Modeling Concentration Distribution and Deformation During Convection-Enhanced Drug Delivery into Brain Tissue

Image-guided patient-specific optimization of catheter placement for convection-enhanced nanoparticle delivery in recurrent glioblastoma

BACKGROUND

Proper catheter placement for convection-enhanced delivery (CED) is required to maximize tumor coverage and minimize exposure to healthy tissue. We developed an image-based model to patient-specifically optimize the catheter placement for rhenium-186 (186Re)-nanoliposomes (RNL) delivery to treat recurrent glioblastoma (rGBM).

METHODS

The model consists of the 1) fluid fields generated via catheter infusion, 2) dynamic transport of RNL, and 3) transforming RNL concentration to the SPECT signal. Patient-specific tissue geometries were assigned from pre-delivery MRIs. Model parameters were personalized with either 1) individual-based calibration with longitudinal SPECT images, or 2) population-based assignment via leave-one-out cross-validation. The concordance correlation coefficient (CCC) was used to quantify the agreement between the predicted and measured SPECT signals. The model was then used to simulate RNL distributions from a range of catheter placements, resulting in a ratio of the cumulative RNL dose outside versus inside the tumor, the "off-target ratio" (OTR). Optimal catheter placement) was identified by minimizing OTR.

RESULTS

Fifteen patients with rGBM from a Phase I/II clinical trial (NCT01906385) were recruited to the study. Our model, with either individual-calibrated or population-assigned parameters, achieved high accuracy (CCC > 0.80) for predicting RNL distributions up to 24 h after delivery. The optimal catheter placements identified using this model achieved a median (range) of 34.56 % (14.70 %-61.12 %) reduction on OTR at the 24 h post-delivery in comparison to the original placements.

CONCLUSIONS

Our image-guided model achieved high accuracy for predicting patient-specific RNL distributions and indicates value for optimizing catheter placement for CED of radiolabeled liposomes.

A Comprehensive Review on Modeling Aspects of Infusion-Based Drug Delivery in the Brain

Brain disorders represent an ever-increasing health challenge worldwide. While conventional drug therapies are less effective due to the presence of the blood-brain barrier, infusion-based methods of drug delivery to the brain represent a promising option. Since these methods are mechanically controlled and involve multiple physical phases ranging from the neural and molecular scales to the brain scale, highly efficient and precise delivery procedures can significantly benefit from a comprehensive understanding of drug-brain and device-brain interactions. Behind these interactions are principles of biophysics and biomechanics that can be described and captured using mathematical models. Although biomechanics and biophysics have received considerable attention, a comprehensive mechanistic model for modeling infusion-based drug delivery in the brain has yet to be developed. Therefore, this article reviews the state-of-the-art mechanistic studies that can support the development of next-generation models for infusion-based brain drug delivery from the perspective of fluid mechanics, solid mechanics, and mathematical modeling. The supporting techniques and database are also summarized to provide further insights. Finally, the challenges are highlighted and perspectives on future research directions are provided. STATEMENT OF SIGNIFICANCE: Despite the immense potential of infusion-based drug delivery methods for bypassing the blood-brain barrier and efficiently delivering drugs to the brain, achieving optimal drug distribution remains a significant challenge. This is primarily due to our limited understanding of the complex interactions between drugs and the brain that are governed by principles of biophysics and biomechanics, and can be described using mathematical models. This article provides a comprehensive review of state-of-the-art mechanistic studies that can help to unravel the mechanism of drug transport in the brain across the scales, which underpins the development of next-generation models for infusion-based brain drug delivery. More broadly, this review will serve as a starting point for developing more effective treatments for brain diseases and mechanistic models that can be used to study other soft tissue and biomaterials.

Image-based predictive modelling frameworks for personalised drug delivery in cancer therapy

Personalised drug delivery enables a tailored treatment plan for each patient compared to conventional drug delivery, where a generic strategy is commonly employed. It can not only achieve precise treatment to improve effectiveness but also reduce the risk of adverse effects to improve patients' quality of life. Drug delivery involves multiple interconnected physiological and physicochemical processes, which span a wide range of time and length scales. How to consider the impact of individual differences on these processes becomes critical. Multiphysics models are an open system that allows well-controlled studies on the individual and combined effects of influencing factors on drug delivery outcomes while accommodating the patient-specific in vivo environment, which is not economically feasible through experimental means. Extensive modelling frameworks have been developed to reveal the underlying mechanisms of drug delivery and optimise effective delivery plans. This review provides an overview of currently available models, their integration with advanced medical imaging modalities, and code packages for personalised drug delivery. The potential to incorporate new technologies (i.e., machine learning) in this field is also addressed for development.

Modeling of brain efflux: Constraints of brain surfaces

Fluid efflux from the brain plays an important role in solute waste clearance. Current experimental approaches provide little spatial information, and data collection is limited due to short duration or low frequency of sampling. One approach shows tracer efflux to be independent of molecular size, indicating bulk flow, yet also decelerating like simple membrane diffusion. In an apparent contradiction to this report, other studies point to tracer efflux acceleration. We here develop a one-dimensional advection-diffusion model to gain insight into brain efflux principles. The model is characterized by nine physiological constants and three efflux parameters for which we quantify prior uncertainty. Using Bayes' rule and the two efflux studies, we validate the model and calculate data-informed parameter distributions. The apparent contradictions in the efflux studies are resolved by brain surface boundaries being bottlenecks for efflux. To critically test the model, a custom MRI efflux assay measuring solute dispersion in tissue and release to cerebrospinal fluid was employed. The model passed the test with tissue bulk flow velocities in the range 60 to 190 [Formula: see text]m/h. Dimensional analysis identified three principal determinants of efflux, highlighting brain surfaces as a restricting factor for metabolite solute clearance.

Electroosmotic Perfusion, External Microdialysis: Simulation and Experiment

Information about the rates of hydrolysis of neuropeptides by extracellular peptidases can lead to a quantitative understanding of how the steady-state and transient concentrations of neuropeptides are controlled. We have created a small microfluidic device that electroosmotically infuses peptides into, through, and out of the tissue to a microdialysis probe outside the head. The device is created by two-photon polymerization (Nanoscribe). Inferring quantitative estimates of a rate process from the change in concentration of a substrate that has passed through tissue is challenging for two reasons. One is that diffusion is significant, so there is a distribution of peptide substrate residence times in the tissue. This affects the product yield. The other is that there are multiple paths taken by the substrate as it passes through tissue, so there is a distribution of residence times and thus reaction times. Simulation of the process is essential. The simulations presented here imply that a range of first order rate constants of more than 3 orders of magnitude is measurable and that 5-10 min is required to reach a steady state value of product concentration following initiation of substrate infusion. Experiments using a peptidase-resistant d-amino acid pentapeptide, yaGfl, agree with simulations.

