Effect of vascular normalization on drug delivery to different stages of tumor progression: In-silico analysis

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.

Localized radiotherapy of solid tumors using radiopharmaceutical loaded implantable system: insights from a mathematical model

Introduction

Computational models yield valuable insights into biological interactions not fully elucidated by experimental approaches. This study investigates an innovative spatiotemporal model for simulating the controlled release and dispersion of radiopharmaceutical therapy (RPT) using 177Lu-PSMA, a prostate-specific membrane antigen (PSMA) targeted radiopharmaceutical, within solid tumors via a dual-release implantable delivery system. Local delivery of anticancer agents presents a strategic approach to mitigate adverse effects while optimizing therapeutic outcomes.

Methods

This study evaluates various factors impacting RPT efficacy, including hypoxia region extension, binding affinity, and initial drug dosage, employing a novel 3-dimensional computational model. Analysis gauges the influence of these factors on radiopharmaceutical agent concentration within the tumor microenvironment. Furthermore, spatial and temporal radiopharmaceutical distribution within both the tumor and surrounding tissue is explored.

Results

Analysis indicates a significantly higher total concentration area under the curve within the tumor region compared to surrounding normal tissue. Moreover, drug distribution exhibits notably superior efficacy compared to the radiation source. Additionally, low microvascular density in extended hypoxia regions enhances drug availability, facilitating improved binding to PSMA receptors and enhancing therapeutic effectiveness. Reductions in the dissociation constant (KD) lead to heightened binding affinity and increased internalized drug concentration. Evaluation of initial radioactivities (7.1×107, 7.1×108, and 7.1×109 [Bq]) indicates that an activity of 7.1×108 [Bq] offers a favorable balance between tumor cell elimination and minimal impact on normal tissues.

Discussion

These findings underscore the potential of localized radiopharmaceutical delivery strategies and emphasize the crucial role of released drugs relative to the radiation source (implant) in effective tumor treatment. Decreasing the proximity of the drug to the microvascular network and enhancing its distribution within the tumor promote a more effective therapeutic outcome. The study furnishes valuable insights for future experimental investigations and clinical trials, aiming to refine medication protocols and minimize reliance on in vivo testing.

Ultrasound-mediated nano-sized drug delivery systems for cancer treatment: Multi-scale and multi-physics computational modeling

Computational modeling enables researchers to study and understand various complex biological phenomena in anticancer drug delivery systems (DDSs), especially nano-sized DDSs (NSDDSs). The combination of NSDDSs and therapeutic ultrasound (TUS), that is, focused ultrasound and low-intensity pulsed ultrasound, has made significant progress in recent years, opening many opportunities for cancer treatment. Multiple parameters require tuning and optimization to develop effective DDSs, such as NSDDSs, in which mathematical modeling can prove advantageous. In silico computational modeling of ultrasound-responsive DDS typically involves a complex framework of acoustic interactions, heat transfer, drug release from nanoparticles, fluid flow, mass transport, and pharmacodynamic governing equations. Owing to the rapid development of computational tools, modeling the different phenomena in multi-scale complex problems involved in drug delivery to tumors has become possible. In the present study, we present an in-depth review of recent advances in the mathematical modeling of TUS-mediated DDSs for cancer treatment. A detailed discussion is also provided on applying these computational models to improve the clinical translation for applications in cancer treatment. This article is categorized under: Nanotechnology Approaches to Biology > Nanoscale Systems in Biology Therapeutic Approaches and Drug Discovery > Nanomedicine for Oncologic Disease.

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.

Investigation of the evolution of tumor-induced microvascular network under the inhibitory effect of anti-angiogenic factor, angiostatin: A mathematical study

Anti-angiogenesis as a treatment strategy for normalizing the microvascular network of tumors is of great interest among researchers, especially in combination with chemotherapy or radiotherapy. According to the vital role that angiogenesis plays in tumor growth and in exposing the tumor to therapeutic agents, this work develops a mathematical framework to study the influence of angiostatin, a plasminogen fragment that shows the anti-angiogenic function, in the evolutionary behavior of tumor-induced angiogenesis. Angiostatin-induced microvascular network reformation is investigated in a two-dimensional space by considering two parent vessels around a circular tumor by a modified discrete angiogenesis model in different tumor sizes. The effects of imposing modifications on the existing model, i.e., the matrix-degrading enzyme effect, proliferation and death of endothelial cells, matrix density function, and a more realistic chemotactic function, are investigated in this study. Results show a decrease in microvascular density in response to the angiostatin. A functional relationship exists between angiostatin's ability to normalize the capillary network and tumor size or progression stage, such that capillary density decreases by 55%, 41%, 24%, and 13% in tumors with a non-dimensional radius of 0.4, 0.3, 0.2, and 0.1, respectively, after angiostatin administration.

