Voxelized model of interstitial transport in the rat spinal cord following direct infusion into white matter

A Spatial Interpolation Approach to Assign Magnetic Resonance Imaging-Derived Material Properties for Finite Element Models of Adeno-Associated Virus Infusion Into a Recurrent Brain Tumor

Adeno-associated virus (AAV) is a clinically useful gene delivery vehicle for treating neurological diseases. To deliver AAV to focal targets, direct infusion into brain tissue by convection-enhanced delivery (CED) is often needed due to AAV's limited penetration across the blood-brain-barrier and its low diffusivity in tissue. In this study, computational models that predict the spatial distribution of AAV in brain tissue during CED were developed to guide future placement of infusion catheters in recurrent brain tumors following primary tumor resection. The brain was modeled as a porous medium, and material property fields that account for magnetic resonance imaging (MRI)-derived anatomical regions were interpolated and directly assigned to an unstructured finite element mesh. By eliminating the need to mesh complex surfaces between fluid regions and tissue, mesh preparation was expedited, increasing the model's clinical feasibility. The infusion model predicted preferential fluid diversion into open fluid regions such as the ventricles and subarachnoid space (SAS). Additionally, a sensitivity analysis of AAV delivery demonstrated that improved AAV distribution in the tumor was achieved at higher tumor hydraulic conductivity or lower tumor porosity. Depending on the tumor infusion site, the AAV distribution covered 3.67-70.25% of the tumor volume (using a 10% AAV concentration threshold), demonstrating the model's potential to inform the selection of infusion sites for maximal tumor coverage.

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.

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.

Voxelized simulation of cerebral oxygen perfusion elucidates hypoxia in aged mouse cortex

Departures of normal blood flow and metabolite distribution from the cerebral microvasculature into neuronal tissue have been implicated with age-related neurodegeneration. Mathematical models informed by spatially and temporally distributed neuroimage data are becoming instrumental for reconstructing a coherent picture of normal and pathological oxygen delivery throughout the brain. Unfortunately, current mathematical models of cerebral blood flow and oxygen exchange become excessively large in size. They further suffer from boundary effects due to incomplete or physiologically inaccurate computational domains, numerical instabilities due to enormous length scale differences, and convergence problems associated with condition number deterioration at fine mesh resolutions. Our proposed simple finite volume discretization scheme for blood and oxygen microperfusion simulations does not require expensive mesh generation leading to the critical benefit that it drastically reduces matrix size and bandwidth of the coupled oxygen transfer problem. The compact problem formulation yields rapid and stable convergence. Moreover, boundary effects can effectively be suppressed by generating very large replica of the cortical microcirculation in silico using an image-based cerebrovascular network synthesis algorithm, so that boundaries of the perfusion simulations are far removed from the regions of interest. Massive simulations over sizeable portions of the cortex with feature resolution down to the micron scale become tractable with even modest computer resources. The feasibility and accuracy of the novel method is demonstrated and validated with in vivo oxygen perfusion data in cohorts of young and aged mice. Our oxygen exchange simulations quantify steep gradients near penetrating blood vessels and point towards pathological changes that might cause neurodegeneration in aged brains. This research aims to explain mechanistic interactions between anatomical structures and how they might change in diseases or with age. Rigorous quantification of age-related changes is of significant interest because it might aide in the search for imaging biomarkers for dementia and Alzheimer’s disease.

Brain function critically depends on the maintenance of physiological blood supply and metabolism in the cortex. Disturbances to adequate perfusion have been linked to age-related neurodegeneration. However, the precise correlation between age-related hemodynamic changes and the resulting decline in oxygen delivery is not well understood and has not been quantified. Therefore, we introduce a new compact, and therefore highly scalable, computational method for predicting the physiological relationship between hemodynamics and cortical oxygen perfusion for large sections of the cortical microcirculation. We demonstrate the novel mesh generation-free (MGF), multi-scale simulation approach through realistic in vivo case studies of cortical microperfusion in the mouse brain. We further validate mechanistic correlations and a quantitative relationship between blood flow and brain oxygenation using experimental data from cohorts of young, middle aged and old mouse brains. Our computational approach overcomes size and performance limitations of previous unstructured meshing techniques to enable the prediction of oxygen tension with a spatial resolution of least two orders of magnitude higher than previously possible. Our simulation results support the hypothesis that structural changes in the microvasculature induce hypoxic pockets in the aged brain that are absent in the healthy, young mouse.