Multiphysics modeling and simulation of local transport and absorption kinetics of intramuscularly injected lipids nanoparticles

Recent clinical applications of mRNA vaccines highlight the critical role of drug delivery, especially when using lipid nanoparticles (LNPs) as the carrier for genetic payloads. However, kinetic and transport mechanisms for locally injected LNPs, such as lymphatic or cellular uptake and drug release, remain poorly understood. Herein, we developed a bottom-up multiphysics computational model to simulate the injection and absorption processes of LNPs in muscular tissues. Our purpose was to seek underlying connections between formulation attributes and local exposure kinetics of LNPs and the delivered drug. We were also interested in modeling the absorption kinetics from the local injection site to the systemic circulation. In our model, the tissue was treated as the homogeneous, poroelastic medium in which vascular and lymphatic vessel densities are considered. Tissue deformation and interstitial fluid flow (modeled using Darcy's Law) were also implemented. Transport of LNPs was described based on diffusion and advection; local disintegration and cellular uptake were also integrated. Sensitivity analyses of LNP and drug properties and tissue attributes were conducted using the simulation model. It was found that intrinsic tissue porosity and lymphatic vessel density affect the local transport kinetics; diffusivity, lymphatic permeability, and intracellular update kinetics also play critical roles. Simulated results were commensurate with experimental observations. This study could shed light on the development of LNP formulations and enable further development of whole-body pharmacokinetic models.

Estimates of the permeability of extra-cellular pathways through the astrocyte endfoot sheath

BACKGROUND

Astrocyte endfoot processes are believed to cover all micro-vessels in the brain cortex and may play a significant role in fluid and substance transport into and out of the brain parenchyma. Detailed fluid mechanical models of diffusive and advective transport in the brain are promising tools to investigate theories of transport.

METHODS

We derive theoretical estimates of astrocyte endfoot sheath permeability for advective and diffusive transport and its variation in microvascular networks from mouse brain cortex. The networks are based on recently published experimental data and generated endfoot patterns are based on Voronoi tessellations of the perivascular surface. We estimate corrections for projection errors in previously published data.

RESULTS

We provide structural-functional relationships between vessel radius and resistance that can be directly used in flow and transport simulations. We estimate endfoot sheath filtration coefficients in the range [Formula: see text] to [Formula: see text], diffusion membrane coefficients for small solutes in the range [Formula: see text] to [Formula: see text], and gap area fractions in the range 0.2-0.6%, based on a inter-endfoot gap width of 20 nm.

CONCLUSIONS

The astrocyte endfoot sheath surrounding microvessels forms a secondary barrier to extra-cellular transport, separating the extra-cellular space of the parenchyma and the perivascular space outside the endothelial layer. The filtration and membrane diffusion coefficients of the endfoot sheath are estimated to be an order of magnitude lower than those of the extra-cellular matrix while being two orders of magnitude higher than those of the vessel wall.

Multi-compartmental model of glymphatic clearance of solutes in brain tissue

The glymphatic system is the subject of numerous pieces of research in biology. Mathematical modelling plays a considerable role in this field since it can indicate the possible physical effects of this system and validate the biologists' hypotheses. The available mathematical models that describe the system at the scale of the brain (i.e. the macroscopic scale) are often solely based on the diffusion equation and do not consider the fine structures formed by the perivascular spaces. We therefore propose a mathematical model representing the time and space evolution of a mixture flowing through multiple compartments of the brain. We adopt a macroscopic point of view in which the compartments are all present at any point in space. The equations system is composed of two coupled equations for each compartment: One equation for the pressure of a fluid and one for the mass concentration of a solute. The fluid and solute can move from one compartment to another according to certain membrane conditions modelled by transfer functions. We propose to apply this new modelling framework to the clearance of 14C-inulin from the rat brain.

A 1D-0D-3D coupled model for simulating blood flow and transport processes in breast tissue

In this work, we present mixed dimensional models for simulating blood flow and transport processes in breast tissue and the vascular tree supplying it. These processes are considered, to start from the aortic inlet to the capillaries and tissue of the breast. Large variations in biophysical properties and flow conditions exist in this system necessitating the use of different flow models for different geometries and flow regimes. In total, we consider four different model types. First, a system of 1D nonlinear hyperbolic partial differential equations (PDEs) is considered to simulate blood flow in larger arteries with highly elastic vessel walls. Second, we assign 1D linearized hyperbolic PDEs to model the smaller arteries with stiffer vessel walls. The third model type consists of ODE systems (0D models). It is used to model the arterioles and peripheral circulation. Finally, homogenized 3D porous media models are considered to simulate flow and transport in capillaries and tissue within the breast volume. Sink terms are used to account for the influence of the venous and lymphatic systems. Combining the four model types, we obtain two different 1D-0D-3D coupled models for simulating blood flow and transport processes: The first model results in a fully coupled 1D-0D-3D model covering the complete path from the aorta to the breast combining a generic arterial network with a patient specific breast network and geometry. The second model is a reduced one based on the separation of the generic and patient specific parts. The information from a calibrated fully coupled model is used as inflow condition for the patient specific sub-model allowing a significant computational cost reduction. Several numerical experiments are conducted to calibrate the generic model parameters and to demonstrate realistic flow simulations compared to existing data on blood flow in the human breast and vascular system. Moreover, we use two different breast vasculature and tissue data sets to illustrate the robustness of our reduced sub-model approach.

