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

Microneedle patch capable of dual drug release for drug delivery to brain tumors

Primary brain tumors are mostly managed using surgical resection procedures. Nevertheless, in certain cases, a thin layer of tumors may remain outside of the resection process due to the possibility of permanent injury; these residual tumors expose patients to the risk of tumor recurrence. This study has introduced the use of microneedle patches implanted after surgery with a dual-release mechanism for the administration of doxorubicin. The proposed patches possess the capability to administer drugs directly to the residual tumors and initiate chemotherapy immediately following surgical procedures. Three-dimensional simulation of drug delivery to residual tumors in the brain has been performed based on a finite element method. The impact of four important parameters on drug delivery has been investigated, involving the fraction of drug released in the burst phase, the density of microneedles on the patch, the length of microneedles, and the microvascular density of the tumor. The simulation findings indicate that lowering the fraction of drug released in the initial burst phase reduces the maximum average concentration, but the sustained release that continues for a longer period, increasing the bioavailability of free drug. However, the area under curve (AUC) for different release rates remains unchanged due to the fact that an identical dose of drug is supplied in each instance. By increasing the density of microneedles on the patch, concentration accumulation is provided over an extensive region of tumor, which in turn induces more cancer cell death. A comparative analysis of various lengths reveals that longer microneedles facilitate profound penetration into the tumor layers and present better therapeutic response due to extensive area of the tumor which is exposure to chemotherapeutic drugs. Furthermore, high microvascular density, as a characteristic of the tumor microenvironment, is shown to have a significant impact on the blood microvessels drainage of drugs and consequently lower therapeutic response outcome. Our approach offers a computational framework for creating localized drug delivery systems and addressing the challenges related to residual brain tumors.

Flow mechanisms of the air-blood barrier

The air-blood barrier protects the lung from blood/serum entering the air spaces, i.e., from "drowning in your own fluids". Failure leads to pulmonary edema, a regularly fatal complication during the Covid-19 pandemic which claimed 7 million lives worldwide. Finding no mathematical models for the underlying fluid mechanics, we created the first. Governing flow equations for alveolar capillary, interstitium, and alveolus are coupled by crossflows at the capillary and epithelial membranes and end-exit flows to the lymphatics. Case examples include normal/recovery, cardiogenic pulmonary edema, acute respiratory distress syndrome, effects of positive end expiratory pressure, and a wide range of parameter values for permeability of the membranes and interstitial matrix. Previously unknown membrane fluid shear stresses calculate to values that affect cell function in many systems. We add active epithelial reabsorption which has two effects: shifting streamlines to favor alveolar-lymphatic clearance and adding to the direct alveolar-capillary clearance. Simple algebraic equations are derived for the interstitial fluid pressure, pi, membrane crossflow velocities and the critical capillary pressure, pcrit, above which edema occurs. For validation, the pcrit predictions fit clinical definitions and flow calculations of lymphatic vs capillary clearance match animal experimental data. For decades the value of pi has been imposed as an input, whereas we calculate the value as an output. They don't agree. Since the space is too small for measurements, the ability to calculate pi and pcrit offers new insights, questions long-held beliefs, and opens applications from physiological studies to personalized clinical care.

Image-guided patient-specific prediction of interstitial fluid flow and drug transport in solid tumors

Tumor fluid dynamics and drug delivery simulations in solid tumors are highly relevant topics in clinical oncology. The current study introduces a novel method combining computational fluid dynamics (CFD) modeling, quantitative magnetic resonance imaging (MRI; including dynamic contrast-enhanced (DCE) MRI and diffusion-weighted (DW) MRI), and a novel ex-vivo protocol to generate patient-specific models of solid tumors in four patients with peritoneal metastases. DCE-MRI data were analyzed using the extended Tofts model to estimate the spatial distribution of tumor capillary permeability using the Ktrans parameter. DW-MRI data analysis provided a 3D representation of drug diffusivity, and DW-MRI coupled to an ex-vivo measurement protocol informed the spatial heterogeneity of the hydraulic conductivity of tumor tissue. The patient-specific data were subsequently incorporated into a computational fluid dynamics (CFD) model to simulate individualized tumor perfusion and drug transport maps. The results on interstitial fluid flow demonstrated noticeable heterogeneity of interstitial fluid pressure and velocity within the tumor, along with heterogeneous drug penetration profiles among different tumors, even with a similar drug administration regimen.

The role of initial lymphatics in the absorption of monoclonal antibodies after subcutaneous injection

The subcutaneous injection is the most common method of administration of monoclonal antibodies (mAbs) due to the patient's comfort and cost-effectiveness. However, the available knowledge about the transport and absorption of this type of biotherapeutics after subcutaneous injection is limited. Here, a mathematical framework to study the subcutaneous drug delivery of mAbs from injection to lymphatic uptake is presented. A poro-hyperelastic model of the tissue is exploited to find the biomechanical response of the tissue together with a transport model based on an advection-diffusion equation in large-deformation poro-hyperelastic Media. The process of mAbs transport to the lymphatic system has two major parts. First is the initial phase, where mAbs are dispersed in the tissue due to momentum exerted by injection. This stage lasts for only a few minutes after the injection. Then there is the second stage, which can take tens of hours, and as a result, mAb molecules are transported from the subcutaneous layer towards initial lymphatics in the dermis to enter the lymphatic system. In this study, we investigate both stages. The process of plume formation, interstitial pressure, and velocity development is explored. Then, the effect of the injection delivery parameters, injection site, and sensitivity of long-term lymphatic uptake due to variability in permeability, diffusivity, viscosity, and binding of mAbs are investigated. Finally, we study two different injection scenarios with variable injection volume and drug concentration inside the syringe and evaluate them based on the rate of lymphatic uptake. We use our results to find an equivalent lymphatic uptake coefficient similar to the coefficient widely used in pharmacokinetic (PK) models to study the absorption of mAbs. Ultimately, we validate our computational model against available experiments in the literature.

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).

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.

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.

Radiopharmaceutical transport in solid tumors via a 3-dimensional image-based spatiotemporal model

Lutetium-177 prostate-specific membrane antigen (177Lu-PSMA)-targeted radiopharmaceutical therapy is a clinically approved treatment for patients with metastatic castration-resistant prostate cancer (mCRPC). Even though common practice reluctantly follows "one size fits all" approach, medical community believes there is significant room for deeper understanding and personalization of radiopharmaceutical therapies. To pursue this aim, we present a 3-dimensional spatiotemporal radiopharmaceutical delivery model based on clinical imaging data to simulate pharmacokinetic of 177Lu-PSMA within the prostate tumors. The model includes interstitial flow, radiopharmaceutical transport in tissues, receptor cycles, association/dissociation with ligands, synthesis of PSMA receptors, receptor recycling, internalization of radiopharmaceuticals, and degradation of receptors and drugs. The model was studied for a range of values for injection amount (100-1000 nmol), receptor density (10-500 nmol•l-1), and recycling rate of receptors (10-4 to 10-1 min-1). Furthermore, injection type, different convection-diffusion-reaction mechanisms, characteristic time scales, and length scales are discussed. The study found that increasing receptor density, ligand amount, and labeled ligands improved radiopharmaceutical uptake in the tumor. A high receptor recycling rate (0.1 min-1) increased radiopharmaceutical concentration by promoting repeated binding to tumor cell receptors. Continuous infusion results in higher radiopharmaceutical concentrations within tumors compared to bolus administration. These insights are crucial for advancing targeted therapy for prostate cancer by understanding the mechanism of radiopharmaceutical distribution in tumors. Furthermore, measures of characteristic length and advection time scale were computed. The presented spatiotemporal tumor transport model can analyze different physiological parameters affecting 177Lu-PSMA delivery.

