation parameters: E=10 kPa, ?=0.35, k.sub.0=1.0e-13 m.sup.4 N.sup.?1 s.sup.?1, and ?.sub.0=1 kPa with instantaneous loading.

(32) Reconstruction techniques follow the principle of stacking two-dimensional images on the top of each other to create a three-dimensional image. This is a common technique described among others in Linninger et al., Mimic Image Reconstruction for Computer-Assisted Brain Analysis, Mimic Innovation Awards 2005.

(33) Positron emission tomography (PET) is a nuclear medicine imaging technique which produces a three-dimensional image or map of functional processes in the body. The system detects pairs of gamma rays emitted indirectly by a positron-emitting radioisotope, which is introduced into the body on a metabolically active molecule. Images of metabolic activity in space are then reconstructed by computer analysis, often in modern scanners aided by results from a CT X-ray scan performed on the patient at the same time, in the same machine.

(34) Single photon emission computed tomography (SPECT) is a nuclear medicine tomographic imaging technique using gamma rays. It is very similar to conventional nuclear medicine planar imaging using a gamma camera. However, it is able to provide true 3D information. This information is typically presented as cross-sectional slices through the patient, but can be freely reformatted or manipulated as required.

(35) Darcy's law describes the flow of a fluid and is a simple proportional relationship between the instantaneous discharge rate through a porous medium, the viscosity of the fluid and the pressure drop over a given distance. Darcy's law is known since 1856.

(36) The segmentation techniques such has region-growing-based methods is described among others in EP 1 768 062 A1 which teaching is included in this application. An example for such segmentation technique is: Segmenting method comprises preparing a reference data set assigned to a body structure image data set, determining the total imaging function which maps the reference data set onto the body structure image data set and defining limited body structures using the mapped reference data set in the body structure data set. Preferred Features: The total mapping function portion is determined by the decomposition of the body structure into structural parts and their individual new arrangement in front of the other total mapping function portion.

(37) Further, the method to calculate the volume for an infusion fluid is described in Morrison papers, Linninger paper (Linninger et al., Mimic Image Reconstruction for Computer-Assisted Brain Analysis, Mimic Innovation Awards 2005), Chen paper (Annals of Biomedical Engineering, 2007) and Raghavan paper (Neurosurg, Focus 20, 2006). An example for such method is described in U.S. Pat. No. 6,549,803 and is summarized as follows:

(38) Movement of material in an organism, such as a drug injected into a brain, is modelled by a uniformly structured field of static constants governing transport by moving fluid and diffusion within the fluid. This supports planning of material introduction, (e.g., infusion, perfusion, retroperfusion, injections, etc.) to achieve a desired distribution of the material, continuing real-time feedback as to whether imaged material is moving as planned and will be distributed as desired, and real-time plan modification to improve results.

(39) A further example for such method is described below in Chen paper (Annals of Biomedical Engineering, 2007):

(40) Methods

(41) Mechanics Model

(42) A brief description of the biphasic theory used in the model is presented. For a more expanded description, the reader is referred to Mow et al. Nervous tissue was treated as a mixture, which includes a solid phase (label: s) and a fluid phase (label: f). Both solid and fluid phases were assumed to be incompressible with the solid matrix fully saturated with fluid. The fluid phase included the infusate which was assumed to have the same fluid properties as the interstitial fluid. Low solute concentrations were assumed, and the influence of the solute on fluid flow and tissue deformation was considered negligible. Also, osmotic effects were not considered.

(43) The constitutive equations for solid and fluid phases are
?.sup.r=??.sup.spI+?.sup.E(?.sup.E=?eI+2??)(1)
?.sup.f=??.sup.fpI(2)
where ?.sup.s and ?.sup.f are the Cauchy stress tensors of the solid and fluid phases; ?.sup.E is the contact stress from deformation of the solid matrix; ?.sup.s and ?.sup.f are the solid and fluid volume fractions (?.sup.s+?.sup.f=1); ? is the infinitesimal strain tensor of the solid matrix (?=?[?u+?u.sup.T] where u is the displacement vector); e is the dilatation e=Tr(?); ? and ? are the Lam? elastic constants of the solid matrix; p is the pore (interstitial) fluid pressure; and I is the identity tensor.