Convection-Enhanced Delivery In Silico Study for Brain Cancer Treatment

Brain cancer therapy remains a formidable challenge in oncology. Convection-enhanced delivery (CED) is an innovative and promising local drug delivery method for the treatment of brain cancer, overcoming the challenges of the systemic delivery of drugs to the brain. To improve our understanding about CED efficacy and drug transport, we present an in silico methodology for brain cancer CED treatment simulation. To achieve this, a three-dimensional finite element formulation is utilized which employs a brain model representation from clinical imaging data and is used to predict the drug deposition in CED regimes. The model encompasses biofluid dynamics and the transport of drugs in the brain parenchyma. Drug distribution is studied under various patho-physiological conditions of the tumor, in terms of tumor vessel wall pore size and tumor tissue hydraulic conductivity as well as for drugs of various sizes, spanning from small molecules to nanoparticles. Through a parametric study, our contribution reports the impact of the size of the vascular wall pores and that of the therapeutic agent on drug distribution during and after CED. The in silico findings provide useful insights of the spatio-temporal distribution and average drug concentration in the tumor towards an effective treatment of brain cancer.

Understanding Formulation and Temperature Effects on Dermal Transport Kinetics by IVPT and Multiphysics Simulation

PURPOSE

It is often unclear how complex topical product formulation factors influence the transport kinetics through skin tissue layers, because of multiple confounding attributes. Environmental factors such as temperature effect are also poorly understood. In vitro permeation testing (IVPT) is frequently used to evaluate drug absorption across skin, but the flux results from these studies are from a combination of mechanistic processes.

METHOD

Two different commercially available formulations of oxybenzone-containing sunscreen cream and continuous spray were evaluated by IVPT in human skin. Temperature influence between typical skin surface temperature (32°C) and an elevated 37°C was also assessed. Furthermore, a multiphysics-based simulation model was developed and utilized to compute the flux of modeled formulations.

RESULTS

Drug transport kinetics differed significantly between the two drug products. Flux was greatly influenced by the environmental temperature. The multiphysical simulation results could reproduce the experimental observations. The computation further indicated that the drug diffusion coefficient plays a dominant role in drug transport kinetics, influenced by the water content which is also affected by temperature.

CONCLUSION

The in vitro testing and bottom-up simulation shed insight into the mechanism of dermal absorption kinetics from dissimilar topical products.

Role of Tissue Hydraulic Permeability in Convection-Enhanced Delivery of Nanoparticle-Encapsulated Chemotherapy Drugs to Brain Tumour

PURPOSE

Tissue hydraulic permeability of brain tumours can vary considerably depending on the tissue microstructure, compositions in interstitium and tumour cells. Its effects on drug transport and accumulation remain poorly understood.

METHODS

Mathematical modelling is applied to predict the drug delivery outcomes in tumours with different tissue permeability upon convection-enhanced delivery. The modelling is based on a 3-D realistic tumour model that is extracted from patient magnetic resonance images.

RESULTS

Modelling results show that infusing drugs into a permeable tumour can facilitate a more favourable hydraulic environment for drug transport. The infused drugs will exhibit a relatively uniform distribution and cover a larger tumour volume for effective cell killing. Cross-comparisons show the delivery outcomes are more sensitive to the changes in tissue hydraulic permeability and blood pressure than the fluid flow from the brain ventricle. Quantitative analyses demonstrate that increasing the fluid gain from both the blood and brain ventricle can further improve the interstitial fluid flow, and thereby enhance the delivery outcomes. Furthermore, similar responses to the changes in tissue hydraulic permeability can be found for different types of drugs.

CONCLUSIONS

Tissue hydraulic permeability as an intrinsic property can influence drug accumulation and distribution. Results from this study can deepen the understanding of the interplays between drug and tissues that are involved in the drug delivery processes in chemotherapy.

Insights into Infusion-Based Targeted Drug Delivery in the Brain: Perspectives, Challenges and Opportunities

Targeted drug delivery in the brain is instrumental in the treatment of lethal brain diseases, such as glioblastoma multiforme, the most aggressive primary central nervous system tumour in adults. Infusion-based drug delivery techniques, which directly administer to the tissue for local treatment, as in convection-enhanced delivery (CED), provide an important opportunity; however, poor understanding of the pressure-driven drug transport mechanisms in the brain has hindered its ultimate success in clinical applications. In this review, we focus on the biomechanical and biochemical aspects of infusion-based targeted drug delivery in the brain and look into the underlying molecular level mechanisms. We discuss recent advances and challenges in the complementary field of medical robotics and its use in targeted drug delivery in the brain. A critical overview of current research in these areas and their clinical implications is provided. This review delivers new ideas and perspectives for further studies of targeted drug delivery in the brain.

On the microstructural origin of brain white matter hydraulic permeability

Brain microstructure plays a key role in driving the transport of drug molecules directly administered to the brain tissue, as in Convection-Enhanced Delivery procedures. The proposed research analyzes the hydraulic permeability of two white matter (WM) areas (corpus callosum and fornix) whose three-dimensional microstructure was reconstructed starting from the acquisition of electron microscopy images. We cut the two volumes with 20 equally spaced planes distributed along two perpendicular directions, and, on each plane, we computed the corresponding permeability vector. Then, we considered that the WM structure is mainly composed of elongated and parallel axons, and, using a principal component analysis, we defined two principal directions, parallel and perpendicular, with respect to the axons' main direction. The latter were used to define a reference frame onto which the permeability vectors were projected to finally obtain the permeability along the parallel and perpendicular directions. The results show a statistically significant difference between parallel and perpendicular permeability, with a ratio of about two in both the WM structures analyzed, thus demonstrating their anisotropic behavior. Moreover, we find a significant difference between permeability in corpus callosum and fornix, which suggests that the WM heterogeneity should also be considered when modeling drug transport in the brain. Our findings, which demonstrate and quantify the anisotropic and heterogeneous character of the WM, represent a fundamental contribution not only for drug-delivery modeling, but also for shedding light on the interstitial transport mechanisms in the extracellular space.