Enlarging the thermal coagulation volume during thermochemical ablation with alternating acid-base injection by shortening the injection interval: A computational study

BACKGROUND AND OBJECTIVES

Thermochemical ablation (TCA) is a cancer treatment that utilises the heat released from the neutralisation of acid and base to raise tissue temperature to levels sufficient to induce thermal coagulation. Computational studies have demonstrated that the coagulation volume produced by sequential injection is smaller than that with simultaneous injection. By injecting the reagents in an ensuing manner, the region of contact between acid and base is limited to a thin contact layer sandwiched between the distribution of acid and base. It is hypothesised that increasing the frequency of acid-base injections into the tissue by shortening the injection interval for each reagent can increase the effective area of contact between acid and base, thereby intensifying neutralisation and the exothermic heat released into the tissue.

METHODS

To verify this hypothesis, a computational model was developed to simulate the thermochemical processes involved during TCA with sequential injection. Four major processes that take place during TCA were considered, i.e., the flow of acid and base, their neutralisation, the release of exothermic heat and the formation of thermal damage inside the tissue. Equimolar acid and base at 7.5 M was injected into the tissue intermittently. Six injection intervals, namely 3, 6, 15, 20, 30 and 60 s were investigated.

RESULTS

Shortening of the injection interval led to the enlargement of coagulation volume. If one considers only the coagulation volume as the determining factor, then a 15 s injection interval was found to be optimum. Conversely, if one places priority on safety, then a 3 s injection interval would result in the lowest amount of reagent residue inside the tissue after treatment. With a 3 s injection interval, the coagulation volume was found to be larger than that of simultaneous injection with the same treatment parameters. Not only that, the volume also surpassed that of radiofrequency ablation (RFA); a conventional thermal ablation technique commonly used for liver cancer treatment.

CONCLUSION

The numerical results verified the hypothesis that shortening the injection interval will lead to the formation of larger thermal coagulation zone during TCA with sequential injection. More importantly, a 3 s injection interval was found to be optimum for both efficacy (large coagulation volume) and safety (least amount of reagent residue).

Computational Multi-Scale Modeling of Drug Delivery into an Anti-Angiogenic Therapy-Treated Tumor

The present study develops a numerical model, which is the most complex one, in comparison to previous research to investigate drug delivery accompanied by the anti-angiogenesis effect. This paper simulates intravascular blood flow and interstitial fluid flow using a dynamic model. The model accounts for the non-Newtonian behavior of blood and incorporates the adaptation of the diameter of a heterogeneous microvascular network derived from modeling the evolution of endothelial cells toward a circular tumor sprouting from two-parent vessels, with and without imposing the inhibitory effect of angiostatin on a modified discrete angiogenesis model. The average solute exposure and its uniformity in solid tumors of different sizes are studied by numerically solving the convection-diffusion equation. Three different methodologies are considered for simulating anti-angiogenesis: modifying the capillary network, updating the transport properties, and considering both microvasculature and transport properties modifications. It is shown that anti-angiogenic therapy decreases drug wash-out in the periphery of the tumor. Results show the decisive role of microvascular structure, particularly its distribution, and interstitial transport properties modifications induced via vascular normalization on the quality of drug delivery, such that it is improved by 39% in uniformity by the second approach in R = 0.2 cm.

Numerical investigation of the pharmacokinetics and pharmacodynamics of the chemotherapeutic drug in avascular and vascular stages of a brain tumor

One of the most commonly used approaches for treating solid tumors is the systemic delivery of chemotherapeutic drugs. However, our understanding of the factors influencing treatment efficacy through this method is still limited. This study presents a comprehensive and realistic mathematical model that incorporates the dynamics of tumor growth, capillary network extension, and drug delivery in a coupled and simultaneous manner. The model covers two stages of tumor growth: avascular and vascular. For tumor growth, a continuum model is employed using the phase field interface-capturing method. The neo-vascularization process is modeled using a hybrid discrete-continuum approach. Additionally, a multi-scale model is used to describe the pharmacokinetics of doxorubicin, considering various agents. The study investigates the effect of haptotaxis and reveals that a higher haptotaxis coefficient leads to faster tumor growth (up to 2.6 times) and a quicker progression to angiogenesis. The impact of tumor-related and drug-related parameters is also examined, including tumor size, tumor sensitivity to the drug, chemotherapy initialization, treatment cycle duration, drug affinity to cells, and drug dose. The findings indicate that chemotherapy is more effective during the angiogenesis stage when active loops have formed. Other clinical methods such as radiotherapy and surgery may be more appropriate during the avascular stage or the transition period between angiogenesis initialization and loop formation. The penetration depth of the drug decreases by approximately 50% with an increase in the drug binding rate to surface-cell receptors. As a result, high-associate-rate drugs are preferred for chemotherapy after active loops have formed, while low-associate-rate drugs are suitable for earlier stages.

Drug transport modeling in solid tumors: A computational exploration of spatial heterogeneity of biophysical properties

Inadequate uptake of therapeutic agents by tumor cells is still a major barrier in clinical cancer therapy. Mathematical modeling is a powerful tool to describe and investigate the transport phenomena involved. However, current models for interstitial flow and drug delivery in solid tumors have not yet embedded the existing heterogeneity of tumor biomechanical properties. The purpose of this study is to introduce a novel and more realistic methodology for computational models of solid tumor perfusion and drug delivery accounting for these regional heterogeneities as well as lymphatic drainage effects. Several tumor geometries were studied using an advanced computational fluid dynamics (CFD) modeling approach of intratumor interstitial fluid flow and drug transport. Hereby, the following novelties were implemented: (i) the heterogeneity of tumor-specific hydraulic conductivity and capillary permeability; (ii) the effect of lymphatic drainage on interstitial fluid flow and drug penetration. Tumor size and shape both have a crucial role on the interstitial fluid flow regime as well as drug transport illustrating a direct correlation with interstitial fluid pressure (IFP) and an inverse correlation with drug penetration, except for large tumors having a diameter larger than 50 mm. The results also suggest that the interstitial fluid flow and drug penetration in small tumors depend on tumor shape. A parameter study on the necrotic core size illustrated that the core effect (i.e. fluid flow and drug penetration alteration) was only profound in small tumors. Interestingly, the impact of a necrotic core on drug penetration differs depending on the tumor shape from having no effect in ideally spherical tumors to a clear effect in elliptical tumors with a necrotic core. A realistic presence of lymphatic vessels only slightly affected tumor perfusion, having no substantial effect on drug delivery. In conclusion, our findings illustrated that our novel parametric CFD modeling strategy in combination with accurate profiling of heterogeneous tumor biophysical properties can provide a powerful tool for better insights into tumor perfusion and drug transport, enabling effective therapy planning.

Computational pulmonary edema: A microvascular model of alveolar capillary and interstitial flow

We present a microvascular model of fluid transport in the alveolar septa related to pulmonary edema. It consists of a two-dimensional capillary sheet coursing by several alveoli. The alveolar epithelial membrane runs parallel to the capillary endothelial membrane with an interstitial layer in between, making one long septal tract. A coupled system of equations uses lubrication theory for the capillary blood, Darcy flow for the porous media of the interstitium, a passive alveolus, and the Starling equation at both membranes. Case examples include normal physiology, cardiogenic pulmonary edema, acute respiratory distress syndrome (ARDS), hypoalbuminemia, and effects of PEEP. COVID-19 has dramatically increased ARDS in the world population, raising the urgency for such a model to create an analytical framework. Under normal conditions fluid exits the alveolus, crosses the interstitium, and enters the capillary. For edema, this crossflow is reversed with fluid leaving the capillary and entering the alveolus. Because both the interstitial and capillary pressures decrease downstream, the reversal can occur within a single septal tract, with edema upstream and clearance downstream. Clinically useful solution forms are provided allowing calculation of interstitial fluid pressure, crossflows, and critical capillary pressures. Overall, the interstitial pressures are found to be significantly more positive than values used in the traditional physiological literature. That creates steep gradients near the upstream and downstream end outlets, driving significant flows toward the distant lymphatics. This new physiological flow provides an explanation to the puzzle, noted since 1896, of how pulmonary lymphatics can function so far from the alveoli: the interstitium is self-clearing.

