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

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.

1D Thermoembolization Model Using CT Imaging Data for Porcine Liver

Objective

Innovative therapies such as thermoembolization are expected to play an important role in improving care for patients with diseases such as hepatocellular carcinoma. Thermoembolization is a minimally invasive strategy that combines thermal ablation and embolization in a single procedure. This approach exploits an exothermic chemical reaction that occurs when an acid chloride is delivered via an endovascular route. However, comprehension of the complexities of the biophysics of thermoembolization is challenging. Mathematical models can aid in understanding such complex processes and assisting clinicians in making informed decisions. In this study, we used a Hagen-Poiseuille 1D blood flow model to predict the mass transport and possible embolization locations in a porcine hepatic artery.

Method

The 1D flow model was used on imaging data of in-vivo embolization imaging data of three pigs. The hydrolysis time constant of acid chloride chemical reaction was optimized for each pig, and LOOCV method was used to test the model's predictive ability.

Conclusion

This basic model provided a balanced accuracy rate of 66.8% for identifying the possible locations of damage in the hepatic artery. Use of the model provides an initial understanding of the vascular transport phenomena that are predicted to occur as a result of thermoembolization.

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.

Heterogeneous Mechanical Stress and Interstitial Fluid Flow Predictions Derived from DCE-MRI for Rat U251N Orthotopic Gliomas

Mechanical stress and fluid flow influence glioma cell phenotype in vitro, but measuring these quantities in vivo continues to be challenging. The purpose of this study was to predict these quantities in vivo, thus providing insight into glioma physiology and potential mechanical biomarkers that may improve glioma detection, diagnosis, and treatment. Image-based finite element models of human U251N orthotopic glioma in athymic rats were developed to predict structural stress and interstitial flow in and around each animal's tumor. In addition to accounting for structural stress caused by tumor growth, our approach has the advantage of capturing fluid pressure-induced structural stress, which was informed by in vivo interstitial fluid pressure (IFP) measurements. Because gliomas and the brain are soft, elevated IFP contributed substantially to tumor structural stress, even inverting this stress from compressive to tensile in the most compliant cases. The combination of tumor growth and elevated IFP resulted in a concentration of structural stress near the tumor boundary where it has the greatest potential to influence cell proliferation and invasion. MRI-derived anatomical geometries and tissue property distributions resulted in heterogeneous interstitial fluid flow with local maxima near cerebrospinal fluid spaces, which may promote tumor invasion and hinder drug delivery. In addition, predicted structural stress and interstitial flow varied markedly between irradiated and radiation-naïve animals. Our modeling suggests that relative to tumors in stiffer tissues, gliomas experience unusual mechanical conditions with potentially important biological (e.g., proliferation and invasion) and clinical consequences (e.g., drug delivery and treatment monitoring).

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.

Hydraulic conductivity of human cancer tissue: A hybrid study

Background

Elevated tumor tissue interstitial fluid pressure (IFP) is an adverse biomechanical biomarker that predicts poor therapy response and an aggressive phenotype. Advances in functional imaging have opened the prospect of measuring IFP non-invasively. Image-based estimation of the IFP requires knowledge of the tissue hydraulic conductivity (K), a measure for the ease of bulk flow through the interstitium. However, data on the magnitude of K in human cancer tissue are not available.

Methods

We measured the hydraulic conductivity of tumor tissue using modified Ussing chambers in surgical resection specimens. The effect of the tumor microenvironment (TME) on K was investigated by quantifying the collagen content, cell density, and fibroblast density of the tested samples using quantitative immune histochemistry. Also, we developed a computational fluid dynamics (CFD) model to evaluate the role of K on interstitial fluid flow and drug transport in solid tumors.

Results

The results show that the hydraulic conductivity of human tumor tissues is very limited, ranging from approximately 10-15 to 10-14 m2/Pa∙s. Moreover, K values varied significantly between tumor types and between different samples from the same tumor. A significant inverse correlation was found between collagen fiber density and hydraulic conductivity values. However, no correlation was detected between K and cancer cell or fibroblast densities. The computational model demonstrated the impact of K on the interstitial fluid flow and the drug concentration profile: higher K values led to a lower IFP and deeper drug penetration.