Patient specific, imaging-informed modeling of rhenium-186 nanoliposome delivery via convection-enhanced delivery in glioblastoma multiforme

Convection-enhanced delivery of rhenium-186 (¹⁸⁶Re)-nanoliposomes is a promising approach to provide precise delivery of large localized doses of radiation for patients with recurrent glioblastoma multiforme. Current approaches for treatment planning utilizing convection-enhanced delivery are designed for small molecule drugs and not for larger particles such as¹⁸⁶Re-nanoliposomes. To enable the treatment planning for¹⁸⁶Re-nanoliposomes delivery, we have developed a computational fluid dynamics approach to predict the distribution of nanoliposomes for individual patients. In this work, we construct, calibrate, and validate a family of computational fluid dynamics models to predict the spatio-temporal distribution of¹⁸⁶Re-nanoliposomes within the brain, utilizing patient-specific pre-operative magnetic resonance imaging (MRI) to assign material properties for an advection-diffusion transport model. The model family is calibrated to single photon emission computed tomography (SPECT) images acquired during and after the infusion of¹⁸⁶Re-nanoliposomes for five patients enrolled in a Phase I/II trial (NCT Number NCT01906385), and is validated using a leave-one-out bootstrapping methodology for predicting the final distribution of the particles. After calibration, our models are capable of predicting the mid-delivery and final spatial distribution of¹⁸⁶Re-nanoliposomes with a Dice value of 0.69 ± 0.18 and a concordance correlation coefficient of 0.88 ± 0.12 (mean ± 95% confidence interval), using only the patient-specific, pre-operative MRI data, and calibrated model parameters from prior patients. These results demonstrate a proof-of-concept for a patient-specific modeling framework, which predicts the spatial distribution of nanoparticles. Further development of this approach could enable optimizing catheter placement for future studies employing convection-enhanced delivery.

Convection-Enhanced Delivery and Principles of Extracellular Transport in the Brain

Stereotactic neurosurgery involves a targeted intervention based on congruence of image guidance to a reference fiducial system. This discipline has widespread applications in radiosurgery, tumor therapy, drug delivery, functional lesioning, and neuromodulation. In this article, we focused on convection-enhanced delivery to deliver therapeutic agents to the brain addressing areas of research and clinical development. We performed a robust literature review of all relevant articles highlighting current efforts and challenges of making this delivery technique more widely understood. We further described key biophysical properties of molecular transport in the extracellular space that may impact the efficacy and control of drug delivery using stereotactic methods. Understanding these principles is critical for further refinement of predictive models that can inform advances in stereotactic techniques for convection-enhanced delivery of therapeutic agents to the brain.

Multiphysics Modeling and Simulation of Subcutaneous Injection and Absorption of Biotherapeutics: Model Development

PURPOSE

Many monoclonal antibodies (mAbs) are administered via subcutaneous (SC) injection. Local transport and absorption kinetics and mechanisms, however, remain poorly understood. A multiphysics computational model was developed to simulate the injection and absorption processes of a protein solution in the SC tissue.

METHODS

Quantitative relationships among tissue properties and transport behaviors of an injected solution were described by respective physical laws. SC tissue was treated as a 3-dimensional homogenous, poroelastic medium, in which vasculatures and lymphatic vessels were implicitly treated. Tissue deformation was considered, and interstitial fluid flow was modeled by Darcy's law. Transport of the drug mass was described based on diffusion and advection, which was integrated with tissue mechanics and interstitial fluid dynamics.

RESULTS

Injection and absorption of albumin and IgG solutions were simulated. Upon injection, a sharp rise in tissue pressure, porosity, and fluid velocity could be observed at the injection tip. Largest tissue deformation appeared at the model surface. Transport of drug mass out of the injection zone was minimal. Absorption by local lymphatics was found to last several weeks.

CONCLUSIONS

A bottom-up method was developed to simulate drug transport and absorption of protein solutions in skin tissue base on physical principles. The results appear to match experimental observations.

Infusion Mechanisms in Brain White Matter and Their Dependence on Microstructure: An Experimental Study of Hydraulic Permeability

OBJECTIVE

Hydraulic permeability is a topic of deep interest in biological materials because of its important role in a range of drug delivery-based therapies. The strong dependence of permeability on the geometry and topology of pore structure and the lack of detailed knowledge of these parameters in the case of brain tissue makes the study more challenging. Although theoretical models have been developed for hydraulic permeability, there is limited consensus on the validity of existing experimental evidence to complement these models. In the present study, we measure the permeability of white matter (WM) of fresh ovine brain tissue considering the localised heterogeneities in the medium using an infusion-based experimental set up, iPerfusion. We measure the flow across different parts of the WM in response to applied pressures for a sample of specific dimensions and calculate the permeability from directly measured parameters. Furthermore, we directly probe the effect of anisotropy of the tissue on permeability by considering the directionality of tissue on the obtained values. Additionally, we investigate whether WM hydraulic permeability changes with post-mortem time. To our knowledge, this is the first report of experimental measurements of the localised WM permeability, also demonstrating the effect of axon directionality on permeability. This work provides a significant contribution to the successful development of intra-tumoural infusion-based technologies, such as convection-enhanced delivery (CED), which are based on the delivery of drugs directly by injection under positive pressure into the brain.

Integrating Diffusion Tensor Imaging and Neurite Orientation Dispersion and Density Imaging to Improve the Predictive Capabilities of CED Models

This paper aims to develop a comprehensive and subject-specific model to predict the drug reach in Convection-Enhanced Delivery (CED) interventions. To this end, we make use of an advance diffusion imaging technique, namely the Neurite Orientation Dispersion and Density Imaging (NODDI), to incorporate a more precise description of the brain microstructure into predictive computational models. The NODDI dataset is used to obtain a voxel-based quantification of the extracellular space volume fraction that we relate to the white matter (WM) permeability. Since the WM can be considered as a transversally isotropic porous medium, two equations, respectively for permeability parallel and perpendicular to the axons, are derived from a numerical analysis on a simplified geometrical model that reproduces flow through fibre bundles. This is followed by the simulation of the injection of a drug in a WM area of the brain and direct comparison of the outcomes of our results with a state-of-the-art model, which uses conventional diffusion tensor imaging. We demonstrate the relevance of the work by showing the impact of our newly derived permeability tensor on the predicted drug distribution, which differs significantly from the alternative model in terms of distribution shape, concentration profile and infusion linear penetration length.

