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 simulation of the effect of necrosis area in systemic delivery of magnetic nanoparticles in hyperthermia cancer treatment.

In a magnetic hyperthermia treatment, malignant cancerous cells are ablated by the heat production of magnetic nanoparticles (MNP) under an external magnetic field. This novel approach is a promising tool to eliminate the tumor cells by a higher temperature inside the tumor microenvironment. MNPs are needed inside the tumor microenvironment to increase the heat, and this could be possible with intravenous drug injection. However, tumors with necrosis regions are more resistant to drug penetration, and this can cause inadequate and non-homogeneous temperature distribution in the tumor. Hence, in this study, we used numerical methods to investigate the Spatio-temporal temperature field distribution in the necrotic tumor and its surrounding tissue. To this end, an intravenous bolus injection is used to simulate the effect of systemic drug delivery in tumors with necrosis region. Results show that the temperature field with the necrosis region with 10% of the tumor radius is more prone to higher temperature values. The hypoxia region is affected by the high temperature despite the necrosis region in the tumor. However, a broader necrosis region impedes drug penetration inside the inner layers of tumors, which leads to a lower heat generation by the MNPs. Results also demonstrate that only 15.5% of MNP concentration distributed to the necrosis with 50% of tumor radius, leading a temperature of 42∘C in the necrosis region, which is not sufficient for the tumor ablation. Therefore, the temperature distribution is dependant on the sizes of necrosis regions in tumors, and tumors with a larger necrotic region (over 20% of tumor radius) are challenging to treat with hyperthermia treatment. This study could help the future in vitro and in vivo studies of hyperthermia treatment in necrotic tumors.

Spatio-temporal investigation of doxorubicin in a 3D heterogeneous tumor microenvironment.

Doxorubicin (Adriamycin) is a type of chemotherapy drugs using to treat diseases such as breast cancer, bladder cancer, Kaposi's sarcoma, and lymphoma. Additionally, it can be first prescribed to reduce tumor size. The ratio of killed cells is varied depending on the clinical dosage regimen. Hence, the exact dosage of the drug must be administered to prevent the toxicity that could impair the immune system or leading to heart failure. In the present study, a 3D heterogeneous geometry with a solid tumor and healthy tissue is modeled for the drug delivery investigation. At the first stage, the physical properties of tumor microenvironment are obtained. Then, a five-compartmental model is used to evaluate the free, bound and internalized drug via the convection-diffusion-reaction (CDR) equation. Results are shown that a percent increase of 37.5% and 47.1% for the 75 mg m-2 to 50 mg m-2 in the AUC of bound drug and free drug concentration, respectively. The free and bound drugs have the same trend in time showing an apex at the earliest time of injection and then drops to the lowest amount about 9 hours after treatment. Moreover, the internalized drug has a different trend in time. It increases and reaches a constant amount of drug concentration in the cells. Besides, the fraction of surviving cells is also evaluated for both tumor and healthy tissues showing a 88.62% and 97.76% of surviving cells with 50 mg m-2 of doxorubicin after the treatment, respectively. This model is developed to predict the heterogenous distribution of doxorubicin in three different drug concentrations for patient-specific drug treatment. This model could be used for different drugs to show the rate of perfusion and the ability to kill cancerous cells regarding their different doses and toxicity effects.

Modeling of FMISO [F18] nanoparticle PET tracer in normal-cancerous tissue based on real clinical image.

Hypoxia as one of the principal properties of tumor cells is a reaction to the deprivation of oxygen. The location of tumor cells could be identified by assessment of oxygen and nutrient level in human body. Positron emission tomography (PET) is a well-known non-invasive method that is able to measure hypoxia based on the FMISO (Fluoromisonidazole) tracer dynamic. This paper aims to study the PET tracer concentration through convection-diffusion-reaction equations in a real human capillary-like network. A non-uniform oxygen pressure along the capillary path and convection mechanism for FMISO transport are taken into account to accurately model the characteristics of the tracer. To this end, a multi-scale model consists of laminar blood flow through the capillary network, interstitial pressure, oxygen pressure, FMISO diffusion and FMISO convection transport in the extravascular region is developed. The present model considers both normal and tumor tissue regions in computational domain. The accuracy of numerical model is verified with the experimental results available in the literature. The convection and diffusion types of transport mechanism are employed in order to calculate the concentration of FMISO in the normal and tumor sub-domain. The influences of intravascular oxygen pressure, FMISO transport mechanisms, capillary density and different types of tissue on the FMISO concentration have been investigated. According to result (Table 4) the convection mechanism of FMISO molecules transportation is negligible, but it causes more accuracy of the proposed model. The approach of present study can be employed in order to investigate the effects of various parameters, such as tumor shape, on the dynamic behavior of different PET tracers, such as FDG, can be extended to different case study problems, such as drug delivery.

Correction: The Vital Role of Blood Flow-Induced Proliferation and Migration in Capillary Network Formation in a Multiscale Model of Angiogenesis.

[This corrects the article DOI: 10.1371/journal.pone.0128878.].

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.

Blood flow and endothelial cell phenotype regulation during sprouting angiogenesis.