Conclusions

Human tumor tissue is characterized by a very limited hydraulic conductivity, representing a barrier to effective drug transport. The results of this study can inform the development of realistic computational models, facilitate non-invasive IFP estimation, and contribute to stromal targeting anticancer therapies.

Biophysics in tumor growth and progression: from single mechano-sensitive molecules to mechanomedicine

Evidence from physical sciences in oncology increasingly suggests that the interplay between the biophysical tumor microenvironment and genetic regulation has significant impact on tumor progression. Especially, tumor cells and the associated stromal cells not only alter their own cytoskeleton and physical properties but also remodel the microenvironment with anomalous physical properties. Together, these altered mechano-omics of tumor tissues and their constituents fundamentally shift the mechanotransduction paradigms in tumorous and stromal cells and activate oncogenic signaling within the neoplastic niche to facilitate tumor progression. However, current findings on tumor biophysics are limited, scattered, and often contradictory in multiple contexts. Systematic understanding of how biophysical cues influence tumor pathophysiology is still lacking. This review discusses recent different schools of findings in tumor biophysics that have arisen from multi-scale mechanobiology and the cutting-edge technologies. These findings range from the molecular and cellular to the whole tissue level and feature functional crosstalk between mechanotransduction and oncogenic signaling. We highlight the potential of these anomalous physical alterations as new therapeutic targets for cancer mechanomedicine. This framework reconciles opposing opinions in the field, proposes new directions for future cancer research, and conceptualizes novel mechanomedicine landscape to overcome the inherent shortcomings of conventional cancer diagnosis and therapies.

Convection-Enhanced Delivery of Antiangiogenic Drugs and Liposomal Cytotoxic Drugs to Heterogeneous Brain Tumor for Combination Therapy

Simple Summary

Although developed anticancer drugs have shown desirable effects in preclinical trials, the clinical efficacy of chemotherapy against brain cancer remains disappointing. One of the important obstacles is the highly heterogeneous environment in tumors. This study aims to evaluate the performance of an emerging treatment using antiangiogenic and cytotoxic drugs. Our mathematical modelling confirms the advantage of this combination therapy in homogenizing the intratumoral environment for better drug delivery outcomes. In addition, the effects of local microvasculature and cell density on this therapy are also discussed. The results would contribute to the development of more effective treatments for brain cancer.

Abstract

Although convection-enhanced delivery can successfully bypass the blood-brain barrier, its clinical performance remains disappointing. This is primarily attributed to the heterogeneous intratumoral environment, particularly the tumor microvasculature. This study investigates the combined convection-enhanced delivery of antiangiogenic drugs and liposomal cytotoxic drugs in a heterogeneous brain tumor environment using a transport-based mathematical model. The patient-specific 3D brain tumor geometry and the tumor’s heterogeneous tissue properties, including microvascular density, porosity and cell density, are extracted from dynamic contrast-enhanced magnetic resonance imaging data. Results show that antiangiogenic drugs can effectively reduce the tumor microvascular density. This change in tissue structure would inhibit the fluid loss from the blood to prevent drug concentration from dilution, and also reduce the drug loss by blood drainage. The comparisons between different dosing regimens demonstrate that the co-infusion of liposomal cytotoxic drugs and antiangiogenic drugs has the advantages of homogenizing drug distribution, increasing drug accumulation, and enlarging the volume where tumor cells can be effectively killed. The delivery outcomes are susceptible to the location of the infusion site. This combination treatment can be improved by infusing drugs at higher microvascular density sites. In contrast, infusion at a site with high cell density would lower the treatment effectiveness of the whole brain tumor. Results obtained from this study can deepen the understanding of this combination therapy and provide a reference for treatment design and optimization that can further improve survival and patient quality of life.