Solute Transport across the Lymphatic Vasculature in a Soft Skin Tissue

Convective transport of drug solutes in biological tissues is regulated by the interstitial fluid pressure, which plays a crucial role in drug absorption into the lymphatic system through the subcutaneous (SC) injection. In this paper, an approximate continuum poroelasticity model is developed to simulate the pressure evolution in the soft porous tissue during an SC injection. This poroelastic model mimics the deformation of the tissue by introducing the time variation of the interstitial fluid pressure. The advantage of this method lies in its computational time efficiency and simplicity, and it can accurately model the relaxation of pressure. The interstitial fluid pressure obtained using the proposed model is validated against both the analytical and the numerical solution of the poroelastic tissue model. The decreasing elasticity elongates the relaxation time of pressure, and the sensitivity of pressure relaxation to elasticity decreases with the hydraulic permeability, while the increasing porosity and permeability due to deformation alleviate the high pressure. An improved Kedem-Katchalsky model is developed to study solute transport across the lymphatic vessel network, including convection and diffusion in the multi-layered poroelastic tissue with a hybrid discrete-continuum vessel network embedded inside. At last, the effect of different structures of the lymphatic vessel network, such as fractal trees and Voronoi structure, on the lymphatic uptake is investigated. In this paper, we provide a novel and time-efficient computational model for solute transport across the lymphatic vasculature connecting the microscopic properties of the lymphatic vessel membrane to the macroscopic drug absorption.

Magnetic Resonance Imaging-Derived Microvascular Perfusion Modeling to Assess Peripheral Artery Disease

Background Computational fluid dynamics has shown good agreement with contrast-enhanced magnetic resonance imaging measurements in cardiovascular disease applications. We have developed a biomechanical model of microvascular perfusion using contrast-enhanced magnetic resonance imaging signal intensities derived from skeletal calf muscles to study peripheral artery disease (PAD). Methods and Results The computational microvascular model was used to study skeletal calf muscle perfusion in 56 individuals (36 patients with PAD, 20 matched controls). The recruited participants underwent contrast-enhanced magnetic resonance imaging and ankle-brachial index testing at rest and after 6-minute treadmill walking. We have determined associations of microvascular model parameters including the transfer rate constant, a measure of vascular leakiness; the interstitial permeability to fluid flow which reflects the permeability of the microvasculature; porosity, a measure of the fraction of the extracellular space; the outflow filtration coefficient; and the microvascular pressure with known markers of patients with PAD. Transfer rate constant, interstitial permeability to fluid flow, and microvascular pressure were higher, whereas porosity and outflow filtration coefficient were lower in patients with PAD than those in matched controls (all P values ≤0.014). In pooled analyses of all participants, the model parameters (transfer rate constant, interstitial permeability to fluid flow, porosity, outflow filtration coefficient, microvascular pressure) were significantly associated with the resting and exercise ankle-brachial indexes, claudication onset time, and peak walking time (all P values ≤0.013). Among patients with PAD, interstitial permeability to fluid flow, and microvascular pressure were higher, while porosity and outflow filtration coefficient were lower in treadmill noncompleters compared with treadmill completers (all P values ≤0.001). Conclusions Computational microvascular model parameters differed significantly between patients with PAD and matched controls. Thus, computational microvascular modeling could be of interest in studying lower extremity ischemia.

Predictive Design and Analysis of Drug Transport by Multiscale Computational Models Under Uncertainty

Computational modeling of drug delivery is becoming an indispensable tool for advancing drug development pipeline, particularly in nanomedicine where a rational design strategy is ultimately sought. While numerous in silico models have been developed that can accurately describe nanoparticle interactions with the bioenvironment within prescribed length and time scales, predictive design of these drug carriers, dosages and treatment schemes will require advanced models that can simulate transport processes across multiple length and time scales from genomic to population levels. In order to address this problem, multiscale modeling efforts that integrate existing discrete and continuum modeling strategies have recently emerged. These multiscale approaches provide a promising direction for bottom-up in silico pipelines of drug design for delivery. However, there are remaining challenges in terms of model parametrization and validation in the presence of variability, introduced by multiple levels of heterogeneities in disease state. Parametrization based on physiologically relevant in vitro data from microphysiological systems as well as widespread adoption of uncertainty quantification and sensitivity analysis will help address these challenges.

An in silico assessment on the potential of using saline infusion to overcome non-confluent coagulation zone during two-probe, no-touch bipolar radiofrequency ablation of liver cancer

No-touch bipolar radiofrequency ablation (bRFA) is known to produce incomplete tumour ablation with a 'butterfly-shaped' coagulation zone when the interelectrode distance exceeds a certain threshold. Although non-confluent coagulation zone can be avoided by not implementing the no-touch mode, doing so exposes the patient to the risk of tumour track seeding. The present study investigates if prior infusion of saline into the tissue can overcome the issues of non-confluent or butterfly-shaped coagulation. A computational modelling approach based on the finite element method was carried out. A two-compartment model comprising the tumour that is surrounded by healthy liver tissue was developed. Three cases were considered; i) saline infusion into the tumour centre; ii) one-sided saline infusion outside the tumour; and iii) two-sided saline infusion outside the tumour. For each case, three different saline volumes were considered, i.e. 6, 14 and 22 ml. Saline concentration was set to 15% w/v. Numerical results showed that saline infusion into the tumour centre can overcome the butterfly-shaped coagulation only if the infusion volume is sufficient. On the other hand, one-sided infusion outside the tumour did not overcome this. Two-sided infusion outside the tumour produced confluent coagulation zone with the largest volume. Results obtained from the present study suggest that saline infusion, when carried out correctly, can be used to effectively eradicate liver cancer. This presents a practical solution to address non-confluent coagulation zone typical of that during two-probe bRFA treatment.

Lymphatic uptake of biotherapeutics through a 3D hybrid discrete-continuum vessel network in the skin tissue

Subcutaneous administration is a common approach for the delivery of biotherapeutics, which is achieved mainly through the absorption across lymphatic vessels. In this paper, the drug transport and lymphatic uptake through a three-dimensional hybrid discrete-continuum vessel network in the skin tissue are investigated through high-fidelity numerical simulations. We find that the local lymphatic uptake through the explicit vessels significantly affects macroscopic drug absorption. The diffusion of drug solute through the explicit vessel network affects the lymphatic uptake after the injection. This effect, however, cannot be captured using previously developed continuum models. The lymphatic uptake is dominated by the convection due to lymphatic drainage driven by the pressure difference, which is rarely studied in experiments and simulations. Furthermore, the effects of injection volume and depth on the lymphatic uptake are investigated in a multi-layered domain. We find that the injection volume significantly affects the rate of lymphatic uptake through the heterogeneous vessel network, while the injection depth has little influence, which is consistent with the experimental results. At last, the binding and metabolism of drug molecules are studied to bridge the simulations to the drug clearance experients. We provide a new approach to study the diffusion and convection of drug molecules into the lymphatic system through the hybrid vessel network.