On the poro-elastic models for microvascular blood flow resistance: An in vitro validation

Nowadays, adequate and accurate representation of the microvascular flow resistance constitutes one of the major challenges in computational haemodynamic studies. In this work, a theoretical, porous media framework, ultimately designed for representing downstream resistance, is presented and compared against an in vitro experimental results. The resistor consists of a poro-elastic tube, with either a constant or variable porosity profile in space. The underlying physics, characterizing the fluid flow through the porous media, is analysed by considering flow variables at different network locations. Backward reflections, originated in the reservoir of the in vitro model, are accounted for through a reflection coefficient imposed as an outflow network condition. The simulation results are in good agreement with the measurements for both the homogenous and heterogeneous porosity conditions. In addition, the comparison allows identification of the range of values representing experimental reservoir reflection coefficients. The pressure drops across the heterogeneous porous media increases with respect to the simpler configuration, whilst flow remains almost unchanged. The effect of some fluid network features, such as tube Young's modulus and fluid viscosity, on the theoretical results is also elucidated, providing a reference for the invitro and insilico simulation of different microvascular conditions.

Tumor ablation due to inhomogeneous anisotropic diffusion in generic three-dimensional topologies

In recent decades computer-aided technologies have become prevalent in medicine, however, cancer drugs are often only tested on in vitro cell lines from biopsies. We derive a full three-dimensional model of inhomogeneous -anisotropic diffusion in a tumor region coupled to a binary population model, which simulates in vivo scenarios faster than traditional cell-line tests. The diffusion tensors are acquired using diffusion tensor magnetic resonance imaging from a patient diagnosed with glioblastoma multiform. Then we numerically simulate the full model with finite element methods and produce drug concentration heat maps, apoptosis hotspots, and dose-response curves. Finally, predictions are made about optimal injection locations and volumes, which are presented in a form that can be employed by doctors and oncologists.

A 3D-1D coupled blood flow and oxygen transport model to generate microvascular networks

In this work, we introduce an algorithmic approach to generate microvascular networks starting from larger vessels that can be reconstructed without noticeable segmentation errors. Contrary to larger vessels, the reconstruction of fine-scale components of microvascular networks shows significant segmentation errors, and an accurate mapping is time and cost intense. Thus there is a need for fast and reliable reconstruction algorithms yielding surrogate networks having similar stochastic properties as the original ones. The microvascular networks are constructed in a marching way by adding vessels to the outlets of the vascular tree from the previous step. To optimise the structure of the vascular trees, we use Murray's law to determine the radii of the vessels and bifurcation angles. In each step, we compute the local gradient of the partial pressure of oxygen and adapt the orientation of the new vessels to this gradient. At the same time, we use the partial pressure of oxygen to check whether the considered tissue block is supplied sufficiently with oxygen. Computing the partial pressure of oxygen, we use a 3D-1D coupled model for blood flow and oxygen transport. To decrease the complexity of a fully coupled 3D model, we reduce the blood vessel network to a 1D graph structure and use a bi-directional coupling with the tissue which is described by a 3D homogeneous porous medium. The resulting surrogate networks are analysed with respect to morphological and physiological aspects.

Electrokinetic Convection-Enhanced Delivery of Solutes to the Brain

Pressure-induced infusion of solutions into brain tissue is used both in research and in medicine. In medicine, convection enhanced delivery (CED) may be used to deliver agents to localized areas of the brain, such as with gene therapy to functional targets or with deep tumors not readily amenable to resection. However, clinical trials have demonstrated mixed results from CED. CED is limited by a lack of control of the infusion flow path and may cause damage or even neurological deficits due to neuronal distortion. In laboratory research, infusions may be achieved using pressure or using brief bursts of electrical current in iontophoresis. Electrokinetic convection enhanced delivery (ECED) has the potential to deliver drugs and other bioactive substances to local regions in the brain with improved control and lower applied pressures than pressure-based CED. ECED improves control over the infusion profile because the fluid follows the electrical current path and thus can be directed. Both small molecules and macromolecules can be delivered. Here we demonstrate proof-of-principal that electrokinetic (electroosmosis and electrophoresis) convection-enhanced delivery is a viable means for delivering solutes to the brain. We assessed the volume of tissue exposed to the infusates tris(2,2'-bipyridine)ruthenium(II) and fluorescent dextrans. Control of the direction of the transport was also achieved over distances ranging from several hundred micrometers to more than 4 mm. Electrokinetic delivery has the potential to improve control over infusions.

Apparent diffusion coefficient estimates based on 24 hours tracer movement support glymphatic transport in human cerebral cortex

The recently proposed glymphatic system suggests that bulk flow is important for clearing waste from the brain, and as such may underlie the development of e.g. Alzheimer’s disease. The glymphatic hypothesis is still controversial and several biomechanical modeling studies at the micro-level have questioned the system and its assumptions. In contrast, at the macro-level, there are many experimental findings in support of bulk flow. Here, we will investigate to what extent the CSF tracer distributions seen in novel magnetic resonance imaging (MRI) investigations over hours and days are suggestive of bulk flow as an additional component to diffusion. In order to include the complex geometry of the brain, the heterogeneous CSF flow around the brain, and the transport over the time-scale of days, we employed the methods of partial differential constrained optimization to identify the apparent diffusion coefficient (ADC) that would correspond best to the MRI findings. We found that the computed ADC in the cortical grey matter was 5–26% larger than the ADC estimated with DTI, which suggests that diffusion may not be the only mechanism governing transport.

Effect of tissue permeability and drug diffusion anisotropy on convection-enhanced delivery

Although convection-enhanced delivery (CED) can successfully facilitate a bypass of the blood brain barrier, its treatment efficacy remains highly limited in clinic. This can be partially attributed to the brain anisotropic characteristics that lead to the difficulties in controlling the drug spatial distribution. Here, the responses of six different drugs to the tissue anisotropy are examined through a parametric study performed using a multiphysics model, which considers interstitial fluid flow, tissue deformation and interlinked drug transport processes in CED. The delivery outcomes are evaluated in terms of the penetration depth and delivery volume for effective therapy. Simulation results demonstrate that the effective penetration depth in a given direction can be improved with the increase of the corresponding component of anisotropic characteristics. The anisotropic tissue permeability could only reshape the drug distribution in space but has limited contribution to the total effective delivery volume. On the other hand, drugs respond in different ways to the anisotropic diffusivity. The large delivery volumes of fluorouracil, carmustine, cisplatin and doxorubicin could be achieved in relatively isotropic tissue, while paclitaxel and methotrexate are able to cover enlarged regions into anisotropic tissues. Results obtained from this study serve as a guide for the design of CED treatments.