Spatiotemporal multi-scale modeling of radiopharmaceutical distributions in vascularized solid tumors

We present comprehensive mathematical modeling of radiopharmaceutical spatiotemporal distributions within vascularized solid tumors. The novelty of the presented model is at mathematical level. From the mathematical viewpoint, we provide a general modeling framework for the process of radiopharmaceutical distribution in the tumor microenvironment to enable an analysis of the effect of various tumor-related parameters on the distribution of different radiopharmaceuticals. We argue that partial differential equations (PDEs), beyond conventional methods, including ODE-based kinetic compartment modeling, can be used to evaluate radiopharmaceutical distribution in both time and space. In addition, we consider the spatially-variable dynamic structure of tumor microvascular networks to simulate blood flow distribution. To examine the robustness of the model, the effects of microvessel density (MVD) and tumor size, as two important factors in tumor prognosis, on the radiopharmaceutical distribution within the tumor are investigated over time (in the present work, we focus on the radiopharmaceutical [¹⁸F]FDG, yet the framework is broadly applicable to radiopharmaceuticals). Results demonstrate that the maximum total uptake of [¹⁸F]FDG at all time frames occurs in the tumor area due to the high capillary permeability and lack of a functional lymphatic system. As the MVD of networks increases, the mean total uptake in the tumor is also enhanced, where the rate of diffusion from vessel to tissue has the highest contribution and the rate of convection transport has the lowest contribution. The results of this study can be used to better investigate various phenomena and bridge a gap among cancer biology, mathematical oncology, medical physics, and radiology.

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.

Longitudinal Monitoring of Simulated Interstitial Fluid Pressure for Pancreatic Ductal Adenocarcinoma Patients Treated with Stereotactic Body Radiotherapy

Simple Summary

High vessel permeability, poor perfusion, low lymphatic drainage, and dense abundant stroma elevate interstitial fluid pressures (IFP) in pancreatic ductal adenocarcinoma (PDAC). The present study aims to monitor longitudinal changes in simulated tumor IFP and velocity (IFV) values using a dynamic contrast-enhanced (DCE)-MRI-based computational fluid modeling (CFM) approach in PDAC. Nine PDAC patients underwent DCE-MRI acquisition on a 3-Tesla MRI scanner at pre-treatment (TX (0)), immediately after the first fraction of stereotactic body radiotherapy (SBRT, (D1-TX)), and six weeks post-TX (D2-TX). The partial differential equation of IFP formulated from the continuity equation using the Starling Principle of fluid exchange and Darcy velocity–pressure relationship was solved in COMSOL Multiphysics software to generate IFP and IFV parametric maps using relevant tumor tissue physiological parameters. Initial results suggest that after validation, IFP and IFV can be imaging biomarkers of early response to therapy that may guide precision medicine in PDAC.

Abstract

The present study aims to monitor longitudinal changes in simulated tumor interstitial fluid pressure (IFP) and velocity (IFV) values using dynamic contrast-enhanced (DCE)-MRI-based computational fluid modeling (CFM) in pancreatic ductal adenocarcinoma (PDAC) patients. Nine PDAC patients underwent MRI, including DCE-MRI, on a 3-Tesla MRI scanner at pre-treatment (TX (0)), after the first fraction of stereotactic body radiotherapy (SBRT, (D1-TX)), and six weeks post-TX (D2-TX). The partial differential equation of IFP formulated from the continuity equation, incorporating the Starling Principle of fluid exchange, Darcy velocity, and volume transfer constant (K^trans), was solved in COMSOL Multiphysics software to generate IFP and IFV maps. Tumor volume (V_t), K^trans, IFP, and IFV values were compared (Wilcoxon and Spearman) between the time- points. D2-TX K^trans values were significantly different from pre-TX and D1-TX (p < 0.05). The D1-TX and pre-TX mean IFV values exhibited a borderline significant difference (p = 0.08). The IFP values varying <3.0% between the three time-points were not significantly different (p > 0.05). V_t and IFP values were strongly positively correlated at pre-TX (ρ = 0.90, p = 0.005), while IFV exhibited a strong negative correlation at D1-TX (ρ = −0.74, p = 0.045). V_t, K^trans, IFP, and IFV hold promise as imaging biomarkers of early response to therapy in PDAC.

