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

Effect of tumor heterogeneity on enhancing drug delivery to vascularized tumors using thermo-sensitive liposomes triggered by hyperthermia: A multi-scale and multi-physics computational model

In this study, a novel multi-scale and multi-physics image-based computational model is introduced to assess the delivery of doxorubicin (Dox) loaded temperature-sensitive liposomes (TSLs) in the presence of hyperthermia. Unlike previous methodologies, this approach incorporates capillary network geometry extracted from images, resulting in a more realistic physiological tumor model. This model holds significant promise in advancing personalized medicine by integrating patient-specific tumor properties. The finite element method is employed to solve the equations governing intravascular and interstitial fluid flows, as well as the transport of therapeutic agents within the tissue. Realistic biological conditions and intricate processes like intravascular pressure, drug binding to cells, and cellular uptake are also considered to enhance the model's accuracy. The results underscore the significant impact of vascular architecture on treatment outcomes. Variation in vascular network pattern yielded changes of up to 38 % in the fraction of killed cells (FKCs) parameter under identical conditions. Pressure control of the parent vessels can also improve FKCs by approximately 17 %. Tailoring the treatment plan based on tumor-specific parameters emerged as a critical factor influencing treatment efficacy. For instance, changing the time interval between the administration of Dox-loaded TSLs and hyperthermia can result in a 48 % improvement in treatment outcomes. Additionally, devising a customized heating schedule led to a 20 % increase in treatment efficacy. Our proposed model highlights the significant effect of tumor characteristics and vascular network structure on the final treatment outcomes of the presented combination treatment.

Hydraulic conductivity of human cancer tissue: A hybrid study

Background

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

Methods

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

Results

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

Conclusions

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

Reconstructing microvascular network skeletons from 3D images: What is the ground truth?

Structural changes to microvascular networks are increasingly highlighted as markers of pathogenesis in a wide range of disease, e.g. Alzheimer's disease, vascular dementia and tumour growth. This has motivated the development of dedicated 3D imaging techniques, alongside the creation of computational modelling frameworks capable of using 3D reconstructed networks to simulate functional behaviours such as blood flow or transport processes. Extraction of 3D networks from imaging data broadly consists of two image processing steps: segmentation followed by skeletonisation. Much research effort has been devoted to segmentation field, and there are standard and widely-applied methodologies for creating and assessing gold standards or ground truths produced by manual annotation or automated algorithms. The Skeletonisation field, however, lacks widely applied, simple to compute metrics for the validation or optimisation of the numerous algorithms that exist to extract skeletons from binary images. This is particularly problematic as 3D imaging datasets increase in size and visual inspection becomes an insufficient validation approach. In this work, we first demonstrate the extent of the problem by applying 4 widely-used skeletonisation algorithms to 3 different imaging datasets. In doing so we show significant variability between reconstructed skeletons of the same segmented imaging dataset. Moreover, we show that such a structural variability propagates to simulated metrics such as blood flow. To mitigate this variability we introduce a new, fast and easy to compute super metric that compares the volume, connectivity, medialness, bifurcation point identification and homology of the reconstructed skeletons to the original segmented data. We then show that such a metric can be used to select the best performing skeletonisation algorithm for a given dataset, as well as to optimise its parameters. Finally, we demonstrate that the super metric can also be used to quickly identify how a particular skeletonisation algorithm could be improved, becoming a powerful tool in understanding the complex implication of small structural changes in a network.

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.

Multi-Scale and Multi-Physics Models of the Transport of Therapeutic/Diagnostic Cancer Agents

The effectiveness of tumor treatment heavily relies on the successful delivery of anticancer drugs [...].