The role of the endothelial cell environment and shear stress induced by blood flow in phenotype determination and lumen formation has been clearly illustrated in recent studies. In the present work, a model is developed to map environmental and flow induced signals in sprouting angiogenesis to endothelial cell phenotype and lumen formation. To follow the endothelial cell lumen formation, its signaling pathway is incorporated in the present work within the phenotype determination pathway that has been recently utilized to model endothelial cell migration, proliferation, and apoptosis. Moreover, a signaling cascade for shear stress activation of endothelial cells is proposed and used for phenotype determination with activation of blood flow. A Boolean network model is employed to build a hybrid map for the relation between the endothelial cell environmental signals and the endothelial cell fate in sprouting angiogenesis with and without blood flow. This map is very useful in the development of models for sprouting angiogenesis. Moreover, this study shows that inhibition of intracellular signaling molecules, solely or in pairs, blocks angiogenic-signaling pathways and can be used to inhibit angiogenesis.

Activation of Apoptotic Signal in Endothelial Cells through Intracellular Signaling Molecules Blockade in Tumor-Induced Angiogenesis.

Tumor-induced angiogenesis is the bridge between avascular and vascular tumor growth phases. In tumor-induced angiogenesis, endothelial cells start to migrate and proliferate toward the tumor and build new capillaries toward the tumor. There are two stages for sprout extension during angiogenesis. The first stage is prior to anastomosis, when single sprouts extend. The second stage is after anastomosis when closed flow pathways or loops are formed and blood flows in the closed loops. Prior to anastomosis, biochemical and biomechanical signals from extracellular matrix regulate endothelial cell phenotype; however, after anastomosis, blood flow is the main regulator of endothelial cell phenotype. In this study, the critical signaling pathways of each stage are introduced. A Boolean network model is used to map environmental and flow induced signals to endothelial cell phenotype (proliferation, migration, apoptosis, and lumen formation). Using the Boolean network model, blockade of intracellular signaling molecules of endothelial cell is investigated prior to and after anastomosis and the cell fate is obtained in each case. Activation of apoptotic signal in endothelial cell can prevent the extension of new vessels and may inhibit angiogenesis. It is shown that blockade of a few signaling molecules in endothelial cell activates apoptotic signal that are proposed as antiangiogenic strategies.

The Vital Role of Blood Flow-Induced Proliferation and Migration in Capillary Network Formation in a Multiscale Model of Angiogenesis.

Sprouting angiogenesis and capillary network formation are tissue scale phenomena. There are also sub-scale phenomena involved in angiogenesis including at the cellular and intracellular (molecular) scales. In this work, a multiscale model of angiogenesis spanning intracellular, cellular, and tissue scales is developed in detail. The key events that are considered at the tissue scale are formation of closed flow path (that is called loop in this article) and blood flow initiation in the loop. At the cellular scale, growth, migration, and anastomosis of endothelial cells (ECs) are important. At the intracellular scale, cell phenotype determination as well as alteration due to blood flow is included, having pivotal roles in the model. The main feature of the model is to obtain the physical behavior of a closed loop at the tissue scale, relying on the events at the cellular and intracellular scales, and not by imposing physical behavior upon it. Results show that, when blood flow is considered in the loop, the anastomosed sprouts stabilize and elongate. By contrast, when the loop is modeled without consideration of blood flow, the loop collapses. The results obtained in this work show that proper determination of EC phenotype is the key for its survival.

Effect of fluid friction on interstitial fluid flow coupled with blood flow through solid tumor microvascular network.

A solid tumor is investigated as porous media for fluid flow simulation. Most of the studies use Darcy model for porous media. In Darcy model, the fluid friction is neglected and a few simplified assumptions are implemented. In this study, the effect of these assumptions is studied by considering Brinkman model. A multiscale mathematical method which calculates fluid flow to a solid tumor is used in this study to investigate how neglecting fluid friction affects the solid tumor simulation. The mathematical method involves processes such as blood flow through vessels and solute and fluid diffusion, convective transport in extracellular matrix, and extravasation from blood vessels. The sprouting angiogenesis model is used for generating capillary network and then fluid flow governing equations are implemented to calculate blood flow through the tumor-induced capillary network. Finally, the two models of porous media are used for modeling fluid flow in normal and tumor tissues in three different shapes of tumors. Simulations of interstitial fluid transport in a solid tumor demonstrate that the simplifications used in Darcy model affect the interstitial velocity and Brinkman model predicts a lower value for interstitial velocity than the values that Darcy model predicts.

Effect of tumor shape, size, and tissue transport properties on drug delivery to solid tumors.

BACKGROUND: The computational methods provide condition for investigation related to the process of drug delivery, such as convection and diffusion of drug in extracellular matrices, drug extravasation from microvessels or to lymphatic vessels. The information of this process clarifies the mechanisms of drug delivery from the injection site to absorption by a solid tumor. In this study, an advanced numerical method is used to solve fluid flow and solute transport equations simultaneously to investigate the effect of tumor shape and size on drug delivery to solid tumor. METHODS: The advanced mathematical model used in our previous work is further developed by adding solute transport equation to the governing equations. After applying appropriate boundary and initial conditions on tumor and surrounding tissue geometry, the element-based finite volume method is used for solving governing equations of drug delivery in solid tumor. Also, the effects of size and shape of tumor and some of tissue transport parameters such as effective pressure and hydraulic conductivity on interstitial fluid flow and drug delivery are investigated. RESULTS: Sensitivity analysis shows that drug delivery in prolate shape is significantly better than other tumor shapes. Considering size effect, increasing tumor size decreases drug concentration in interstitial fluid. This study shows that dependency of drug concentration in interstitial fluid to osmotic and intravascular pressure is negligible. CONCLUSIONS: This study shows that among diffusion and convection mechanisms of drug transport, diffusion is dominant in most different tumor shapes and sizes. In tumors in which the convection has considerable effect, the drug concentration is larger than that of other tumors at the same time post injection.