Computational Modeling of Interstitial Fluid Pressure and Velocity in Head and Neck Cancer Based on Dynamic Contrast-Enhanced Magnetic Resonance Imaging: Feasibility Analysis

We developed and tested the feasibility of computational fluid modeling (CFM) based on dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) for quantitative estimation of interstitial fluid pressure (IFP) and velocity (IFV) in patients with head and neck (HN) cancer with locoregional lymph node metastases. Twenty-two patients with HN cancer, with 38 lymph nodes, underwent pretreatment standard MRI, including DCE-MRI, on a 3-Tesla scanner. CFM simulation was performed with the finite element method in COMSOL Multiphysics software. The model consisted of a partial differential equation (PDE) module to generate 3D parametric IFP and IFV maps, using the Darcy equation and Ktrans values (min⁻¹, estimated from the extended Tofts model) to reflect fluid influx into tissue from the capillary microvasculature. The Spearman correlation (ρ) was calculated between total tumor volumes and CFM estimates of mean tumor IFP and IFV. CFM-estimated tumor IFP and IFV mean ± standard deviation for the neck nodal metastases were 1.73 ± 0.39 (kPa) and 1.82 ± 0.9 × (10⁻⁷ m/s), respectively. High IFP estimates corresponds to very low IFV throughout the tumor core, but IFV rises rapidly near the tumor boundary where the drop in IFP is precipitous. A significant correlation was found between pretreatment total tumor volume and CFM estimates of mean tumor IFP (ρ = 0.50, P = 0.004). Future studies can validate these initial findings in larger patients with HN cancer cohorts using CFM of the tumor in concert with DCE characterization, which holds promise in radiation oncology and drug-therapy clinical trials.

Imaging-based characterization of convective tissue properties

Convective transport is an important phenomenon for nanomedicine delivery. We present an imaging-based approach to recover tissue properties that are significant in the accumulation of nanoparticles delivered via systemic methods. The classical pharmacokinetic analysis develops governing equations for the particle transport from a first principle mass balance. Fundamentally, the governing equations for compartmental mass balance represent a spatially invariant mass transport between compartments and do not capture spatially variant convection phenomena. Further, the parameters recovered from this approach do not necessarily have direct meaning with respect to the governing equations for convective transport. In our approach, a framework is presented for directly measuring permeability in the sense of Darcy flow through porous tissue. Measurements from our approach are compared to an extended Tofts model as a control. We demonstrate that a pixel-wise iterative clustering algorithm may be applied to reduce the parameter space of the measurements. We show that measurements obtained from our approach are correlated with measurements obtained from the extended Tofts model control. These correlations demonstrate that the proposed approach contains similar information to an established compartmental model and may be useful in providing an alternative theoretical framework for parameterizing mathematical models for treatment planning and diagnostic studies involving nanomedicine where convection dominated effects are important.

Computational Modeling of Interstitial Fluid Pressure and Velocity in Non-small Cell Lung Cancer Brain Metastases Treated With Stereotactic Radiosurgery

Background: Early imaging-based treatment response assessment of brain metastases following stereotactic radiosurgery (SRS) remains challenging. The aim of this study is to determine whether early (within 12 weeks) intratumoral changes in interstitial fluid pressure (IFP) and velocity (IFV) estimated from computational fluid modeling (CFM) using dynamic contrast-enhanced (DCE) MRI can predict long-term outcomes of lung cancer brain metastases (LCBMs) treated with SRS.

Methods: Pre- and post-treatment T₁-weighted DCE-MRI data were obtained in 41 patients treated with SRS for intact LCBMs. The imaging response was assessed using RANO-BM criteria. For each lesion, extravasation of contrast agent measured from Extended Tofts pharmacokinetic Model (volume transfer constant, K^trans) was incorporated into a computational fluid model to estimate tumor IFP and IFV. Estimates of mean IFP and IFV and heterogeneity (skewness and kurtosis) were calculated for each lesion from pre- and post-SRS imaging. The Wilcoxon rank-sum test was utilized to assess for significant differences in IFP, IFV, and IFP/IFV change (Δ) between response groups.