Stimuli-sensitive nano-drug delivery with programmable size changes to enhance accumulation of therapeutic agents in tumors

Nano-based drug delivery systems hold significant promise for cancer therapies. Presently, the poor accumulation of drug-carrying nanoparticles in tumors has limited their success. In this study, based on a combination of the paradigms of intravascular and extravascular drug release, an efficient nanosized drug delivery system with programmable size changes is introduced. Drug-loaded smaller nanoparticles (secondary nanoparticles), which are loaded inside larger nanoparticles (primary nanoparticles), are released within the microvascular network due to temperature field resulting from focused ultrasound. This leads to the scale of the drug delivery system decreasing by 7.5 to 150 times. Subsequently, smaller nanoparticles enter the tissue at high transvascular rates and achieve higher accumulation, leading to higher penetration depths. In response to the acidic pH of tumor microenvironment (according to the distribution of oxygen), they begin to release the drug doxorubicin at very slow rates (i.e., sustained release). To predict the performance and distribution of therapeutic agents, a semi-realistic microvascular network is first generated based on a sprouting angiogenesis model and the transport of therapeutic agents is then investigated based on a developed multi-compartment model. The results show that reducing the size of the primary and secondary nanoparticles can lead to higher cell death rate. In addition, tumor growth can be inhibited for a longer time by enhancing the bioavailability of the drug in the extracellular space. The proposed drug delivery system can be very promising in clinical applications. Furthermore, the proposed mathematical model is applicable to broader applications to predict the performance of drug delivery systems.

A comparative study between conventional chemotherapy and photothermal activated nano-sized targeted drug delivery to solid tumor

Delivery of chemotherapeutic medicines to solid tumors is critical for optimal therapeutic success and minimal adverse effects. We mathematically developed a delivery method using thermosensitive nanocarriers activated by light irradiation. To assess its efficacy and identify critical events and parameters affecting therapeutic response, we compared this method to bolus and continuous infusions of doxorubicin for both single and multiple administrations. A hybrid sprouting angiogenesis approach generates a semi-realistic microvascular network to evaluate therapeutic drug distribution and microvascular heterogeneity. A pharmacodynamics model evaluates treatment success based on tumor survival cell percentage. The study found that whereas bolus injection boosted extracellular drug concentration levels by 90%, continuous infusion improved therapeutic response due to improved bioavailability. Cancer cell death increases by 6% with several injections compared to single injections due to prolonged chemotherapeutic medication exposure. However, responsive nanocarriers supply more than 2.1 times more drug than traditional chemotherapy in extracellular space, suppressing tumor development longer. Also, controlled drug release decreases systemic side effects substantial through diminishing the concentration of free drug in the circulation. The primary finding of this work highlights the significance of high bioavailability in treatment response. The results indicate that responsive nanocarriers contribute to increased bioavailability, leading to improved therapeutic benefits. By including drug delivery features in a semi-realistic model, this numerical study sought to improve drug-bio interaction comprehension. The model provides a good framework for understanding preclinical and clinical targeted oncology study outcomes.

Image-Based Modeling of Drug Delivery during Intraperitoneal Chemotherapy in a Heterogeneous Tumor Nodule

Intraperitoneal (IP) chemotherapy is a promising treatment approach for patients diagnosed with peritoneal carcinomatosis, allowing the direct delivery of therapeutic agents to the tumor site within the abdominal cavity. Nevertheless, limited drug penetration into the tumor remains a primary drawback of this method. The process of delivering drugs to the tumor entails numerous complications, primarily stemming from the specific pathophysiology of the tumor. Investigating drug delivery during IP chemotherapy and studying the parameters affecting it are challenging due to the limitations of experimental studies. In contrast, mathematical modeling, with its capabilities such as enabling single-parameter studies, and cost and time efficiency, emerges as a potent tool for this purpose. In this study, we developed a numerical model to investigate IP chemotherapy by incorporating an actual image of a tumor with heterogeneous vasculature. The tumor's geometry is reconstructed using image processing techniques. The model also incorporates drug binding and uptake by cancer cells. After 60 min of IP treatment with Doxorubicin, the area under the curve (AUC) of the average free drug concentration versus time curve, serving as an indicator of drug availability to the tumor, reached 295.18 mol·m-3·s-1. Additionally, the half-width parameter W1/2, which reflects drug penetration into the tumor, ranged from 0.11 to 0.14 mm. Furthermore, the treatment resulted in a fraction of killed cells reaching 20.4% by the end of the procedure. Analyzing the spatial distribution of interstitial fluid velocity, pressure, and drug concentration in the tumor revealed that the heterogeneous distribution of tumor vasculature influences the drug delivery process. Our findings underscore the significance of considering the specific vascular network of a tumor when modeling intraperitoneal chemotherapy. The proposed methodology holds promise for application in patient-specific studies.