(44) Fluid flow is described by Darcy's law as
?k?p=v?v.sup.s(3)
where ?=?.sup.s?.sup.s+?.sup.fv.sup.f is the volume-averaged bulk velocity; ?.sup.s and ?.sup.f are the velocity vectors of solid and fluid phases; and k is the hydraulic permeability. Hydraulic permeability has been found to be deformation-dependent due to localized changes in porosity for soft tissues such as cartilage and hydrogels. For small deformation, Lai and Mow proposed an exponential relationship
k=k.sub.0exp(Me)(4)
where M is a material constant and k.sub.0 is the baseline hydraulic permeability at zero strain (no deformation). The spatially varying porosity, ?.sup.f, due to solid deformation is related to the initial porosity, ?.sup.f.sub.02, and the Jacobian, J=dV/dV.sub.0, by ?.sup.f=1?(1??.sup.f.sub.0)/J. For small deformation J=1+e, and the porosity is calculated by

(45) $\begin{array}{cc}{?}^f=\frac{e+{?}_0^f}{1+e}.& \left(5\right)\end{array}$

(46) The conservation of mass for tissue is given by
?.Math.v=q.sup.f(6)
where q.sup.f is the source term for the fluid phase. We assumed no fluid source term for the fluid phase. Absorption of fluid by capillaries was assumed to be negligible, and there are no lymphatics in nervous tissue. In addition, although there exists slow cerebro-spinal fluid (CSF) circulation within the brain, which arises out of the continuous bulk flow of CSF from the choroids plexus formation sites to the arachnoid villi absorptions sites, this bulk flow was considered negligible compared with induced flow due to infusion. Taking divergence on both sides of Eq. (3) and applying Eq. (6) results in

(47) $\begin{array}{cc}?.Math.\left(k?p\right)=\frac{?e}{?t}+q^f& \left(7\right)\end{array}$
where q.sup.f=??(?p/?t) in the FE formulation (see below). Neglecting inertia and body force terms, the balance of momentum for the solid-fluid mixture requires
?.Math.(?.sup.s+?.sup.f)=?.Math.(?pI+?.sup.E)=0(8)
The nature of the coupled solid-fluid interaction can be further illustrated by rewriting Eq. (8) using e=?u and taking divergence on both sides
(?+2?)?.sup.2e=?.sup.2p(9)
Assuming initial conditions, p(x, t)=e(x, t)=0 at t=0, results in
p=H.sub.A.Math.e(H.sub.A=?+2?)(10)
and Eq. (7) can be written as

(48) $\begin{array}{cc}?.Math.\left(\stackrel{\_}{k}{H}_A?e\right)=\frac{?e}{?t}\left(\stackrel{\_}{k}=\frac{k}{1+?H_A}\right)& \left(11\right)\end{array}$
which is similar in form to equations of heat conduction or diffusion. The FE formulation assumed ?=constant, even though no fluid source term was assumed. Hydraulic permeability of the tissue, k, was related to input hydraulic permeability, k, using Eq. (11).
Solute Transport Model

(49) Mass conservation for the solute in tissue is given by

(50) $\begin{array}{cc}\frac{?M_{c}c}{?t}+?.Math.\left(M_c{\mathrm{cv}}^c\right)=q^c& \left(12\right)\end{array}$
where c is the solute concentration in mole per unit volume of the whole mixture; M.sub.c is the molecular weight of the solute; ?.sup.c is the velocity of solute; and q.sup.c is the source term for the solute. We consider solute transport that is confined to the fluid and solute phases only (extracellular). Transport behavior is described by Fick's law
c(v.sup.c?v)=?D.sub.eff.Math.?c(13)
where D.sub.eff is the effective diffusion tensor of the solute in the porous media.