Convection-Enhanced Delivery: Connection to and Impact of Interstitial Fluid Flow

Convection-enhanced delivery (CED) is a method used to increase transport of therapeutics in and around brain tumors. CED works through locally applying a pressure differential to drive fluid flow throughout the tumor, such that convective forces dominate over diffusive transport. This allows therapies to bypass the blood brain barrier that would otherwise be too large or solely rely on passive diffusion. However, this also drives fluid flow out through the tumor bulk into surrounding brain parenchyma, which results in increased interstitial fluid (IF) flow, or fluid flow within extracellular spaces in the tissue. IF flow has been associated with altered transport of molecules, extracellular matrix rearrangement, and triggering of cellular motility through a number of mechanisms. Thus, the results of a simple method to increase drug delivery may have unintended consequences on tissue morphology. Clinically, prediction of dispersal of agents via CED is important to catheter design, placement, and implementation to optimize contact of tumor cells with therapeutic agent. Prediction software can aid in this problem, yet we wonder if there is a better way to predict therapeutic distribution based simply on IF flow pathways as determined from pre-intervention imaging. Overall, CED based therapy has seen limited success and we posit that integration and appreciation of altered IF flow may enhance outcomes. Thus, in this manuscript we both review the current state of the art in CED and IF flow mechanistic understanding and relate these two elements to each other in a clinical context.

Improving the Predictions of Computational Models of Convection-Enhanced Drug Delivery by Accounting for Diffusion Non-gaussianity

Convection-enhanced delivery (CED) is an innovative method of drug delivery to the human brain, that bypasses the blood-brain barrier by injecting the drug directly into the brain. CED aims to target pathological tissue for central nervous system conditions such as Parkinson's and Huntington's disease, epilepsy, brain tumors, and ischemic stroke. Computational fluid dynamics models have been constructed to predict the drug distribution in CED, allowing clinicians advance planning of the procedure. These models require patient-specific information about the microstructure of the brain tissue, which can be collected non-invasively using magnetic resonance imaging (MRI) pre-infusion. Existing models employ the diffusion tensor, which represents Gaussian diffusion in brain tissue, to provide predictions for the drug concentration. However, those predictions are not always in agreement with experimental observations. In this work we present a novel computational fluid dynamics model for CED that does not use the diffusion tensor, but rather the diffusion probability that is experimentally measured through diffusion MRI, at an individual-participant level. Our model takes into account effects of the brain microstructure on the motion of drug molecules not taken into account in previous approaches, namely the restriction and hindrance that those molecules experience when moving in the brain tissue, and can improve the drug concentration predictions. The duration of the associated MRI protocol is 19 min, and therefore feasible for clinical populations. We first prove theoretically that the two models predict different drug distributions. Then, using in vivo high-resolution diffusion MRI data from a healthy participant, we derive and compare predictions using both models, in order to identify the impact of including the effects of restriction and hindrance. Including those effects results in different drug distributions, and the observed differences exhibit statistically significant correlations with measures of diffusion non-Gaussianity in brain tissue. The differences are more pronounced for infusion in white-matter areas of the brain. Using experimental results from the literature along with our simulation results, we show that the inclusion of the effects of diffusion non-Gaussianity in models of CED is necessary, if reliable predictions that can be used in the clinic are to be generated by CED models.

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.

Convection-enhanced delivery to the central nervous system

Convection-enhanced delivery (CED) is a bulk flow–driven process. Its properties permit direct, homogeneous, targeted perfusion of CNS regions with putative therapeutics while bypassing the blood-brain barrier. Development of surrogate imaging tracers that are co-infused during drug delivery now permit accurate, noninvasive real-time tracking of convective infusate flow in nervous system tissues. The potential advantages of CED in the CNS over other currently available drug delivery techniques, including systemic delivery, intrathecal and/or intraventricular distribution, and polymer implantation, have led to its application in research studies and clinical trials. The authors review the biophysical principles of convective flow and the technology, properties, and clinical applications of convective delivery in the CNS.