Vascular phenotyping of the invasive front in breast cancer using a 3D angiogenesis atlas

OBJECTIVE

Vascular remodeling at the invasive tumor front (ITF) plays a critical role in progression and metastasis of triple negative breast cancer (TNBC). Therefore, there is a crucial need to characterize the vascular phenotype (i.e. changes in the structure and function of vasculature) of the ITF and tumor core (TC) in TNBC. This requires high-resolution, 3D structural and functional microvascular data that spans the ITF and TC (i.e. ∼4-5 mm from the tumor's edge). Since such data are often challenging to obtain with most conventional imaging approaches, we employed a unique "3D whole-tumor angiogenesis atlas" derived from orthotopic xenografts to characterize the vascular phenotype of the ITF and TC in TNBC.

METHODS

First, high-resolution (8 μm) computed tomography (CT) images of "whole-tumor" microvasculature were acquired from eight orthotopic TNBC xenografts, of which three tumors were excised at post-inoculation day 21 (i.e. early-stage) and five tumors were excised at post-inoculation day 35 (i.e. advanced-stage). These 3D morphological CT data were combined with soft tissue contrast from MRI as well as functional data generated in silico using image-based hemodynamic modeling to generate a multi-layered "angiogenesis atlas". Employing this atlas, blood vessels were first spatially stratified within the ITF (i.e. ≤1 mm from the tumor's edge) and TC (i.e. >1 mm from the tumor's edge) of each tumor xenograft. Then, a novel method was developed to visualize and characterize microvascular remodeling and perfusion changes in terms of distance from the tumor's edge.

RESULTS

The angiogenesis atlas enabled the 3D visualization of changes in tumor vessel growth patterns, morphology and perfusion within the ITF and TC. Early and advanced stage tumors demonstrated significant differences in terms of their edge-to-center distributions for vascular surface area density, vascular length density, intervessel distance and simulated perfusion density (p ≪ 0.01). Elevated vascular length density, vascular surface area density and perfusion density along the circumference of the ITF was suggestive of a preferential spatial pattern of angiogenic growth in this tumor cohort. Finally, we demonstrated the feasibility of differentiating the vascular phenotypes of ITF and TC in these TNBC xenografts.

CONCLUSIONS

The combination of a 3D angiogenesis atlas and image-based hemodynamic modeling heralds a new approach for characterizing the role of vascular remodeling in cancer and other diseases.

Computational simulations of tumor growth and treatment response: Benefits of high-frequency, low-dose drug regimens and concurrent vascular normalization

Implementation of effective cancer treatment strategies requires consideration of how the spatiotemporal heterogeneities within the tumor microenvironment (TME) influence tumor progression and treatment response. Here, we developed a multi-scale three-dimensional mathematical model of the TME to simulate tumor growth and angiogenesis and then employed the model to evaluate an array of single and combination therapy approaches. Treatments included maximum tolerated dose or metronomic (i.e., frequent low doses) scheduling of anti-cancer drugs combined with anti-angiogenic therapy. The results show that metronomic therapy normalizes the tumor vasculature to improve drug delivery, modulates cancer metabolism, decreases interstitial fluid pressure and decreases cancer cell invasion. Further, we find that combining an anti-cancer drug with anti-angiogenic treatment enhances tumor killing and reduces drug accumulation in normal tissues. We also show that combined anti-angiogenic and anti-cancer drugs can decrease cancer invasiveness and normalize the cancer metabolic microenvironment leading to reduced hypoxia and hypoglycemia. Our model simulations suggest that vessel normalization combined with metronomic cytotoxic therapy has beneficial effects by enhancing tumor killing and limiting normal tissue toxicity.