Computational pulmonary edema: A microvascular model of alveolar capillary and interstitial flow

We present a microvascular model of fluid transport in the alveolar septa related to pulmonary edema. It consists of a two-dimensional capillary sheet coursing by several alveoli. The alveolar epithelial membrane runs parallel to the capillary endothelial membrane with an interstitial layer in between, making one long septal tract. A coupled system of equations is derived using lubrication theory for the capillary blood, Darcy flow for the porous media of the interstitium, a passive alveolus, and the Starling equation at both membranes. Case examples include normal physiology, cardiogenic pulmonary edema, noncardiogenic edema Acute Respiratory Distress Syndrome (ARDS) and hypoalbuminemia, and the effects of positive end expiratory pressure. COVID-19 has dramatically increased ARDS in the world population, raising the urgency for such a model to create an analytical framework. Under normal conditions, the fluid exits the alveolus, crosses the interstitium, and enters the capillary. For edema, this crossflow is reversed with the fluid leaving the capillary and entering the alveolus. Because both the interstitial and capillary pressures decrease downstream, the reversal can occur within a single septal tract, with edema upstream and clearance downstream. Overall, the interstitial pressures are found to be significantly more positive than values used in the traditional physiological literature that creates steep gradients near the upstream and downstream end outlets, driving significant flows toward the distant lymphatics. This new physiological flow may provide a possible explanation to the puzzle, noted since 1896, of how pulmonary lymphatics can function so far from the alveoli: the interstitium can be self-clearing.

An in silico derived dosage and administration guide for effective thermochemical ablation of biological tissues with simultaneous injection of acid and base

BACKGROUND AND OBJECTIVES

Thermochemical ablation (TCA) is a thermal ablation technique involving the injection of acid and base, either sequentially or simultaneously, into the target tissue. TCA remains at the conceptual stage with existing studies unable to provide recommendations on the optimum injection rate, and reagent concentration and volume. Limitations in current experimental methodology have prevented proper elucidation of the thermochemical processes inside the tissue during TCA. Nevertheless, the computational TCA framework developed recently by Mak et al. [Mak et al., Computers in Biology and Medicine, 2022, 145:105494] has opened new avenues in the development of TCA. Specifically, a recommended safe dosage is imperative in driving TCA research beyond the conceptual stage.

METHODS

The aforesaid computational TCA framework for sequential injection was applied and adapted to simulate TCA with simultaneous injection of acid and base at equimolar and equivolume. The developed framework, which describes the flow of acid and base, their neutralisation, the rise in tissue temperature and the formation of thermal damage, was solved numerically using the finite element method. The framework will be used to investigate the effects of injection rate, reagent concentration, volume and type (weak/strong acid-base combination) on temperature rise and thermal coagulation formation.

RESULTS

A higher injection rate resulted in higher temperature rise and larger thermal coagulation. Reagent concentration of 7500 mol/m³ was found to be optimum in producing considerable thermal coagulation without the risk of tissue overheating. Thermal coagulation volume was found to be consistently larger than the total volume of acid and base injected into the tissue, which is beneficial as it reduces the risk of chemical burn injury. Three multivariate second-order polynomials that express the targeted coagulation volume as functions of injection rate and reagent volume, for the weak-weak, weak-strong and strong-strong acid-base combinations were also derived based on the simulated data.

CONCLUSIONS

A guideline for a safe and effective implementation of TCA with simultaneous injection of acid and base was recommended based on the numerical results of the computational model developed. The guideline correlates the coagulation volume with the reagent volume and injection rate, and may be used by clinicians in determining the safe dosage of reagents and optimum injection rate to achieve a desired thermal coagulation volume during TCA.

Interstitial fluid pressure as an emerging biomarker in solid tumors

The physical microenvironment of cancer is characterized by elevated stiffness and tissue pressure, the main component of which is the interstitial fluid pressure (IFP). Elevated IFP is an established negative predictive and prognostic parameter, directly affecting malignant behavior and therapy response. As such, measurement of the IFP would allow to develop strategies aimed at engineering the physical microenvironment of cancer. Traditionally, IFP measurement required the use of invasive methods. Recent progress in dynamic and functional imaging methods such as dynamic contrast enhanced (DCE) magnetic resonance imaging and elastography, combined with numerical models and simulation, allows to comprehensively assess the biomechanical landscape of cancer, and may help to overcome physical barriers to drug delivery and immune cell infiltration. Here, we provide a comprehensive overview of the origin of elevated IFP, and its role in the malignant phenotype. Also, we review the methods used to measure IFP using invasive and imaging based methods, and highlight remaining obstacles and potential areas of progress in order to implement IFP measurement in clinical practice.

A spatiotemporal multi-scale computational model for FDG PET imaging at different stages of tumor growth and angiogenesis

A deeper understanding of the tumor microenvironment (TME) and its role in metabolic activity at different stages of vascularized tumors can provide useful insights into cancer progression and better support clinical assessments. In this study, a robust and comprehensive multi-scale computational model for spatiotemporal transport of F-18 fluorodeoxyglucose (FDG) is developed to incorporate important aspects of the TME, spanning subcellular-, cellular-, and tissue-level scales. Our mathematical model includes biophysiological details, such as radiopharmaceutical transport within interstitial space via convection and diffusion mechanisms, radiopharmaceutical exchange between intracellular and extracellular matrices by glucose transporters, cellular uptake of radiopharmaceutical, as well as its intracellular phosphorylation by the enzyme. Further, to examine the effects of tumor size by varying microvascular densities (MVDs) on FDG dynamics, four different capillary networks are generated by angiogenesis modeling. Results demonstrate that as tumor grows, its MVD increases, and hence, the spatiotemporal distribution of total FDG uptake by tumor tissue changes towards a more homogenous distribution. In addition, spatiotemporal distributions in tumor with lower MVD have relatively smaller magnitudes, due to the lower diffusion rate of FDG as well as lower local intravenous FDG release. Since mean standardized uptake value (SUV_mean) differs at various stages of microvascular networks with different tumor sizes, it may be meaningful to normalize the measured values by tumor size and the MVD prior to routine clinical reporting. Overall, the present framework has the potential for more accurate investigation of biological phenomena within TME towards personalized medicine.

Drug delivery through nanoparticles in solid tumors: a mechanistic understanding

Aim: In this study, the main goal was to apply a multi-scale computational model in evaluating nano-sized drug-delivery systems, following extracellular drug release, into solid tumors in order to predict treatment efficacy. Methods: The impact of several parameters related to tumor (size, shape, vessel-wall pore size, and necrotic core size) and therapeutic agents (size of nanoparticles, binding affinity of drug, drug release rate from nanoparticles) are examined in detail. Results: This study illustrates that achieving a higher treatment efficacy requires smaller nanoparticles (NPs) or a low binding affinity and drug release rate. Long-term analysis finds that a slow release rate in extracellular space does not always improve treatment efficacy compared with a rapid release rate; NP size as well as binding affinity of drug are also highly influential. Conclusions: The presented methodology can be used as a step forward towards optimization of patient-specific nanomedicine plans.