(51) $\stackrel{\_}{v}=\frac{1}{p}\underset{?=f,c}{\overset{}{.Math.}}{p}^{?}{v}^{?}$
is the density-averaged velocity of the fluid and solute mixture, ?.sup.? is the apparent density of constituent ?, and p=?.sub.?=f,cp.sup.?. We assumed the solute concentration was too low to influence the density of the mixture and the velocity of the fluid. Thus, ? can be approximated by ?.sup.f. In addition, the solid matrix-solute interaction will hinder the convection transport, which is corrected by including a retardation coefficient, ?. Thus, ?=? ?.sup.f. Substituting Eq. (13) into Eq. (12) results in the relation

(52) $\begin{array}{cc}\frac{?c}{?t}+?.Math.\left(c?v^f-D_{\mathrm{eff}}.Math.?c\right)=\frac{q^c}{M_c}& \left(14\right)\end{array}$

(53) Volumetric extravasation, absorption, and degradation of the tracer solute were assumed negligible (q.sup.c=0) during direct infusion. In addition, ? and D.sub.eff are affected by the porosity which changes with tissue deformation. In this study, unless otherwise mentioned, ?=1, and D.sub.eff was assumed to be independent of tissue deformation. Changes in diffusional transport may be small compared to the overall distribution if interstitial transport is dominated by convection.

(54) Numerical Implementation

(55) The computational model was developed using the FE software package ADINA (version 8.2.2, ADINA R&D Inc., Watertown, Mass.) along with user-defined subroutines and a custom C++ program. Three modules were used to solve for solid deformation, fluid flow, and solute transport equations (denoted by ADINA-S, ADINA-T, and ADINA-F, respectively). The coupled solid deformation and fluid flow equations (Eqs. 7 and 8 expressed in terms of u and p) were solved using ADINA-S and ADINA-T modules simultaneously. The Newton-Raphson iteration method was used to solve FE-discretized equations, and an Euler-backward integration scheme was used for the transient solutions. u and p solutions were obtained at each time point. Note that solutions were obtained assuming ?=constant and related to the case ?=0 using the hydraulic permeability relation defined by Eq. (11).

(56) The quasi-static biphasic solution was incorporated in the solute transport problem (Eq. 14) using the ADINA-F module. The biphasic-solute transport solution interface was achieved using a custom C++ program which: (1) calculated the nodal dilatation, porosity, and fluid velocity at each time step; and (2) created and compiled the model for solute transport computation using the fluid velocity field at that time step. Nodal deformation velocity was calculated by dividing the displacement difference between two neighboring time steps with the time step, ?.sub.1.sup.s=(u.sub.t?u.sub.t-?t)/?t. ?.sup.f was calculated using the relations ?=?.sup.s?.sup.s+?.sup.f?.sup.f and Eq (5). Since fluid velocity was output at the integration point, nodal fluid velocity was then approximated by averaging the fluid velocities at the surrounding integration points.

(57) Tissue Infusion Model

(58) We considered solute infusion into gray matter which was idealized as a homogeneous, isotropic, biphasic media with no fluid source or sink regions and negligible endogenous interstitial fluid flow. A symmetric, spherical geometry was modeled and the infusion site was a spherical cavity with radius, ?. The initial radius of the infusion cavity corresponded to the external diameter of a 28-gauge cannula, ?.sub.0=0.18 mm. The outer radius was 20 ?.sub.0=3.6 mm. Previous infusion analyses show that pore pressure, displacement, and fluid velocity change negligibly at radial positions more than 20?.sub.0 away. A FE mesh was created using 4-node tetrahedral elements (?42,000 elements) with finer meshing in the region close to the infusion site (FIG. 19). Zero initial pore pressure, strain, and fluid flow were assumed.

(59) Pressure within the infusion cavity was assumed uniform, and a ramp-hold pressure was applied at the spherical boundary. Solid, fluid, and solute transport boundary conditions were applied separately. Previous studies by Kenyon and Hou et al. used a zero contact stress (?.sup.E=0) applied to the solid phase at the interface between fluid and porous media. Since the stress calculated in the solid module of ADINA-S was the total stress for the bulk material (?.sup.s+?.sup.f), the infusion pressure was applied at the porous media-fluid interface at r=?, i.e., the infusion cavity surface, which moves during infusion. Also, a constant solute concentration boundary condition was applied on this surface. Zero pore pressure and free displacement were applied along the outer tissue boundary. Symmetric boundary conditions were applied to symmetry faces (zero displacement, flow flux, and mass flux normal to the surface). Infusion parameters were varied, and sensitivity to changes in infusion pressure, ?.sub.0, over the range 1-10 kPa (7.5-75 mmHg), was determined. Infusion pressure is likely on the lower end of this range based on experiments of Prabhu et al., who observed a range of infusion pressures in the rat caudate of 1.6?4.2 kPa (12-32 mmHg) for infusion rates varying between 0.17 and 1.5 ?L/min (25-gauge needle). The lower pressure value is also in the vicinity of the consolidated tissue pressure (?2.4 kPa) measured after an hour of infusion at 0.5 ?L/min into the white matter of the corona radiata of cats. The time to reach constant pressure, I.sub.0 to, was considered of short duration.