Ultrasound-mediated nano drug delivery for treating cancer: Fundamental physics to future directions

The application of biocompatible nanocarriers in medicine has provided several benefits over conventional treatment methods. However, achieving high treatment efficacy and deep penetration of nanocarriers in tumor tissue is still challenging. To address this, stimuli-responsive nano-sized drug delivery systems (DDSs) are an active area of investigation in delivering anticancer drugs. While ultrasound is mainly used for diagnostic purposes, it can also be applied to affect cellular function and the delivery/release of anticancer drugs. Therapeutic ultrasound (TUS) has shown potential as both a stand-alone anticancer treatment and a method to induce targeted drug release from nanocarrier systems. TUS approaches have been used to overcome various physiological obstacles, including endothelial barriers, the tumor microenvironment (TME), and immunological hurdles. Combining nanomedicine and ultrasound as a smart DDS can increase in situ drug delivery and improve access to impermeable tissues. Furthermore, smart DDSs can perform targeted drug release in response to distinctive TMEs, external triggers, or dual/multi-stimulus. This results in enhanced treatment efficacy and reduced damage to surrounding healthy tissue or organs at risk. Integrating DDSs and ultrasound is still in its early stages. More research and clinical trials are required to fully understand ultrasound's underlying physical mechanisms and interactions with various types of nanocarriers and different types of cells and tissues. In the present review, ultrasound-mediated nano-sized DDS, specifically focused on cancer treatment, is presented and discussed. Ultrasound interaction with nanoparticles (NPs), drug release mechanisms, and various types of ultrasound-sensitive NPs are examined. Additionally, in vitro, in vivo, and clinical applications of TUS are reviewed in light of the critical challenges that need to be considered to advance TUS toward an efficient, secure, straightforward, and accessible cancer treatment. This study also presents effective TUS parameters and safety considerations for this treatment modality and gives recommendations about system design and operation. Finally, future perspectives are considered, and different TUS approaches are examined and discussed in detail. This review investigates drug release and delivery through ultrasound-mediated nano-sized cancer treatment, both pre-clinically and clinically.

Multiphysics Modeling of Low-Intensity Pulsed Ultrasound Induced Chemotherapeutic Drug Release from the Surface of Gold Nanoparticles

Currently, no numerical model for low-intensity pulsed ultrasound (LIPUS)-triggered anticancer drug release from gold nanoparticle (GNP) drug carriers exists in the literature. In this work, LIPUS-induced doxorubicin (DOX) release from GNPs was achieved in an ex vivo tissue model. Transmission electronic microscopy (TEM) imaging was performed before and after LIPUS exposure, and significant aggregation of the GNPs was observed upon DOX release. Subsequently, GNP surface potential was determined before and after LIPUS-induced DOX release, using a Zetasizer. A numerical model was then created to predict GNP aggregation, and the subsequent DOX release, via combining a thermal field simulation by solving the bioheat transfer equation (in COMSOL) and the Derjaguin, Landau, Verwey, and Overbeek (DLVO) total interaction potential (in MATLAB). The DLVO model was applied to the colloidal DOX-loaded GNPs by summing the attractive van der Waals and electrostatic repulsion interaction potentials for any given GNP pair. DLVO total interaction potential was found before and after LIPUS exposure, and an energy barrier for aggregation was determined. The DLVO interaction potential peak amplitude was found to drop from 1.36 k_BT to 0.24 k_BT after LIPUS exposure, translating to an 82.4% decrease in peak amplitude value. It was concluded that the interaction potential energy threshold for GNP aggregation (and, as a result, DOX release) was equal to 0.24 k_BT.

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.