A computational framework to simulate the thermochemical process during thermochemical ablation of biological tissues

Thermochemical ablation (TCA) is a thermal ablation therapy that utilises heat released from acid-base neutralisation reaction to destroy tumours. This procedure is a promising low-cost solution to existing thermal ablation treatments such as radiofrequency ablation (RFA) and microwave ablation (MWA). Studies have demonstrated that TCA can produce thermal damage that is on par with RFA and MWA when employed properly. Nevertheless, TCA remains a concept that is tested only in a few animal trials due to the risks involved as the result of uncontrolled infusion and incomplete acid-base reaction. In this study, a computational framework that simulates the thermochemical process of TCA is developed. The proposed framework consists of three physics, namely chemical flow, neutralisation reaction and heat transfer. An important parameter in the TCA framework is the neutralisation reaction rate constant, which has values in the order of 10⁸ m³/(mol⋅s). The present study will demonstrate that since the rate constant impacts only the rate and direction of the reaction but has little influence on the extent of reaction, it is possible to replicate the thermochemical process of TCA by employing significantly smaller values of rate constant that are numerically tractable. Comparisons of the numerical results against experimental studies from the literature supports this. The aim of this framework is for researchers to advance and develop TCA to gain an in-depth understanding of the fundamental mechanisms of TCA and to develop a safe treatment protocol of TCA in the hope of advancing TCA into clinical trials.

Numerical Investigation on the Anti-Angiogenic Therapy-Induced Normalization in Solid Tumors

This study numerically analyzes the fluid flow and solute transport in a solid tumor to comprehensively examine the consequence of normalization induced by anti-angiogenic therapy on drug delivery. The current study leads to a more accurate model in comparison to previous research, as it incorporates a non-homogeneous real-human solid tumor including necrotic, semi-necrotic, and well-vascularized regions. Additionally, the model considers the effects of concurrently chemotherapeutic agents (three macromolecules of IgG, F(ab')2, and F(ab')) and different normalization intensities in various tumor sizes. Examining the long-term influence of normalization on the quality of drug uptake by necrotic area is another contribution of the present study. Results show that normalization decreases the interstitial fluid pressure (IFP) and spreads the pressure gradient and non-zero interstitial fluid velocity (IFV) into inner areas. Subsequently, wash-out of the drug from the tumor periphery is decreased. It is also demonstrated that normalization can improve the distribution of solute concentration in the interstitium. The efficiency of normalization is introduced as a function of the time course of perfusion, which depends on the tumor size, drug type, as well as normalization intensity, and consequently on the dominant mechanism of drug delivery. It is suggested to accompany anti-angiogenic therapy by F(ab') in large tumor size (Req=2.79  cm) to improve reservoir behavior benefit from normalization. However, IgG is proposed as the better option in the small tumor (Req=0.46  cm), in which normalization finds the opportunity of enhancing uniformity of IgG average exposure by 22%. This study could provide a perspective for preclinical and clinical trials on how to take advantage of normalization, as an adjuvant treatment, in improving drug delivery into a non-homogeneous solid tumor.

Computational modeling of PET tracer distribution in solid tumors integrating microvasculature

BACKGROUND

We present computational modeling of positron emission tomography radiotracer uptake with consideration of blood flow and interstitial fluid flow, performing spatiotemporally-coupled modeling of uptake and integrating the microvasculature. In our mathematical modeling, the uptake of fluorodeoxyglucose F-18 (FDG) was simulated based on the Convection-Diffusion-Reaction equation given its high accuracy and reliability in modeling of transport phenomena. In the proposed model, blood flow and interstitial flow are solved simultaneously to calculate interstitial pressure and velocity distribution inside cancer and normal tissues. As a result, the spatiotemporal distribution of the FDG tracer is calculated based on velocity and pressure distributions in both kinds of tissues.

RESULTS

Interstitial pressure has maximum value in the tumor region compared to surrounding tissue. In addition, interstitial fluid velocity is extremely low in the entire computational domain indicating that convection can be neglected without effecting results noticeably. Furthermore, our results illustrate that the total concentration of FDG in the tumor region is an order of magnitude larger than in surrounding normal tissue, due to lack of functional lymphatic drainage system and also highly-permeable microvessels in tumors. The magnitude of the free tracer and metabolized (phosphorylated) radiotracer concentrations followed very different trends over the entire time period, regardless of tissue type (tumor vs. normal).

CONCLUSION

Our spatiotemporally-coupled modeling provides helpful tools towards improved understanding and quantification of in vivo preclinical and clinical studies.

Evaluation of solid tumor response to sequential treatment cycles via a new computational hybrid approach

The development of an in silico approach that evaluates and identifies appropriate treatment protocols for individuals could help grow personalized treatment and increase cancer patient lifespans. With this motivation, the present study introduces a novel approach for sequential treatment cycles based on simultaneously examining drug delivery, tumor growth, and chemotherapy efficacy. This model incorporates the physical conditions of tumor geometry, including tumor, capillary network, and normal tissue assuming real circumstances, as well as the intravascular and interstitial fluid flow, drug concentration, chemotherapy efficacy, and tumor recurrence. Three treatment approaches-maximum tolerated dose (MTD), metronomic chemotherapy (MC), and chemo-switching (CS)-as well as different chemotherapy schedules are investigated on a real tumor geometry extracted from image. Additionally, a sensitivity analysis of effective parameters of drug is carried out to evaluate the potential of using different other drugs in cancer treatment. The main findings are: (i) CS, MC, and MTD have the best performance in reducing tumor cells, respectively; (ii) multiple doses raise the efficacy of drugs that have slower clearance, higher diffusivity, and lower to medium binding affinities; (iii) the suggested approach to eradicating tumors is to reduce their cells to a predetermined rate through chemotherapy and then apply adjunct therapy.

How does saline backflow affect the treatment of saline-infused radiofrequency ablation?

BACKGROUND AND OBJECTIVE

Saline infusion is applied together with radiofrequency ablation (RFA) to enlarge the ablation zone. However, one of the issues with saline-infused RFA is backflow, which spreads saline along the insertion track. This raises the concern of not only thermally ablating the tissue within the backflow region, but also the loss of saline from the targeted tissue, which may affect the treatment efficacy.

METHODS

In the present study, 2D axisymmetric models were developed to investigate how saline backflow influence saline-infused RFA and whether the aforementioned concerns are warranted. Saline-infused RFA was described using the dual porosity-Joule heating model. The hydrodynamics of backflow was described using Poiseuille law by assuming the flow to be similar to that in a thin annulus. Backflow lengths of 3, 4.5, 6 and 9 cm were considered.

RESULTS

Results showed that there is no concern of thermally ablating the tissue in the backflow region. This is due to the Joule heating being inversely proportional to distance from the electrode to the fourth power. Results also indicated that larger backflow lengths led to larger growth of thermal damage along the backflow region and greater decrease in coagulation volume. Hence, backflow needs to be controlled to ensure an effective treatment of saline-infused RFA.

CONCLUSIONS

There is no risk of ablating tissues around the needle insertion track due to backflow. Instead, the risk of underablation as a result of the loss of saline due to backflow was found to be of greater concern.

Transport and lymphatic uptake of monoclonal antibodies after subcutaneous injection

The subcutaneous injection has emerged to become a feasible self-administration practice for biotherapeutics due to the patient comfort and cost-effectiveness. However, the available knowledge about transport and absorption of these agents after subcutaneous injection is limited. Here, a mathematical framework to study the subcutaneous drug delivery of mAbs from injection to lymphatic uptake is presented. A three-dimensional poroelastic model is exploited to find the biomechanical response of the tissue by taking into account tissue deformation during the injection. The results show that including tissue deformability noticeably changes tissue poromechanical response due to the significant dependence of interstitial pressure on the tissue deformation. Moreover, the importance of the amount of lymph fluid at the injection site and the injection rate on the drug uptake to lymphatic capillaries is highlighted. Finally, variability of lymphatic uptake due to uncertainty in parameters including tissue poromechanical and lymphatic absorption parameters is evaluated. It is found that interstitial pressure due to injection is the major contributing factor in short-term lymphatic absorption, while the amount of lymph fluid at the site of injection determines the long-term absorption of the drug. Finally, it is shown that the lymphatic uptake results are consistent with experimental data available in the literature.