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

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

Synthetic 18F-FDG PET Image Generation Using a Combination of Biomathematical Modeling and Machine Learning

Simple Summary

Training computer-assisted algorithms on medical images, particularly 18F-fluorodeoxyglucose (18F-FDG) positron emission tomography (PET) due to its excellent diagnostic accuracy, is difficult, considering small/fragmented samples or privacy concerns. In computer-vision, deep learning-based models, unlike the conventional data augmentation methods, are highly sought after for creating massive medical samples. For this reason, we developed a multi-scale computational framework to generate synthetic 18F-FDG PET images similar to the real ones in different stages of solid tumor growth and angiogenesis. The framework is developed based on the bio-physiological phenomena of FDG radiotracer uptake in solid tumors using a biomathematical model and a generative adversarial network (GAN)-based architecture. The non-invasive augmented 18F-FDG PET images can be used in clinical practice without the need to manage the patient data. In addition, our spatiotemporal mathematical model can calculate the distribution of various radiopharmaceuticals in different tumor-associated vasculatures.

Abstract

No previous works have attempted to combine generative adversarial network (GAN) architectures and the biomathematical modeling of positron emission tomography (PET) radiotracer uptake in tumors to generate extra training samples. Here, we developed a novel computational model to produce synthetic 18F-fluorodeoxyglucose (18F-FDG) PET images of solid tumors in different stages of progression and angiogenesis. First, a comprehensive biomathematical model is employed for creating tumor-induced angiogenesis, intravascular and extravascular fluid flow, as well as modeling of the transport phenomena and reaction processes of 18F-FDG in a tumor microenvironment. Then, a deep convolutional GAN (DCGAN) model is employed for producing synthetic PET images using 170 input images of 18F-FDG uptake in each of 10 different tumor microvascular networks. The interstitial fluid parameters and spatiotemporal distribution of 18F-FDG uptake in tumor and healthy tissues have been compared against previously published numerical and experimental studies, indicating the accuracy of the model. The structural similarity index measure (SSIM) and peak signal-to-noise ratio (PSNR) of the generated PET sample and the experimental one are 0.72 and 28.53, respectively. Our results demonstrate that a combination of biomathematical modeling and GAN-based augmentation models provides a robust framework for the non-invasive and accurate generation of synthetic PET images of solid tumors in different stages.

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.

Anti-COVID-19 Nanomaterials: Directions to Improve Prevention, Diagnosis, and Treatment

Following the announcement of the outbreak of COVID-19 by the World Health Organization, unprecedented efforts were made by researchers around the world to combat the disease. So far, various methods have been developed to combat this "virus" nano enemy, in close collaboration with the clinical and scientific communities. Nanotechnology based on modifiable engineering materials and useful physicochemical properties has demonstrated several methods in the fight against SARS-CoV-2. Here, based on what has been clarified so far from the life cycle of SARS-CoV-2, through an interdisciplinary perspective based on computational science, engineering, pharmacology, medicine, biology, and virology, the role of nano-tools in the trio of prevention, diagnosis, and treatment is highlighted. The special properties of different nanomaterials have led to their widespread use in the development of personal protective equipment, anti-viral nano-coats, and disinfectants in the fight against SARS-CoV-2 out-body. The development of nano-based vaccines acts as a strong shield in-body. In addition, fast detection with high efficiency of SARS-CoV-2 by nanomaterial-based point-of-care devices is another nanotechnology capability. Finally, nanotechnology can play an effective role as an agents carrier, such as agents for blocking angiotensin-converting enzyme 2 (ACE2) receptors, gene editing agents, and therapeutic agents. As a general conclusion, it can be said that nanoparticles can be widely used in disinfection applications outside in vivo. However, in in vivo applications, although it has provided promising results, it still needs to be evaluated for possible unintended immunotoxicity. Reviews like these can be important documents for future unwanted pandemics.