A poro-hyper-viscoelastic rate-dependent constitutive modeling for the analysis of brain tissues

In this paper, the dynamic behavior of bovine brain tissue, measured from in-vitro unconfined compression tests, is examined and represented through a viscoelastic biphasic model. The experiments have been carried out under three compression speeds of 10, 100, and 1000 mm/s. The results exhibited significant rate-dependent behavior. The brain tissue is modeled as a biphasic continuum consisting of a compressible solid matrix, fully saturated with an incompressible interstitial fluid. The governing equations based on conservation of mass and momentum are used to describe the solid-fluid interactions. An inverse scheme is employed in which a finite element model runs iteratively to optimize constitutive constants. The obtained material parameters of the proposed biphasic model show relatively good agreement (R² ≥ 0.96) with the experimental tissue mechanical responses at different rates. The model can successfully capture the key aspects of the rate-dependency for both solid and fluid phases under large strain deformation. This poro-hyper viscoelastic model can effectively estimate the global and local rate-dependent tissue deformations, the spatial variations in pore spaces, hydrostatic pressure as well as fluid diffusion through the tissue.

A computational fluid dynamics approach to determine white matter permeability

Glioblastomas represent a challenging problem with an extremely poor survival rate. Since these tumour cells have a highly invasive character, an effective surgical resection as well as chemotherapy and radiotherapy is very difficult. Convection-enhanced delivery (CED), a technique that consists in the injection of a therapeutic agent directly into the parenchyma, has shown encouraging results. Its efficacy depends on the ability to predict, in the pre-operative phase, the distribution of the drug inside the tumour. This paper proposes a method to compute a fundamental parameter for CED modelling outcomes, the hydraulic permeability, in three brain structures. Therefore, a bidimensional brain-like structure was built out of the main geometrical features of the white matter: axon diameter distribution extrapolated from electron microscopy images, extracellular space (ECS) volume fraction and ECS width. The axons were randomly allocated inside a defined border, and the ECS volume fraction as well as the ECS width maintained in a physiological range. To achieve this result, an outward packing method coupled with a disc shrinking technique was implemented. The fluid flow through the axons was computed by solving Navier-Stokes equations within the computational fluid dynamics solver ANSYS. From the fluid and pressure fields, an homogenisation technique allowed establishing the optimal representative volume element (RVE) size. The hydraulic permeability computed on the RVE was found in good agreement with experimental data from the literature.

A thermoporoelastic model for fluid transport in tumour tissues

In this paper, the effect of coupled thermal dilation and stress on interstitial fluid transport in tumour tissues is evaluated. The tumour is modelled as a spherical deformable poroelastic medium embedded with interstitial fluid, while the transvascular fluid flow is modelled as a uniform distribution of fluid sink and source points. A hyperbolic-decay radial function is used to model the heat source generation along with a rapid decay of tumour blood flow. Governing equations for displacement, fluid flow and temperature are first scaled and then solved with a finite-element scheme. Results are compared with analytical solutions from the literature, while results are presented for different scaling parameters to analyse the various physical phenomena. Results show that temperature affects pressure and velocity fields through the deformable medium. Finally, simulations are performed by assuming that the heat source is periodic, in order to assess the extent to which this condition affects the velocity field. It is reported that in some cases, especially for periodic heating, the combination of thermoelastic and poroelastic deformation led to no monotonic pressure distribution, which can be interesting for applications such as macromolecule drug delivery, in which the advective contribution is very important owing to the low diffusivity.

The need for mathematical modelling of spatial drug distribution within the brain

The blood brain barrier (BBB) is the main barrier that separates the blood from the brain. Because of the BBB, the drug concentration-time profile in the brain may be substantially different from that in the blood. Within the brain, the drug is subject to distributional and elimination processes: diffusion, bulk flow of the brain extracellular fluid (ECF), extra-intracellular exchange, bulk flow of the cerebrospinal fluid (CSF), binding and metabolism. Drug effects are driven by the concentration of a drug at the site of its target and by drug-target interactions. Therefore, a quantitative understanding is needed of the distribution of a drug within the brain in order to predict its effect. Mathematical models can help in the understanding of drug distribution within the brain. The aim of this review is to provide a comprehensive overview of system-specific and drug-specific properties that affect the local distribution of drugs in the brain and of currently existing mathematical models that describe local drug distribution within the brain. Furthermore, we provide an overview on which processes have been addressed in these models and which have not. Altogether, we conclude that there is a need for a more comprehensive and integrated model that fills the current gaps in predicting the local drug distribution within the brain.

Computational modelling of drug delivery to solid tumour: Understanding the interplay between chemotherapeutics and biological system for optimised delivery systems

Drug delivery to solid tumour involves multiple physiological, biochemical and biophysical processes taking place across a wide range of length and time scales. The therapeutic efficacy of anticancer drugs is influenced by the complex interplays among the intrinsic properties of tumours, biophysical aspects of drug transport and cellular uptake. Mathematical and computational modelling allows for a well-controlled study on the individual and combined effects of a wide range of parameters on drug transport and therapeutic efficacy, which would not be possible or economically viable through experimental means. A wide spectrum of mathematical models has been developed for the simulation of drug transport and delivery in solid tumours, including PK/PD-based compartmental models, microscopic and macroscopic transport models, and molecular dynamics drug loading and release models. These models have been used as a tool to identify the limiting factors and for optimal design of efficient drug delivery systems. This article gives an overview of the currently available computational models for drug transport in solid tumours, together with their applications to novel drug delivery systems, such as nanoparticle-mediated drug delivery and convection-enhanced delivery.

Numerical Modeling of Electroosmotic Push-Pull Perfusion and Assessment of Its Application to Quantitative Determination of Enzymatic Activity in the Extracellular Space of Mammalian Tissue

Many sampling methods have been developed to measure the extracellular concentrations of solutes in the extracellular space of mammalian tissue, e.g., brain. However, few have been used to quantitatively study the various processes, such as enzymatic degradation, that determines the fate of these solutes. For a method to be useful in this pursuit, it must be able to (1) perfuse tissue and collect the perfusate for quantitative analysis of the solutes introduced and reaction products produced, (2) control the average residence time of the active solutes, and (3) have the appropriate spatial resolution for the process of interest. Our lab previously developed a perfusion technique based on electroosmosis (EO), called EO push-pull perfusion (EOPPP), that is in principle suitable to meet these needs. However, much like the case for other sampling methods that came before, there are parameters that are needed for quantitative interpretation of data but that cannot be measured easily (or at all). In this paper, we present a robust finite element model that provides a deep understanding of fluid dynamics and mass transport in the EOPPP method, assesses the general applicability of EOPPP to studying enzyme activity in the ECS, and grants a simple approach to data treatment and interpretation to obtain, for example, Vmax and Km for an enzymatic reaction in the extracellular space of the tissue. This model is a valuable tool in optimizing and planning experiments without the need for costly experiments.