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.

A computational model of glioma reveals opposing, stiffness-sensitive effects of leaky vasculature and tumor growth on tissue mechanical stress and porosity

A biphasic computational model of a growing, vascularized glioma within brain tissue was developed to account for unique features of gliomas, including soft surrounding brain tissue, their low stiffness relative to brain tissue, and a lack of draining lymphatics. This model is the first to couple nonlinear tissue deformation with porosity and tissue hydraulic conductivity to study the mechanical interaction of leaky vasculature and solid growth in an embedded glioma. The present model showed that leaky vasculature and elevated interstitial fluid pressure produce tensile stress within the tumor in opposition to the compressive stress produced by tumor growth. This tensile effect was more pronounced in softer tissue and resulted in a compressive stress concentration at the tumor rim that increased when tumor was softer than host. Aside from generating solid stress, fluid pressure-driven tissue deformation decreased the effective stiffness of the tumor while growth increased it, potentially leading to elevated stiffness in the tumor rim. A novel prediction of reduced porosity at the tumor rim was corroborated by direct comparison with estimates from our in vivo imaging studies. Antiangiogenic and radiation therapy were simulated by varying vascular leakiness and tissue hydraulic conductivity. These led to greater solid compression and interstitial pressure in the tumor, respectively, the former of which may promote tumor infiltration of the host. Our findings suggest that vascular leakiness has an important influence on in vivo solid stress, stiffness, and porosity fields in gliomas given their unique mechanical microenvironment.

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.

Multiphysics Modeling and Simulation of Subcutaneous Injection and Absorption of Biotherapeutics: Sensitivity Analysis

PURPOSE

A multiphysics simulation model was recently developed to capture major physical and mechanical processes of local drug transport and absorption kinetics of subcutaneously injected monoclonal antibody (mAb) solutions. To further explore the impact of individual drug attributes and tissue characteristics on the tissue biomechanical response and drug mass transport upon injection, sensitivity analysis was conducted and reported.

METHOD

Various configurations of injection conditions, drug-associated attributes, and tissue properties were simulated with the developed multiphysics model. Simulation results were examined with regard to tissue deformation, porosity change, and spatiotemporal distributions of pressure, interstitial fluid flow, and drug concentration in the tissue.

RESULTS

Injection conditions and tissue properties were found influential on the mechanical response of tissue and interstitial fluid velocity to various extents, leading to distinct drug concentration profiles. Intrinsic tissue porosity, lymphatic vessel density, and drug permeability through the lymphatic membrane were particularly essential in determining the local absorption rate of an mAb injection.

CONCLUSION

The sensitivity analysis study may shed light on the product development of an mAb formulation, as well as on the future development of the simulation method.

Theoretical evaluation of enhanced gold nanoparticle delivery to PC3 tumors due to increased hydraulic conductivity or recovered lymphatic function after mild whole body hyperthermia

The objective of this study is to investigate the effect of hyperthermia-induced improvement of hydraulic conductivity and lymphatic function on both tumoral IFP reduction and nanoparticle delivery to PC3 tumors. We developed a theoretical model for nanoparticle transport in a tumor incorporating Starling's law, Darcy's law, transient convection, and diffusion of chemical species in porous media, and nanoparticle accumulation in tumors. Results have shown that both mechanisms were effective to decrease the IFP at the tumor center from 1600 Pa in the control without heating to 800 Pa in tumors with whole body heating. IFP reductions not only elevate the nanoparticle concentration in the tumor, but also result in a more uniform nanoparticle concentration in the tumor than that in the control without heating. Due to the IFP reductions at the tumor center and/or local blood perfusion increases, the final amount of accumulated nanoparticles in the tumor increased by more than 35-95% when compared to the control without heating. We conclude that increases in the hydraulic conductivity and recovery of lymphatic functions are possible mechanisms that lead to IFP reductions and enhancement in nanoparticle deposition in PC3 tumors observed in our in vivo experimental studies.

Role of saline concentration during saline-infused radiofrequency ablation: Observation of secondary Joule heating along the saline-tissue interface

Infusion of saline prior to radiofrequency ablation (RFA) is known to enlarge the thermal coagulation zone. The abundance of ions in saline elevate the electrical conductivity of the saline-saturated region. This promotes greater electric current flow inside the tissue, which increases the amount of RF energy deposition and subsequently enlarges the coagulation zone. In theory, infusion of higher concentration of saline should lead to larger coagulation zone due to the greater number of ions. Nevertheless, existing studies on the effects of concentration on saline-infused RFA have been conflicting, with the exact role of saline concentration yet to be fully elucidated. In this paper, computational models of saline-infused RFA were developed to investigate the role of saline concentration on the outcome of saline-infused RFA. The elevation in tissue electrical conductivity was modelled using the microscopic mixture model, while RFA was modelled using the coupled dual porosity-Joule heating model. Results obtained indicated that the presence of a concentration threshold to which no further elevation in tissue electrical conductivity and enlargement in thermal coagulation can occur. This threshold was determined to be at 15% NaCl. Analysis of the Joule heating distribution revealed the presence of a secondary Joule heating site located along the interface between wet and dry tissue. This secondary Joule heating was responsible for the enlargement in coagulation volume and its rapid growth phase during ablation.

Drug delivery to solid tumors with heterogeneous microvascular networks: Novel insights from image-based numerical modeling

The present study examines chemotherapy by incorporating multi-scale mathematical modeling to predict drug delivery and its effects. This approach leads to a more-realistic physiological tumor model than is possible with previous approaches, as it obtains the capillary network geometry from an image, and also considers the tumor's necrotic core, drug binding, and cellular uptake. Modeling of the fluid flow and drug transport is then performed in the extracellular matrix. The results demonstrate a 10% drop in the fraction of killed cancer cells 69% rather than the 79% reported earlier for a tumor of similar geometry a more-accurate value. This study examines how tumor-related parameters including the necrotic core size and tumor size, and also drug-related parameters drug dosage, binding affinity of drug, and drug degradation can affect the delivery of the drug to solid tumors. Results indicate that concentration of drug are high in the tumor, low in normal tissue, and remarkably low in the necrotic core. Results also offer a treatment of tumors with smaller necrotic core. Tumor size, which implies the tumor progression, has a considerable impact on treatment outcomes, so to be more effective, treatment should be applied at a specific size of tumor. It is demonstrated that binding affinity of drugs to cell-surface receptors and drug dosage have significant impact on treatment efficacy, so they should be regulated based on a balanced quantification between maximum treatment efficacy and minimum side effects. On the other hand, considering the effects of drug degradation in the model has not significant effect on treatment efficacy. The findings of the present study provide insight into the mechanism of drug delivery to solid tumors based on analyzing the effective parameters and modeling how their behavior in the tumor microenvironment affects treatment efficacy.

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.

Shape-shifting thermal coagulation zone during saline-infused radiofrequency ablation: A computational study on the effects of different infusion location

BACKGROUND AND OBJECTIVE

The majority of the studies on radiofrequency ablation (RFA) have focused on enlarging the size of the coagulation zone. An aspect that is crucial but often overlooked is the shape of the coagulation zone. The shape is crucial because the majority of tumours are irregularly-shaped. In this paper, the ability to manipulate the shape of the coagulation zone following saline-infused RFA by altering the location of saline infusion is explored.

METHODS

A 3D model of the liver tissue was developed. Saline infusion was described using the dual porosity model, while RFA was described using the electrostatic and bioheat transfer equations. Three infusion locations were investigated, namely at the proximal end, the middle and the distal end of the electrode. Investigations were carried out numerically using the finite element method.