Mathematical Modeling of Targeted Drug Delivery Using Magnetic Nanoparticles during Intraperitoneal Chemotherapy

Intraperitoneal (IP) chemotherapy has emerged as a promising method for the treatment of peritoneal malignancies (PMs). However, microenvironmental barriers in the tumor limit the delivery of drug particles and their deep penetration into the tumor, leading to reduced efficiency of treatment. Therefore, new drug delivery systems should be developed to overcome these microenvironmental barriers. One promising technique is magnetically controlled drug targeting (MCDT) in which an external magnetic field is utilized to concentrate drug-coated magnetic nanoparticles (MNPs) to the desired area. In this work, a mathematical model is developed to investigate the efficacy of MCDT in IP chemotherapy. In this model, considering the mechanism of drug binding and internalization into cancer cells, the efficacy of drug delivery using MNPs is evaluated and compared with conventional IP chemotherapy. The results indicate that over 60 min of treatment with MNPs, drug penetration depth increased more than 13 times compared to conventional IPC. Moreover, the drug penetration area (DPA) increased more than 1.4 times compared to the conventional IP injection. The fraction of killed cells in the tumor in magnetic drug delivery was 6.5%, which shows an increase of more than 2.5 times compared to that of the conventional method (2.54%). Furthermore, the effects of magnetic strength, the distance of the magnet to the tumor, and the magnetic nanoparticles’ size were evaluated. The results show that MDT can be used as an effective technique to increase the efficiency of IP chemotherapy.

Towards principled design of cancer nanomedicine to accelerate clinical translation

Nanotechnology in medical applications, especially in oncology as drug delivery systems, has recently shown promising results. However, although these advances have been promising in the pre-clinical stages, the clinical translation of this technology is challenging. To create drug delivery systems with increased treatment efficacy for clinical translation, the physicochemical characteristics of nanoparticles such as size, shape, elasticity (flexibility/rigidity), surface chemistry, and surface charge can be specified to optimize efficiency for a given application. Consequently, interdisciplinary researchers have focused on producing biocompatible materials, production technologies, or new formulations for efficient loading, and high stability. The effects of design parameters can be studied in vitro, in vivo, or using computational models, with the goal of understanding how they affect nanoparticle biophysics and their interactions with cells. The present review summarizes the advances and technologies in the production and design of cancer nanomedicines to achieve clinical translation and commercialization. We also highlight existing challenges and opportunities in the field.

Computational Modeling of Combination of Magnetic Hyperthermia and Temperature-Sensitive Liposome for Controlled Drug Release in Solid Tumor

Combination therapy, a treatment modality that combines two or more therapeutic methods, provides a novel pathway for cancer treatment, as it targets the region of interest (ROI) in a characteristically synergistic or additive manner. To date, liposomes are the only nano-drug delivery platforms that have been used in clinical trials. Here, we speculated that it could be promising to improve treatment efficacy and reduce side effects by intravenous administration of thermo-sensitive liposomes loaded with doxorubicin (TSL-Dox) during magnetic hyperthermia (MHT). A multi-scale computational model using the finite element method was developed to simulate both MHT and temperature-sensitive liposome (TSL) delivery to a solid tumor to obtain spatial drug concentration maps and temperature profiles. The results showed that the killing rate of MHT alone was about 15%, which increased to 50% using the suggested combination therapy. The results also revealed that this combination treatment increased the fraction of killed cells (FKCs) inside the tumor compared to conventional chemotherapy by 15% in addition to reducing side effects. Furthermore, the impacts of vessel wall pore size, the time interval between TSL delivery and MHT, and the initial dose of TSLs were also investigated. A considerable reduction in drug accumulation was observed in the tumor by decreasing the vessel wall pore size of the tumor. The results also revealed that the treatment procedure plays an essential role in the therapeutic potential of anti-cancer drugs. The results suggest that the administration of MHT can be beneficial in the TSL delivery system and that it can be employed as a guideline for upcoming preclinical studies.

Capillary network formation and structure in a modified discrete mathematical model of angiogenesis

Angiogenesis, as part of cancer development, involves hierarchical complicated events and processes. Multiple studies have revealed the significance of the formation and structure of tumor-induced capillary networks. In this study, a discrete mathematical model of angiogenesis is studied and modified to capture the realistic physics of capillary network formation. Modifications are performed on the mathematical foundations of an existing discrete model of angiogenesis. The main modifications are the imposition of the matrix density effect, implementation of realistic boundary and initial conditions, and improvement of the method of governing equations based on physical observation. Results show that endothelial cells accelerate angiogenesis and capillary formation as they migrate toward the tumor and clearly exhibit the physical concept of haptotactic movement. On the other hand, consideration of blood flow-induced stress leads to a dynamic adaptive vascular network of capillaries which intelligibly reflects the brush border effect . The present modified model of capillary network formation is based on the physical rationale that defines a clear mathematical and physical interpretation of angiogenesis, which is likely to be used in cancer development modeling and anti-angiogenic therapies.