Mathematical Modelling of Convection Enhanced Delivery of Carmustine and Paclitaxel for Brain Tumour Therapy

PURPOSE

Convection enhanced delivery (CED) is a promising method of anticancer treatment to bypass the blood-brain barrier. This paper is aimed to study drug transport under different CED operating conditions.

METHODS

The convection enhanced delivery of chemotherapeutics to an intact and a remnant brain tumour after resection is investigated by means of mathematical modelling of the key physical and physiological processes of drug transport. Realistic models of brain tumour and its holding tissue are reconstructed from magnetic resonance images. Mathematical modelling is performed for the delivery of carmustine and paclitaxel with different infusion rates, solution concentrations and locations of infusion site.

RESULTS

Modelling predications show that drug penetration can be improved by raising the infusion rate and the infusion solution concentration. The delivery of carmustine with CED is highly localised. High drug concentration only can be achieved around the infusion site. The transport of paclitaxel is more sensitive to CED-enhanced interstitial fluid as compared to carmustine, with deeper penetration into tumour interior. Infusing paclitaxel in the upstream of interstitial fluid flow leads to high spatial averaged concentration and relatively uniform distribution.

CONCLUSION

Results obtained in this study can be used to guide the design and optimisation of CED treatment regimens.

Voxelized Model of Brain Infusion That Accounts for Small Feature Fissures: Comparison With Magnetic Resonance Tracer Studies

Convection enhanced delivery (CED) is a promising novel technology to treat neural diseases, as it can transport macromolecular therapeutic agents greater distances through tissue by direct infusion. To minimize off-target delivery, our group has developed 3D computational transport models to predict infusion flow fields and tracer distributions based on magnetic resonance (MR) diffusion tensor imaging data sets. To improve the accuracy of our voxelized models, generalized anisotropy (GA), a scalar measure of a higher order diffusion tensor obtained from high angular resolution diffusion imaging (HARDI) was used to improve tissue segmentation within complex tissue regions of the hippocampus by capturing small feature fissures. Simulations were conducted to reveal the effect of these fissures and cerebrospinal fluid (CSF) boundaries on CED tracer diversion and mistargeting. Sensitivity analysis was also conducted to determine the effect of dorsal and ventral hippocampal infusion sites and tissue transport properties on drug delivery. Predicted CED tissue concentrations from this model are then compared with experimentally measured MR concentration profiles. This allowed for more quantitative comparison between model predictions and MR measurement. Simulations were able to capture infusate diversion into fissures and other CSF spaces which is a major source of CED mistargeting. Such knowledge is important for proper surgical planning.

Augmenting Surgery via Multi-scale Modeling and Translational Systems Biology in the Era of Precision Medicine: A Multidisciplinary Perspective

In this era of tremendous technological capabilities and increased focus on improving clinical outcomes, decreasing costs, and increasing precision, there is a need for a more quantitative approach to the field of surgery. Multiscale computational modeling has the potential to bridge the gap to the emerging paradigms of Precision Medicine and Translational Systems Biology, in which quantitative metrics and data guide patient care through improved stratification, diagnosis, and therapy. Achievements by multiple groups have demonstrated the potential for (1) multiscale computational modeling, at a biological level, of diseases treated with surgery and the surgical procedure process at the level of the individual and the population; along with (2) patient-specific, computationally-enabled surgical planning, delivery, and guidance and robotically-augmented manipulation. In this perspective article, we discuss these concepts, and cite emerging examples from the fields of trauma, wound healing, and cardiac surgery.

An analytical model for nanoparticles concentration resulting from infusion into poroelastic brain tissue

We consider the infusion of a diluted suspension of nanoparticles (NPs) into poroelastic brain tissue, in view of relevant biomedical applications such as intratumoral thermotherapy. Indeed, the high impact of the related pathologies motivates the development of advanced therapeutic approaches, whose design also benefits from theoretical models. This study provides an analytical expression for the time-dependent NPs concentration during the infusion into poroelastic brain tissue, which also accounts for particle binding onto cells (by recalling relevant results from the colloid filtration theory). Our model is computationally inexpensive and, compared to fully numerical approaches, permits to explicitly elucidate the role of the involved physical aspects (tissue poroelasticity, infusion parameters, NPs physico-chemical properties, NP-tissue interactions underlying binding). We also present illustrative results based on parameters taken from the literature, by considering clinically relevant ranges for the infusion parameters. Moreover, we thoroughly assess the model working assumptions besides discussing its limitations. While not laying any claims of generality, our model can be used to support the development of more ambitious numerical approaches, towards the preliminary design of novel therapies based on NPs infusion into brain tissue.

Computational Modeling for Enhancing Soft Tissue Image Guided Surgery: An Application in Neurosurgery

With the recent advances in computing, the opportunities to translate computational models to more integrated roles in patient treatment are expanding at an exciting rate. One area of considerable development has been directed towards correcting soft tissue deformation within image guided neurosurgery applications. This review captures the efforts that have been undertaken towards enhancing neuronavigation by the integration of soft tissue biomechanical models, imaging and sensing technologies, and algorithmic developments. In addition, the review speaks to the evolving role of modeling frameworks within surgery and concludes with some future directions beyond neurosurgical applications.

Poro-elastic modeling of Syringomyelia - a systematic study of the effects of pia mater, central canal, median fissure, white and gray matter on pressure wave propagation and fluid movement within the cervical spinal cord

Syringomyelia, fluid-filled cavities within the spinal cord, occurs frequently in association with a Chiari I malformation and produces some of its most severe neurological symptoms. The exact mechanism causing syringomyelia remains unknown. Since syringomyelia occurs frequently in association with obstructed cerebrospinal fluid (CSF) flow, it has been hypothesized that syrinx formation is mechanically driven. In this study we model the spinal cord tissue either as a poro-elastic medium or as a solid linear elastic medium, and simulate the propagation of pressure waves through an anatomically plausible 3D geometry, with boundary conditions based on in vivo CSF pressure measurements. Then various anatomic and tissue properties are modified, resulting in a total of 11 variations of the model that are compared. The results show that an open segment of the central canal and a stiff pia (relative to the cord) both increase the radial pressure gradients and enhance interstitial fluid flow in the central canal. The anterior median fissure, anisotropic permeability of the white matter, and Poisson ratio play minor roles.