Assessing chemotherapy dosing strategies in a spatial cell culture model

Predicting patient responses to chemotherapy regimens is a major challenge in cancer treatment. Experimental model systems coupled with quantitative mathematical models to calculate optimal dose and frequency of drugs can enable improved chemotherapy regimens. Here we developed a simple approach to track two-dimensional cell colonies composed of chemo-sensitive and resistant cell populations via fluorescence microscopy and coupled this to computational model predictions. Specifically, we first developed multiple 4T1 breast cancer cell lines resistant to varying concentrations of doxorubicin, and demonstrated how heterogeneous populations expand in a two-dimensional colony. We subjected cell populations to varied dose and frequency of chemotherapy and measured colony growth. We then built a mathematical model to describe the dynamics of both chemosensitive and chemoresistant populations, where we determined which number of doses can produce the smallest tumor size based on parameters in the system. Finally, using an in vitro model we demonstrated multiple doses can decrease overall colony growth as compared to a single dose at the same total dose. In the future, this system can be adapted to optimize dosing strategies in the setting of heterogeneous cell types or patient derived cells with varied chemoresistance.

Research Progress with Luteolin as an Anti-Tumor Agent

In this review, we outline the new expertise and research progress with luteolin as an antitumor agent, and clarify the related results from the aspects of tumor proliferation, apoptosis, invasion, metastasis, sensitivity to radiotherapy and chemotherapy, angiogenesis, and immunotherapy. In recent years, with the development of medical technology, the early detection rate of tumors has increased significantly. However, the number of cancer patients remains high. Therefore, a new and reasonably effective tumor therapeutic drug is urgently demanded. Luteolin, a flavonoid and widespread in nature, attracts more and more attention due to its universal biological utility, especially in the study of antitumor activity. This article reviews the work published in the past 20 years on the role and mechanism of luteolin as an antitumor agent, showing that this compound has a variety of effects for antitumor treatment by acting on different cytokines. Although clinical studies have not yet been widely carried out, a series of basic studies have confirmed that luteolin is a reasonably effective antineoplastic agent or anticancer adjuvant. Besides, derivatives of luteolin have good application prospects.

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.

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 multiscale cell-based model of tumor growth for chemotherapy assessment and tumor-targeted therapy through a 3D computational approach

OBJECTIVES

Computational modeling of biological systems is a powerful tool to clarify diverse processes contributing to cancer. The aim is to clarify the complex biochemical and mechanical interactions between cells, the relevance of intracellular signaling pathways in tumor progression and related events to the cancer treatments, which are largely ignored in previous studies.

MATERIALS AND METHODS

A three-dimensional multiscale cell-based model is developed, covering multiple time and spatial scales, including intracellular, cellular, and extracellular processes. The model generates a realistic representation of the processes involved from an implementation of the signaling transduction network.

RESULTS

Considering a benign tumor development, results are in good agreement with the experimental ones, which identify three different phases in tumor growth. Simulating tumor vascular growth, results predict a highly vascularized tumor morphology in a lobulated form, a consequence of cells' motile behavior. A novel systematic study of chemotherapy intervention, in combination with targeted therapy, is presented to address the capability of the model to evaluate typical clinical protocols. The model also performs a dose comparison study in order to optimize treatment efficacy and surveys the effect of chemotherapy initiation delays and different regimens.

CONCLUSIONS

Results not only provide detailed insights into tumor progression, but also support suggestions for clinical implementation. This is a major step toward the goal of predicting the effects of not only traditional chemotherapy but also tumor-targeted therapies.

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.

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.

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.

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.

Engineered strategies to enhance tumor penetration of drug-loaded nanoparticles

Nanocarriers have been widely employed in preclinical studies and clinical trials for the delivery of anticancer drugs. The most important causes of failure in clinical translation of nanocarriers is their inefficient accumulation and penetration which arises from special characteristics of tumor microenvironment such as insufficient blood supply, dense extracellular matrix, and elevated interstitial fluid pressure. Various strategies such as engineering extracellular matrix, optimizing the physicochemical properties of nanocarriers have been proposed to increase the depth of tumor penetration; however, these strategies have not been very successful so far. Novel strategies such as transformable nanocarriers, transcellular transport of peptide-modified nanocarriers, and bio-inspired carriers have recently been emerged as an advanced generation of drug carriers. In this study, the latest developments of nanocarrier-based drug delivery to solid tumor are presented with their possible limitations. Then, the prospects of advanced drug delivery systems are discussed in detail.