MRI-based computational model of heterogeneous tracer transport following local infusion into a mouse hind limb tumor

Systemic drug delivery to solid tumors involving macromolecular therapeutic agents is challenging for many reasons. Amongst them is their chaotic microvasculature which often leads to inadequate and uneven uptake of the drug. Localized drug delivery can circumvent such obstacles and convection-enhanced delivery (CED)--controlled infusion of the drug directly into the tissue--has emerged as a promising delivery method for distributing macromolecules over larger tissue volumes. In this study, a three-dimensional MR image-based computational porous media transport model accounting for realistic anatomical geometry and tumor leakiness was developed for predicting the interstitial flow field and distribution of albumin tracer following CED into the hind-limb tumor (KHT sarcoma) in a mouse. Sensitivity of the model to changes in infusion flow rate, catheter placement and tissue hydraulic conductivity were investigated. The model predictions suggest that 1) tracer distribution is asymmetric due to heterogeneous porosity; 2) tracer distribution volume varies linearly with infusion volume within the whole leg, and exponentially within the tumor reaching a maximum steady-state value; 3) infusion at the center of the tumor with high flow rates leads to maximum tracer coverage in the tumor with minimal leakage outside; and 4) increasing the tissue hydraulic conductivity lowers the tumor interstitial fluid pressure and decreases the tracer distribution volume within the whole leg and tumor. The model thus predicts that the interstitial fluid flow and drug transport is sensitive to porosity and changes in extracellular space. This image-based model thus serves as a potential tool for exploring the effects of transport heterogeneity in tumors.

Evaluation of a voxelized model based on DCE-MRI for tracer transport in tumor

Recent advances in the treatment of cancer involving therapeutic agents have shown promising results. However, treatment efficacy can be limited due to inadequate and uneven uptake in solid tumors, thereby making the prediction of drug transport important for developing effective therapeutic strategies. In this study, a patient-specific computational porous media model (voxelized model) was developed for predicting the interstitial flow field and distribution of a systemically delivered magnetic resonance (MR) visible tracer in a tumor. The benefits of a voxel approach include less labor and less computational time (approximately an order of magnitude reduction compared to the traditional computational fluid dynamics (CFD) approach developed earlier by our group). The model results were compared with that obtained from a previous approach based on unstructured meshes along with MR-measured tracer concentration data within tumors, using statistical analysis and qualitative representations. The statistical analysis indicated the similarity between the structured and unstructured models' results with a low root mean square error (RMS) and a high correlation coefficient. The voxelized model captured features of the flow field and tracer distribution such as high interstitial fluid pressure inside the tumor and the heterogeneous distribution of the tracer. Predictions of tracer distribution by the voxelized approach also resulted in low RMS error when compared with MR-measured data over a 1 h time course. The similarity in the voxelized model results with experiment and the nonvoxelized model predictions were maintained across three different tumors. Overall, the voxelized model serves as a reliable and swift alternative to approaches using unstructured meshes in predicting extracellular transport within tumors.

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.

Influences of brain tissue poroelastic constants on intracranial pressure (ICP) during constant-rate infusion

A 3D finite element (FE) model has been developed to study the mean intracranial pressure (ICP) response during constant-rate infusion using linear poroelasticity. Due to the uncertainties in the poroelastic constants for brain tissue, the influence of each of the main parameters on the transient ICP infusion curve was studied. As a prerequisite for transient analysis, steady-state simulations were performed first. The simulated steady-state pressure distribution in the brain tissue for a normal cerebrospinal fluid (CSF) circulation system showed good correlation with experiments from the literature. Furthermore, steady-state ICP closely followed the infusion experiments at different infusion rates. The verified steady-state models then served as a baseline for the subsequent transient models. For transient analysis, the simulated ICP shows a similar tendency to that found in the experiments, however, different values of the poroelastic constants have a significant effect on the infusion curve. The influence of the main poroelastic parameters including the Biot coefficient α, Skempton coefficient B, drained Young's modulus E, Poisson's ratio ν, permeability κ, CSF absorption conductance C(b) and external venous pressure p(b) was studied to investigate the influence on the pressure response. It was found that the value of the specific storage term S(ε) is the dominant factor that influences the infusion curve, and the drained Young's modulus E was identified as the dominant parameter second to S(ε). Based on the simulated infusion curves from the FE model, artificial neural network (ANN) was used to find an optimised parameter set that best fit the experimental curve. The infusion curves from both the FE simulation and using ANN confirmed the limitation of linear poroelasticity in modelling the transient constant-rate infusion.