Results: Fifty-three lesions from 41 patients were included. Median follow-up time after SRS was 11 months. The objective response (OR) rate (partial or complete response) was 79%, with 21% demonstrating stable disease (SD) or progressive disease (PD). There were significant response group differences for multiple posttreatment and Δ CFM parameters: post-SRS IFP skewness (mean −0.405 vs. −0.691, p = 0.022), IFP kurtosis (mean 2.88 vs. 3.51, p = 0.024), and IFV mean (5.75e-09 vs. 4.19e-09 m/s, p = 0.027); and Δ IFP kurtosis (mean −2.26 vs. −0.0156, p = 0.017) and IFV mean (1.91e-09 vs. 2.38e-10 m/s, p = 0.013). Posttreatment and Δ thresholds predicted non-OR with high sensitivity (sens): post-SRS IFP skewness (−0.432, sens 84%), kurtosis (2.89, sens 84%), and IFV mean (4.93e-09 m/s, sens 79%); and Δ IFP kurtosis (−0.469, sens 74%) and IFV mean (9.90e-10 m/s, sens 74%).

Conclusions: Objective response was associated with lower post-treatment tumor heterogeneity, as represented by reductions in IFP skewness and kurtosis. These results suggest that early post-treatment assessment of IFP and IFV can be used to predict long-term response of lung cancer brain metastases to SRS, allowing a timelier treatment modification.

Mathematical modeling of mass and energy transport for thermoembolization

Background: Thermoembolization presents a unique treatment alternative for patients diagnosed with hepatocellular carcinoma. The approach delivers a reagent that undergoes an exothermic chemical reaction and combines the benefits of embolic as well as thermal- and chemical-ablative therapy modalities. The target tissue and vascular bed are subjected to simultaneous hyperthermia, ischemia, and chemical denaturation in a single procedure. To guide optimal delivery, we developed a mathematical model for understanding the competing diffusive and convective effects observed in thermoembolization delivery protocols.Methods: A mixture theory formulation was used to mathematically model thermoembolization as chemically reacting transport of an electrophile, dichloroacetyl chloride (DCACl), within porous living tissue. Mass and energy transport of each relevant constituent are considered. Specifically, DCACl is injected into the vessels and exothermically reacts with water in the blood or tissue to form dichloroacetic acid and hydrochloric acid. Neutralization reactions are assumed instantaneous in this approach. We validated the mathematical model predictions of temperature using MR thermometry of the thermoembolization procedure performed in ex vivo kidney.Results: Mathematical modeling predictions of tissue death were highly dependent on the vascular geometry, injection pressure, and intrinsic amount of exothermic energy released from the chemical species, and were able to recapitulate the temperature distributions observed in MR thermometry.Conclusion: These efforts present a first step toward formalizing a mathematical model for thermoembolization and are promising for providing insight for delivery protocol optimization. While our approach captured the observed experimental temperature measurements, larger-scale experimental validation is needed to prioritize additional model complexity and fidelity.

Phase contrast MRI of creeping flows using stimulated echo

Creeping flows govern many important physiological phenomena such as elevated interstitial fluid flows in tumors, glymphatic flows in the brain, among other applications. However, few methods exist to measure such slow flows non-invasively in optically opaque biological tissues in vivo. Phase-contrast MRI is a velocimetry technique routinely used in the clinic to measure fast flows in biological tissues, such as blood and cerebrospinal fluid (CSF), in the order of cm/s. Use of this technique to encode slower flows is hampered by diffusion weighting and phase error introduced by gradient hardware imperfections. In this study, a new PC-MRI technique is developed using stimulated echo preparation to overcome these challenges. Flows as slow as 1 μm/s are measured and validated using controlled water flow through a pipe at 4.7 T. The error in measured flow rate obtained by integrating the measured velocity over the cross-sectional area of the pipe is less than 10%. The developed method was also able to capture slow natural convection flows appearing in liquids placed inside a horizontal bore magnet. Monitoring the 4D velocity vector field revealed that the natural convection flows decay exponentially with time. This method could be applied in future to study creeping flows, e.g. in tissue.