Mathematical model of the effect of ischemia-reperfusion on brain capillary collapse and tissue swelling

Restoration of an adequate cerebral blood supply after an ischemic attack is a primary clinical goal. However, the blood-brain barrier may break down after a prolonged ischemia causing the fluid in the blood plasma to filtrate and accumulate into the cerebral tissue interstitial space. Accumulation of this filtration fluid causes the cerebral tissue to swell, a condition known as vasogenic oedema. Tissue swelling causes the cerebral microvessels to be compressed, which may further obstruct the blood flow into the tissue, thus leading to the no-reflow phenomenon or a secondary ischemic stroke. The actual mechanism of this however is still not fully understood. A new model is developed here to study the effect of reperfusion on the formation of vasogenic oedema and cerebral microvessel collapse. The formation of vasogenic oedema is modelled using the capillary filtration equation while vessel collapse is modelled using the tube law of microvessel. Tissue swelling is quantified in terms of displacement, which is modelled using poroelastic theory. The results show that there is an increase in tissue displacement and interstitial pressure after reperfusion. In addition, the results also show that vessel collapse can occur at high value of reperfusion pressure, low blood osmotic pressure, high cerebral capillary permeability and low cerebral capillary stiffness. This model provides insight on the formation of ischemia-reperfusion injury by tissue swelling and vessel collapse.

Mechanics of the brain: perspectives, challenges, and opportunities

The human brain is the continuous subject of extensive investigation aimed at understanding its behavior and function. Despite a clear evidence that mechanical factors play an important role in regulating brain activity, current research efforts focus mainly on the biochemical or electrophysiological activity of the brain. Here, we show that classical mechanical concepts including deformations, stretch, strain, strain rate, pressure, and stress play a crucial role in modulating both brain form and brain function. This opinion piece synthesizes expertise in applied mathematics, solid and fluid mechanics, biomechanics, experimentation, material sciences, neuropathology, and neurosurgery to address today’s open questions at the forefront of neuromechanics. We critically review the current literature and discuss challenges related to neurodevelopment, cerebral edema, lissencephaly, polymicrogyria, hydrocephaly, craniectomy, spinal cord injury, tumor growth, traumatic brain injury, and shaken baby syndrome. The multi-disciplinary analysis of these various phenomena and pathologies presents new opportunities and suggests that mechanical modeling is a central tool to bridge the scales by synthesizing information from the molecular via the cellular and tissue all the way to the organ level.

Electroosmotic perfusion of tissue: sampling the extracellular space and quantitative assessment of membrane-bound enzyme activity in organotypic hippocampal slice cultures

This review covers recent advances in sampling fluid from the extracellular space of brain tissue by electroosmosis (EO). Two techniques, EO sampling with a single fused-silica capillary and EO push-pull perfusion, have been developed. These tools were used to investigate the function of membrane-bound enzymes with outward-facing active sites, or ectoenzymes, in modulating the activity of the neuropeptides leu-enkephalin and galanin in organotypic-hippocampal-slice cultures (OHSCs). In addition, the approach was used to determine the endogenous concentration of a thiol, cysteamine, in OHSCs. We have also investigated the degradation of coenzyme A in the extracellular space. The approach provides information on ectoenzyme activity, including Michaelis constants, in tissue, which, as far as we are aware, has not been done before. On the basis of computational evidence, EO push-pull perfusion can distinguish ectoenzyme activity with a ~100 μm spatial resolution, which is important for studies of enzyme kinetics in adjacent regions of the rat hippocampus.

Multi-component modelling of human brain tissue: a contribution to the constitutive and computational description of deformation, flow and diffusion processes with application to the invasive drug-delivery problem

Human brain tissue is complex and multi-component in nature. It consists of an anisotropic hyperelastic solid material composed of tissue cells and blood vessel walls. Brain tissue is permeated by two viscous pore liquids, the interstitial fluid and the blood. Both liquids are mobile within the tissue and exhibit a significant anisotropic perfusion behaviour. To model this complex aggregate, the well-founded Theory of Porous Media, a continuum-mechanical approach for the description of multi-component aggregates, is used. To include microscopic information, the model is enhanced by tissue characteristics obtained from medical imaging techniques. Moreover, the model is applied to invasive drug-delivery strategies, i.e. the direct extra-vascular infusion of therapeutic agents. For this purpose, the overall interstitial fluid is treated as a real two-component mixture of a liquid solvent and a dissolved therapeutic solute. Finally, the continuum-mechanical model results in a set of strongly coupled partial differential equations which are spatially discretised using mixed finite elements and solved in a monolithic manner with an implicit Euler time-integration scheme. Numerical examples demonstrate the applicability of the presented model.

Voxelized computational model for convection-enhanced delivery in the rat ventral hippocampus: comparison with in vivo MR experimental studies

Convection-enhanced delivery (CED) is a promising local delivery technique for overcoming the blood-brain barrier (BBB) and treating diseases of the central nervous system (CNS). For CED, therapeutics are infused directly into brain tissue and the drug agent is spread through the extracellular space, considered to be highly tortuous porous media. In this study, 3D computational models developed using magnetic resonance (MR) diffusion tensor imaging data sets were used to predict CED transport in the rat ventral hippocampus using a voxelized modeling previously developed by our group. Predicted albumin tracer distributions were compared with MR-measured distributions from in vivo CED in the ventral hippocampus up to 10 μL of Gd-DTPA albumin tracer infusion. Predicted and measured tissue distribution volumes and distribution patterns after 5 and 10 μL infusions were found to be comparable. Tracers were found to occupy the underlying landmark structures with preferential transport found in regions with less fluid resistance such as the molecular layer of the dentate gyrus. Also, tracer spread was bounded by high fluid resistance layers such as the granular cell layer and pyramidal cell layer of dentate gyrus. Leakage of tracers into adjacent CSF spaces was observed towards the end of infusions.