An unsteady analysis of two-phase binding of drug in an asymmetric stenosed vessel

In this paper, we investigate endovascular delivery to get a step ahead of the pharmacological limitations it has due to the complexity of dealing with a patient-specific vessel through a mathematical model. We divide the domain of computation into four sub-domains: the lumen, the lumen-tissue interface, the upper tissue and the lower tissue which are extracted from an asymmetric atherosclerotic image derived by the intravascular ultrasound (IVUS) technique. The injected drug at the luminal inlet is transported with the streaming blood which is considered Newtonian. An irreversible uptake kinetics of the injected drug at the lumen-tissue interface from the luminal side to the tissue domains is assumed. Subsequently, the drug is dispersed within the tissue followed by its retention in the extracellular matrix (ECM) and by receptor-mediated binding. The Marker and Cell (MAC) method has been leveraged to get a quantitative insight into the model considered. The effect of the wall absorption parameter on the concentration of all drug forms (free as well as two-phase bound) has been thoroughly investigated, and some other important factors, such as the averaged concentration, the tissue content, the fractional effect, the concentration variance and the effectiveness of drug have been graphically analyzed to gain a clear understanding of endovascular delivery. The simulated results predict that with increasing values of the absorption parameter, the averaged concentrations of all drug forms do decrease. An early saturation of binding sites takes place for smaller values of the absorption parameter, and also rapid saturation of ECM binding sites occurs as compared to receptor binding sites. Results also predict the influence of surface roughness as well as asymmetry of the domain about the centerline on the distribution and retention of drug. A thorough sensitivity analysis has been carried out to determine the influence of some parameters involved.

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.

Mathematical Analysis for the Effects of Medicine Supplies to a Solid Tumor

Objective: 1. Interpretation of the variations of solute medicine amount in blood vessels and TAF concentration with respect to the flow rates of injected drugs into liver and heart. 2. Description of the alteration of tumor cell density versus the time and radius variations. Methodology: Step 1. Compartmental analysis is adopted for the concentration of chemotaxis caused by injected substances L and H based on the assumption: two different medicines I1 and I2 are injected into heart and liver to recover the functions of each organ, respectively, without any side effects. Step 2. A partial differential equation is derived for the growth of TAF considering the diffusion of TAF and the rate of decay of TAF according to the disturbance of medicine M in blood vessels. Step 3. A partial differential equation is derived for the motion of tumor cells in the lights of random motility and chemotaxis in response to TAF gradients. Step 4. Exact solutions are obtained for the concentration of chemotaxis caused by injected substances L and H under the assumption that the loss of mass is proportional to mass itself. Step 5. Exact solution is obtained for the partial differential equation describing the growth of TAF using the separation of variables. Step 6. A finite volume approach is executed to search approximated solutions due to the complexity of the partial differential equation describing the motion of tumor cells. Results: 1. The concentration of medicine (M) decreases as the ratio of flow rate from heart into vessel to flow rate from liver into heart (k1k2) increases. 2. TAF concentration increases with the growth of the value of ratio k1k2 and TAF shows the smallest concentration when the flow rate of each injected medicine is similar. 3. Tumor cells react highly sensitive as soon as medicine supplies and tumor cell’s density is decreased drastically at the moment of medicine injection. 4. Tumor cell density decreases exponentially at an early stage and the density decrease is developed in a fluctuating manner along the radius. Conclusions: 1. The presented mathematical approach has the potential for the profound analysis of the variations of solute medicine amount in blood vessels, TAF concentration, and the alteration of tumor cell density according to the functional recoveries of liver and heart. 2. The mathematical approach may be applicable in the investigation of tumor cell’s behavior on the basis of complex interaction among five represented organs: kidney, liver, heart, spleen, and lung. A mathematical approach is developed to describe the variation of a solid tumor cell density in response to drug supply. The investigation is progressed based on the assumption that two different medicines, I1 and I2, are injected into heart and liver with flow rates k1 and k2 to recover the functions of each organ, respectively. A medicine function system for the reactions of tumor angiogenic factors (TAF) to medicine injection is obtained using a compartmental analysis. The mathematical governing equations for tumor cells motion are derived taking into account random motility and chemotaxis in response to TAF gradients and a finite volume method with time-changing is adopted to obtain numerical solutions due to the complexity of the governing equations. The variation of the flow rates k1 and k2 exerts profound influences on the concentration of medicine, and similar flow rate of k1 and k2 produces the greatest amount of medicine in blood vessels and suppresses strong inhibition in TAF movement. Tumor cells react very sensitively to drug injection and the tumor cell density decreases to less than 20% at an early stage of administration. However, the density of tumor cell diminishes slowly after the early stage of sudden change and the duration for complete therapy of tumor cells requires a long time.