Influence of gravity for optimal head positions in the treatment of head injury patients

BACKGROUND

Brain edema is a major neurological complication of traumatic brain injury (TBI), commonly including a pathologically increased intracranial pressure (ICP) associated with poor outcome. In this study, gravitational force is suggested to have a significant impact on the pressure of the edema zone in the brain tissue and the objective of the study was to investigate the significance of head position on edema at the posterior part of the brain using a finite element (FE) model.

METHODS

A detailed FE model including the meninges, brain tissue and a fully connected cerebrospinal fluid (CSF) system was used in this study. Brain tissue was modelled as a poroelastic material consisting of an elastic solid skeleton composed of neurons and neuroglia, permeated by interstitial fluid. The effect of head positions (supine and prone position) due to gravity was investigated for a localized brain edema at the posterior part of the brain.

RESULTS

The water content increment at the edema zone remained nearly identical for both positions. However, the interstitial fluid pressure (IFP) inside the edema zone decreased around 15% by having the head in a prone position compared with a supine position.

CONCLUSIONS

The decrease of IFP inside the edema zone by changing patient position from supine to prone has the potential to alleviate the damage to central nervous system nerves. These observations indicate that considering the patient's head position during intensive care and at rehabilitation might be of importance to the treatment of edematous regions in TBI patients.

Sensitivity analysis of an image-based solid tumor computational model with heterogeneous vasculature and porosity

An MR image-based computational model of a murine KHT sarcoma is presented that allows the calculation of plasma fluid and solute transport within tissue. Such image-based models of solid tumors may be used to optimize patient-specific therapies. This model incorporates heterogeneous vasculature and tissue porosity to account for nonuniform perfusion of an MR-visible tracer, gadolinium-diethylenetriamine pentaacetic acid (Gd-DTPA). Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) was conducted following intravenous infusion of Gd-DTPA to provide 1 h of tracer-concentration distribution data within tissue. Early time points (19 min) were used to construct 3D K(trans) and porosity maps using a two-compartment model; tracer transport was predicted at later time points using a 3D porous media model. Model development involved selecting an arterial input function (AIF) and conducting a sensitivity analysis of model parameters (tissue, vascular, and initial estimation of solute concentration in plasma) to investigate the effects on transport for a specific tumor. The developed model was then used to predict transport in two additional tumors. The sensitivity analysis suggests that plasma fluid transport is more sensitive to parameter changes than solute transport due to the dominance of transvascular exchange. Gd-DTPA distribution was similar to experimental patterns, but differences in Gd-DTPA magnitude at later time points may result from inaccurate selection of AIF. Thus, accurate AIF estimation is important for later time point prediction of low molecular weight tracer or drug transport in smaller tumors.

A voxelized model of direct infusion into the corpus callosum and hippocampus of the rat brain: model development and parameter analysis

Recent experimental studies have shown convective-enhanced delivery (CED) to be useful for transporting macromolecular therapeutic agents over large tissue volumes in the central nervous system (CNS). There are limited tools currently available for predicting tissue distributions in the brain. We have developed a voxelized modeling methodology in which CNS tissues are modeled as porous media, and transport properties and anatomical boundaries are determined semi-automatically on a voxel-by-voxel basis using diffusion tensor imaging (DTI). By using this methodology, 3D extracellular transport models of the rat brain were developed. Macromolecular tracer distributions following CED in two different infusion sites (corpus callosum and hippocampus) were predicted. Sensitivity of models to changes in infusion parameters, transport properties, and modeling parameters was determined. Predicted tracer distributions were most sensitive to changes in segmentation threshold, DTI resolution, tissue porosity, and infusion site. This DTI-based voxelized modeling methodology provides a potentially rapid means of estimating CED transport.