RESULTS

Results indicated that greater thermal coagulation was found in the region of tissue occupied by the saline bolus. Infusion at the middle of the electrode led to the largest coagulation volume followed by infusion at the proximal and distal ends. It was also found that the ability to delay roll-off, as commonly associated with saline-infused RFA, was true only for the case when infusion is carried out at the middle. When infused at the proximal and distal ends, the occurrence of roll-off was advanced. This may be due to the rapid and more intense heating experienced by the tissue when infusion is carried out at the electrode ends where Joule heating is dominant.

CONCLUSION

Altering the location of saline infusion can influence the shape of the coagulation zone following saline-infused RFA. The ability to 'shift' the coagulation zone to a desired location opens up great opportunities for the development of more precise saline-infused RFA treatment that targets specific regions within the tissue.

Magnetic resonance imaging based modeling of microvascular perfusion in patients with peripheral artery disease

Peripheral artery disease (PAD) is associated with an increased risk of adverse cardiovascular events, impaired lower extremity blood flow and microvascular perfusion abnormalities in the calf muscles which can be determined with contrast-enhanced magnetic resonance imaging (CE-MRI). We developed a computational model of the microvascular perfusion in the calf muscles. We included 20 patients (10 PAD, 10 controls) and utilized the geometry, mean signal intensity and arterial input functions from CE-MRI calf muscle perfusion scans. The model included the microvascular pressure (pv), outflow filtration coefficient (OFC), transfer rate constant (kt), porosity (φ), and the interstitial permeability (Ktissue). Parameters were fitted and the simulations were compared across PAD patients and controls. Intra-observer reproducibility of the simulated mean signal intensities was excellent (intraclass correlation coefficients >0.995). kt and Ktissue were higher in PAD patients compared with controls (4.72 interquartile range (IQR) 3.33, 5.56 vs. 2.47 IQR 2.10, 2.85; p = 0.003; and 3.68 IQR 3.18, 4.41 vs. 1.81 IQR 1.81, 1.81; p < 0.001). Conversely, porosity (φ) was lower in PAD patients compared with controls (0.52 IQR 0.49, 0.54 vs. 0.61 IQR 0.58, 0.64; p = 0.016). Porosity (φ) was correlated with the ankle brachial index (r = 0.64, p = 0.011). The proposed computational microvascular model is robust and reproducible, and essential model parameters differ significantly between PAD patients and controls.

A 3D CFD model of the interstitial fluid pressure and drug distribution in heterogeneous tumor nodules during intraperitoneal chemotherapy

Although intraperitoneal chemotherapy (IPC) has evolved into an established treatment modality for patients with peritoneal metastasis (PM), drug penetration into tumor nodules remains limited. Drug transport during IPC is a complex process that depends on a large number of different parameters (e.g. drug, dose, tumor size, tumor pressure, tumor vascularization). Mathematical modeling allows for a better understanding of the processes that underlie drug transport and the relative importance of the parameters influencing it. In this work, we expanded our previously developed 3D Computational Fluid Dynamics (CFD) model of the drug mass transport in idealized tumor nodules during IP chemotherapy to include realistic tumor geometries and spatially varying vascular properties. DCE-MRI imaging made it possible to distinguish between tumorous tissues, healthy surrounding tissues and necrotic zones based on differences in the vascular properties. We found that the resulting interstitial pressure profiles within tumors were highly dependent on the irregular geometries and different zones. The tumor-specific cisplatin penetration depths ranged from 0.32 mm to 0.50 mm. In this work, we found that the positive relationship between tumor size and IFP does not longer hold in the presence of zones with different vascular properties, while we did observe a positive relationship between the percentage of viable tumor tissue and the maximal IFP. Our findings highlight the importance of incorporating both the irregular tumor geometries and different vascular zones in CFD models of IPC.

Modelling the transport of fluid through heterogeneous, whole tumours in silico

Cancers exhibit spatially heterogeneous, unique vascular architectures across individual samples, cell-lines and patients. This inherently disorganised collection of leaky blood vessels contribute significantly to suboptimal treatment efficacy. Preclinical tools are urgently required which incorporate the inherent variability and heterogeneity of tumours to optimise and engineer anti-cancer therapies. In this study, we present a novel computational framework which incorporates whole, realistic tumours extracted ex vivo to efficiently simulate vascular blood flow and interstitial fluid transport in silico for validation against in vivo biomedical imaging. Our model couples Poiseuille and Darcy descriptions of vascular and interstitial flow, respectively, and incorporates spatially heterogeneous blood vessel lumen and interstitial permeabilities to generate accurate predictions of tumour fluid dynamics. Our platform enables highly-controlled experiments to be performed which provide insight into how tumour vascular heterogeneity contributes to tumour fluid transport. We detail the application of our framework to an orthotopic murine glioma (GL261) and a human colorectal carcinoma (LS147T), and perform sensitivity analysis to gain an understanding of the key biological mechanisms which determine tumour fluid transport. Finally we mimic vascular normalization by modifying parameters, such as vascular and interstitial permeabilities, and show that incorporating realistic vasculatures is key to modelling the contrasting fluid dynamic response between tumour samples. Contrary to literature, we show that reducing tumour interstitial fluid pressure is not essential to increase interstitial perfusion and that therapies should seek to develop an interstitial fluid pressure gradient. We also hypothesise that stabilising vessel diameters and permeabilities are not key responses following vascular normalization and that therapy may alter interstitial hydraulic conductivity. Consequently, we suggest that normalizing the interstitial microenvironment may provide a more effective means to increase interstitial perfusion within tumours.

The structure of tumours varies widely, with dense and chaotically-formed networks of blood vessels that differ between each individual tumour and even between different regions of the same tumour. This atypical environment can inhibit the delivery of anti-cancer therapies. Computational tools are urgently required which facilitate a deeper understanding of the relationship between blood vessel architectures and therapeutic response. We have developed a computational framework which integrates the complex tumour vascular architecture to predict fluid transport across all lengths scales in whole tumours. We apply our model to two tumour cell-lines and show that differences in their inherent vascular structures influence flow through cancerous tissue. We also use our platform to predict the fluid dynamic response following vascular normalization therapy in realistic, static tumour networks and show that the response is dependent on tumour vascular architecture. We hypothesise that therapy may alter the permeability of interstitial tissue to fluid transport and show that lowering interstitial fluid pressure is not a necessary therapeutic outcome to increase tumour perfusion.

Comparison of transport of chemotherapeutic drugs in voxelized heterogeneous model of human brain tumor

Systemic administration of chemotherapeutic drugs is widely used in the treatment of cancer. However, a good understanding of drug transport barriers that influence the treatment efficacy is still lacking. In this study, a voxelized numerical model based on dynamic contrast enhanced-magnetic resonance imaging (DCE-MRI) and computational fluid dynamics (CFD) is employed to study the transport and efficacy of three different chemotherapeutic drugs, namely methotrexate, doxorubicin and cisplatin in human brain tumors. DCE-MRI data provides realistic heterogeneous vasculature of the tumor, the permeability of tissue to contrast agent, interstitial volume fraction (porosity) of the tissue and patient-specific arterial input function (AIF). The permeability of tissue to aforementioned drugs is determined by correlating it with the permeability of tissue to the contrast agent. The model is employed to simulate drug concentration in the tissue and compare the effect of heterogeneous vasculature on the distribution of the drugs in the tumor. The drug accumulation is observed to be higher in high permeability areas initially, and in higher porosity areas at later times. Furthermore, it is observed that methotrexate remains in the interstitial space of the tumor in higher concentration for a longer duration as compared to other two drugs, facilitating more tumor cell killing.