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.

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.

Spatiotemporal distribution modeling of PET tracer uptake in solid tumors

OBJECTIVE

Distribution of PET tracer uptake is elaborately modeled via a general equation used for solute transport modeling. This model can be used to incorporate various transport parameters of a solid tumor such as hydraulic conductivity of the microvessel wall, transvascular permeability as well as interstitial space parameters. This is especially significant because tracer delivery and drug delivery to solid tumors are determined by similar underlying tumor transport phenomena, and quantifying the former can enable enhanced prediction of the latter.

METHODS

We focused on the commonly utilized FDG PET tracer. First, based on a mathematical model of angiogenesis, the capillary network of a solid tumor and normal tissues around it were generated. The coupling mathematical method, which simultaneously solves for blood flow in the capillary network as well as fluid flow in the interstitium, is used to calculate pressure and velocity distributions. Subsequently, a comprehensive spatiotemporal distribution model (SDM) is applied to accurately model distribution of PET tracer uptake, specifically FDG in this work, within solid tumors.

RESULTS

The different transport mechanisms, namely convention and diffusion from vessel to tissue and in tissue, are elaborately calculated across the domain of interest and effect of each parameter on tracer distribution is investigated. The results show the convection terms to have negligible effect on tracer transport and the SDM can be solved after eliminating these terms.

CONCLUSION

The proposed framework of spatiotemporal modeling for PET tracers can be utilized to comprehensively assess the impact of various parameters on the spatiotemporal distribution of PET tracers.

Effects of endothelial cell proliferation and migration rates in a computational model of sprouting angiogenesis

Angiogenesis, the recruitment of new blood vessels, is a critical process for the growth, expansion, and metastatic dissemination of developing tumors. Three types of cells make up the new vasculature: tip cells, which migrate in response to gradients of vascular endothelial growth factor (VEGF), stalk cells, which proliferate and extend the vessels, and phalanx cells, which are quiescent and support the sprout. In this study we examine the contribution of tip cell migration rate and stalk cell proliferation rate on the formation of new vasculature. We calculate several vascular metrics, such as the number of vascular bifurcations per unit volume, vascular segment length per unit volume, and vascular tortuosity. These measurements predict that proliferation rate has a greater effect on the spread and extent of vascular growth compared to migration rate. Together, these findings provide strong implications for designing anti-angiogenic therapies that may differentially target endothelial cell proliferation and migration. Computational models can be used to predict optimal anti-angiogenic therapies in combination with other therapeutics to improve outcome.

Peritumoral tissue compression is predictive of exudate flux in a rat model of cerebral tumor: an MRI study in an embedded tumor

MRI estimates of extracellular volume and tumor exudate flux in peritumoral tissue are demonstrated in an experimental model of cerebral tumor. Peritumoral extracellular volume predicted the tumor exudate flux. Eighteen RNU athymic rats were inoculated intracerebrally with U251MG tumor cells and studied with dynamic contrast enhanced MRI (DCE-MRI) approximately 18 days post implantation. Using a model selection paradigm and a novel application of Patlak and Logan plots to DCE-MRI data, the distribution volume (i.e. tissue porosity) in the leaky rim of the tumor and that in the tissue external to the rim (the outer rim) were estimated, as was the tumor exudate flow from the inner rim of the tumor through the outer rim. Distribution volume in the outer rim was approximately half that of the inner adjacent region (p < 1 × 10(-4)). The distribution volume of the outer ring was significantly correlated (R(2) = 0.9) with tumor exudate flow from the inner rim. Thus, peritumoral extracellular volume predicted the rate of tumor exudate flux. One explanation for these data is that perfusion, i.e. the delivery of blood to the tumor, was regulated by the compression of the mostly normal tissue of the tumor rim, and that the tumor exudate flow was limited by tumor perfusion.