(60) The influence of material parameters on pressure-induced tissue swelling and solute transport was considered. In addition, biphasic and solute transport solutions were compared with rigid model solutions. Table 4 lists the range of parameters used in this study. The value of Young's modulus of the solid matrix was set to range from 1 to 10 kPa. This range corresponds well with modulus values estimated for small strains tested under low strain rate conditions by Miller and Chinzei, E?1 kPa The range of Poisson ratio has been previously estimated by Mostachfi et al. to range between 0.3 and 0.4, based on literature values and the compliant behavior of brain tissues.

(61) Very few experimental studies have attempted to measure the hydraulic permeability of nervous tissue. The baseline hydraulic permeability for the gray matter was chosen between 1.0e-13 and 1.0e-12 m.sup.4N.sup.?1 s.sup.?1. This range was established from the spread of dye through the brain following cold-induced edema by Reulen et al. and the estimated ranges of previous poroelastic brain models. A deformation-dependent hydraulic permeability was also considered and we used the exponential relation by Lai and Mow. The value for the material constant M was varied between 0 and 5 based on a previous range established for cartilage and hydrogels. Porosity was varied between 0.2 and 0.3. The lower range of porosity corresponds to measures by radiotracer methods and iontophoretic measurements of tetramethyl-ammonium (TMA.sup.+) in non-infused tissues. The lower porosity values also match the volume ratio, V.sub.infusion/V.sub.distribution, of CED striatum distribution studies of .sup.14C-albumin by Chen et al. The upper porosity range is characteristic of values reported elsewhere for edematous states, which occur after prolonged infusion or local damage to tissue. Diffusivity of the solute in gray matter was set to correspond to the macromolecular tracer albumin, MW-66 kDa. The apparent diffusion coefficient of fluorescently labeled bovine serum albumin has been measured by Tao and Nicholson in rat cortical slices using an integrative optical imaging system, D.sub.eff=1.6e-11 m.sup.2/s.

(62) TABLE-US-00004 TABLE 4 Material parameter ranges of gray matter brain tissue used in simulation studies. Parameter Range Young's modulus, E 1-10 kPa Poisson ratio, v 0.3-0.4 Baseline hydraulic permeability, k.sub.0 10.sup.?13-10.sup.?12 m.sup.4N.sup.?1s.sup.?1 Nonlinear parameter, M 0-5 Porosity, ?.sup. 0.2-0.3 Diffusivity (albumin), D.sub.eff 1.6 ? 10.sup.?11 m.sup.2/s

(63) The FE biphasic solution was validated by comparing with previous analytical solutions by Basser for infusion into an infinite biphasic media with constant hydraulic permeability. Solutions for pore pressure and fluid velocity following a step change in pressure infusion (t.sub.0=0) were compared (Rather than instantaneously applied pressure, simulations ramp infusion pressure rapidly with a ramp time 0.02 s). FIG. 20 illustrates a validation analysis comparing transient FE and analytical solutions for infusion into tissue. FIG. 20a is a volume-averaged radial fluid velocity, ?.sub.r=?.sup.f?.sup.f, FIG. 20b illustrates pore pressure, ?; FIG. 20c illustrates radial displacement, ? and FIG. 20d illustrates dilation, e, with distance from the infusion cavity boundary. Model simulation parameters: E=10 kPa, ?=0.35, k.sub.0=1.0e-13 m N.sup.?1 s.sup.?1, and ?.sub.0=1 kPa with instantaneous loading. Also, an analytical solution of displacement was solved and compared to the FE solution.