Image-based spatio-temporal model of drug delivery in a heterogeneous vasculature of a solid tumor - Computational approach

The solute transport distribution in a tumor is an important criterion in the evaluation of the cancer treatment efficacy. The fraction of killed cells after each treatment can quantify the therapeutic effect and plays as a helpful tool to evaluate the chemotherapy treatment schedules. In the present study, an image-based spatio-temporal computational model of a solid tumor is provided for calculation of interstitial fluid flow and solute transport. Current model incorporates heterogeneous microvasculature for angiogenesis instead of synthetic mathematical modeling. In this modeling process, a comprehensive model according to Convection-Diffusion-Reaction (CDR) equations is employed due to its high accuracy for simulating the binding and the uptake of the drug by tumor cells. Based on the velocity and the pressure distribution, transient distribution of the different drug concentrations (free, bound, and internalized) is calculated. Then, the fraction of killed cells is obtained according to the internalized concentration. Results indicate the dependence of the drug distribution on both time and space, as well as the microvasculature density. Free and bound drug concentration have the same trend over time, whereas, internalized and total drug concentration increases over time and reaches a constant value. The highest amount of concentration occurred in the tumor region due to the higher permeability of the blood vessels. Moreover, the fraction of killed cells is approximately 78.87% and 24.94% after treatment with doxorubicin for cancerous and normal tissues, respectively. In general, the presented methodology may be applied in the field of personalized medicine to optimize patient-specific treatments. Also, such image-based modeling of solid tumors can be used in laboratories that working on drug delivery and evaluating new drugs before using them for any in vivo or clinical studies.

Toward a noninvasive estimate of interstitial fluid pressure by dynamic contrast-enhanced MRI in a rat model of cerebral tumor

PURPOSE

This study demonstrates a DCE-MRI estimate of tumor interstitial fluid pressure (TIFP) and hydraulic conductivity in a rat model of glioblastoma, with validation against an invasive wick-in-needle (WIN) technique. An elevated TIFP is considered a mark of aggressiveness, and a decreased TIFP a predictor of response to therapy.

METHODS

The DCE-MRI studies were conducted in 36 athymic rats (controls and posttreatment animals) with implanted U251 cerebral tumors, and with TIFP measured using a WIN method. Using a model selection paradigm and a novel application of Patlak and Logan plots to DCE-MRI data, the MRI parameters required for estimating TIFP noninvasively were estimated. Two models, a fluid-mechanical model and a multivariate empirical model, were used for estimating TIFP, as verified against WIN-TIFP.

RESULTS

Using DCE-MRI, the mean estimated hydraulic conductivity (MRI-K) in U251 tumors was (2.3 ± 3.1) × 10^-5 (mm² /mmHg-s) in control studies. Significant positive correlations were found between WIN-TIFP and MRI-TIFP in both mechanical and empirical models. For instance, in the control group of the fluid-mechanical model, MRI-TIFP was a strong predictor of WIN-TIFP (R²  = 0.76, p < .0001). A similar result was found in the bevacizumab-treated group of the empirical model (R²  = 0.93, p = .014).

CONCLUSION

This research suggests that MRI dynamic studies contain enough information to noninvasively estimate TIFP in this, and possibly other, tumor models, and thus might be used to assess tumor aggressiveness and response to therapy.

Numerical modeling of nanodrug distribution in tumors with heterogeneous vasculature

The distribution and accumulation of nanoparticle dosage in a tumor are important in evaluating the effectiveness of cancer treatment. The cell survival rate can quantify the therapeutic effect, and the survival rates after multiple treatments are helpful to evaluate the efficacy of a chemotherapy plan. We developed a mathematical tumor model based on the governing equations describing the fluid flow and particle transport to investigate the drug transportation in a tumor and computed the resulting cumulative concentrations. The cell survival rate was calculated based on the cumulative concentration. The model was applied to a subcutaneous tumor with heterogeneous vascular distributions. Various sized dextrans and doxorubicin were respectively chosen as the nanodrug carrier and the traditional chemotherapeutic agent for comparison. The results showed that: 1) the largest nanoparticle drug in the current simulations yielded the highest cumulative concentration in the well vascular region, but second lowest in the surrounding normal tissues, which implies it has the best therapeutic effect to tumor and at the same time little harmful to normal tissue; 2) on the contrary, molecular chemotherapeutic agent produced the second lowest cumulative concentration in the well vascular tumor region, but highest in the surrounding normal tissue; 3) all drugs have very small cumulative concentrations in the tumor necrotic region, where drug transport is solely through diffusion. This might mean that it is hard to kill tumor stem cells hiding in it. The current model indicated that the effectiveness of the anti-tumor drug delivery was determined by the interplay of the vascular density and nanoparticle size, which governs the drug transport properties. The use of nanoparticles as anti-tumor drug carriers is generally a better choice than molecular chemotherapeutic agent because of its high treatment efficiency on tumor cells and less damage to normal tissues.

Investigation of Biotransport in a Tumor With Uncertain Material Properties Using a Nonintrusive Spectral Uncertainty Quantification Method

In this study, statistical models are developed for modeling uncertain heterogeneous permeability and porosity in tumors, and the resulting uncertainties in pressure and velocity fields during an intratumoral injection are quantified using a nonintrusive spectral uncertainty quantification (UQ) method. Specifically, the uncertain permeability is modeled as a log-Gaussian random field, represented using a truncated Karhunen-Lòeve (KL) expansion, and the uncertain porosity is modeled as a log-normal random variable. The efficacy of the developed statistical models is validated by simulating the concentration fields with permeability and porosity of different uncertainty levels. The irregularity in the concentration field bears reasonable visual agreement with that in MicroCT images from experiments. The pressure and velocity fields are represented using polynomial chaos (PC) expansions to enable efficient computation of their statistical properties. The coefficients in the PC expansion are computed using a nonintrusive spectral projection method with the Smolyak sparse quadrature. The developed UQ approach is then used to quantify the uncertainties in the random pressure and velocity fields. A global sensitivity analysis is also performed to assess the contribution of individual KL modes of the log-permeability field to the total variance of the pressure field. It is demonstrated that the developed UQ approach can effectively quantify the flow uncertainties induced by uncertain material properties of the tumor.

Transport of Liposome Encapsulated Drugs in Voxelized Computational Model of Human Brain Tumors

There are many obstacles in the transport of chemotherapeutic drugs to tumor cells that lead to irregular and non-uniform uptake of drugs inside tumors. The study of these transport problems will help with accurate prediction of drug transport and optimizing treatment strategy. To this end, liposome mediated drug delivery has emerged as an excellent anticancer therapy due to its ability to deliver drugs at site of action and reducing the chances of side effects to the healthy tissues. In this paper, a computational fluid dynamics (CFD) model based on realistic vasculature of human brain tumor is presented. This model utilizes dynamic contrast enhanced-magnetic resonance imaging (DCE-MRI) data to account for heterogeneity in tumor vasculature. Porosity of the interstitial space inside the tumor and normal tissue is determined voxel-wise by processing the DCE-MRI images by general tracer kinetic model (GTKM). The CFD model is applied to predict transport of two different types of liposomes (stealth and conventional) in tumors. The amount of accumulated liposomes is compared with accumulated free drug (doxorubicin) in the interstitial space. Simulation results indicate that stealth liposomes accumulate more and remain for longer periods of time in tumors as compared with conventional liposomes and free drug. The present model provides us a qualitative and quantitative examination on the transport and deposition of liposomes as well as free drugs in actual human brain tumors.