Computational modeling of thermal combination therapies by magneto-ultrasonic heating to enhance drug delivery to solid tumors

For the first time, inspired by magnetic resonance imaging-guidance high intensity focused ultrasound (MR-HIFU) technology, i.e., medication therapy and thermal ablation in one session, in a preclinical setting based on a developed mathematical model, the performance of doxorubicin (Dox) and its encapsulation have been investigated in this study. Five different treatment methods, that combine medication therapy with mild hyperthermia by MRI contrast (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma -{Fe}_{2}{O}_{3}$$\end{document}γ-Fe2O3) and thermal ablation via HIFU, are investigated in detail. A comparison between classical chemotherapy and thermochemistry shows that temperature can improve the therapeutic outcome by stimulating biological properties. On the other hand, the intravascular release of ThermoDox increases the concentration of free drug by 2.6 times compared to classical chemotherapy. The transport of drug in interstitium relies mainly on the diffusion mechanism to be able to penetrate deeper and reach the cancer cells in the inner regions of the tumor. Due to the low drug penetration into the tumor center, thermal ablation has been used for necrosis of the central areas before thermochemotherapy and ThermoDox therapy. Perfusion of the region around the necrotic zone is found to be damaged, while cells in the region are alive and not affected by medication therapy; so, there is a risk of tumor recurrence. Therefore, it is recommended that ablation be performed after the medication therapy. Our model describes a comprehensive assessment of MR-HIFU technology, taking into account many effective details, which can be a reliable guide towards the optimal use of drug delivery systems.

Effects of hypoxia and nanocarrier size on pH-responsive nano-delivery system to solid tumors

One of the special features of solid tumors is the acidity of the tumor microenvironment, which is mainly due to the presence of hypoxic regions. Therefore, pH-responsive drug delivery systems have recently been highly welcomed. In the present study, a comprehensive mathematical model is presented based on extravascular drug release paradigm. Accordingly, drug delivery system using pH-responsive nanocarriers is taken into account to examine the impacts of hypoxic regions as well as the size of nanocarriers for cancerous cell-death. The extent of hypoxic regions is controlled by vascular density. This means that regions with very low vascular density represent regions of hypoxia. Using this mathematical model, it is possible to simulate the extracellular and intracellular concentrations of drug by considering the association/disassociation of the free drug to the cell-surface receptors and cellular uptake. Results show that nanocarriers with smaller sizes are more effective due to higher accumulation in the tumor tissue interstitium. The small size of the nanocarriers also allows them to penetrate deeper, so they can expose a larger portion of the tumor to the drug. Additionally, the presence of hypoxic regions in tumor reduces the fraction of killed cancer cells due to reduced penetration depth. The proposed model can be considered for optimizing and developing pH-sensitive delivery systems to reduce both cost and time of the process.

Enhanced Drug Delivery to Solid Tumors via Drug-Loaded Nanocarriers: An Image-Based Computational Framework

Objective

Nano-sized drug delivery systems (NSDDSs) offer a promising therapeutic technology with sufficient biocompatibility, stability, and drug-loading rates towards efficient drug delivery to solid tumors. We aim to apply a multi-scale computational model for evaluating drug delivery to predict treatment efficacy.

Methodology

Three strategies for drug delivery, namely conventional chemotherapy (one-stage), as well as chemotherapy through two- and three-stage NSDDSs, were simulated and compared. A geometric model of the tumor and the capillary network was obtained by processing a real image. Subsequently, equations related to intravascular and interstitial flows as well as drug transport in tissue were solved by considering real conditions as well as details such as drug binding to cells and cellular uptake. Finally, the role of periodic treatments was investigated considering tumor recurrence between treatments. The impact of different parameters, nanoparticle (NP) size, binding affinity of drug, and the kinetics of release rate, were additionally investigated to determine their therapeutic efficacy.

Results

Using NPs considerably increases the fraction of killed cells (FKCs) inside the tumor compared to conventional chemotherapy. Tumoral FKCs for two-stage DDS with smaller NP size (20nm) is higher than that of larger NPs (100nm), in all investigate release rates. Slower and continuous release of the chemotherapeutic agents from NPs have better treatment outcomes in comparison with faster release rate. In three-stage DDS, for intermediate and higher binding affinities, it is desirable for the secondary particle to be released at a faster rate, and the drug with slower rate. In lower binding affinities, high release rates have better performance. Results also demonstrate that after 5 treatments with three-stage DDS, 99.6% of tumor cells (TCs) are killed, while two-stage DDS and conventional chemotherapy kill 95.6% and 88.5% of tumor cells in the same period, respectively.

Conclusion

The presented framework has the potential to enable decision making for new drugs via computational modeling of treatment responses and has the potential to aid oncologists with personalized treatment plans towards more optimal treatment outcomes.