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.

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.

Computational model of silica nanoparticle penetration into tumor spheroids: Effects of methoxy and carboxy PEG surface functionalization and hyperthermia

Drug delivery to tumors suffers from poor solubility, specificity, diffusion through the tumor micro-environment and nonoptimal interactions with components of the extracellular matrix and cell surface receptors. Nanoparticles and drug-polymer complexes address many of these problems. However, large size exasperates the problem of slow diffusion through the tumor. Three-dimensional tumor spheroids are good models to evaluate approaches to mitigate these difficulties and aid in design strategies to improve the delivery of drugs to treat cancer effectively. Diffusion of drug carriers is highly dependent on cell uptake rate parameters (association/dissociation) and temperature. Hyperthermia increases molecular transport and is known to act synergistically with chemotherapy to improve treatment. This study presents a new inverse estimation approach based on Bayesian probability for estimating nanoparticle cell uptake rates from experiments. The parameters were combined with a finite element computational model of nanoparticle transport under hyperthermia conditions to explore its effect on tumor porosity, diffusion and particle binding (association and dissociation) at cell surfaces. Carboxy-PEG-silane (cPEGSi) nanoparticles showed higher cell uptake compared to methoxy-PEG-silane (mPEGSi) nanoparticles. Simulations were consistent with experimental results from Skov-3 ovarian cancer spheroids. Amorphous silica (cPEGSi) nanoparticles (58 nm) concentrated at the periphery of the tumor spheroids at 37°C but mild hyperthermia (43°C) increased nanoparticle penetration. Thus, hyperthermia may enhance cancer treatment by improving blood delivery to tumors, enhancing extravasation and penetration into tumors, trigger release of drug from the carrier at the tumor site and possibly lead to synergistic anti-cancer activity with the drug.

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.

Chemo-mechanistic multi-scale model of a three-dimensional tumor microenvironment to quantify the chemotherapy response of cancer

Exploring efficient chemotherapy would benefit from a deeper understanding of the tumor microenvironment (TME) and its role in tumor progression. As in vivo experimental methods are unable to isolate or control individual factors of the TME, and in vitro models often cannot include all the contributing factors, some questions are best addressed with mathematical models of systems biology. In this study, we establish a multi-scale mathematical model of the TME to simulate three-dimensional tumor growth and angiogenesis and then implement the model for an array of chemotherapy approaches to elucidate the effect of TME conditions and drug scheduling on controlling tumor progression. The hyperglycemic condition as the most common disorder for cancer patients is considered to evaluate its impact on cancer response to chemotherapy. We show that combining antiangiogenic and anticancer drugs improves the outcome of treatment and can decrease accumulation of the drug in normal tissue and enhance drug delivery to the tumor. Our results demonstrate that although both concurrent and neoadjuvant combination therapies can increase intratumoral drug exposure and therapeutic accuracy, neoadjuvant therapy surpasses this, especially against hyperglycemia. Our model provides mechanistic explanations for clinical observations of tumor progression and response to treatment and establishes a computational framework for exploring better treatment strategies.

Multiscale modeling of tumor growth and angiogenesis: Evaluation of tumor-targeted therapy

The dynamics of tumor growth and associated events cover multiple time and spatial scales, generally including extracellular, cellular and intracellular modifications. The main goal of this study is to model the biological and physical behavior of tumor evolution in presence of normal healthy tissue, considering a variety of events involved in the process. These include hyper and hypoactivation of signaling pathways during tumor growth, vessels' growth, intratumoral vascularization and competition of cancer cells with healthy host tissue. The work addresses two distinctive phases in tumor development-the avascular and vascular phases-and in each stage two cases are considered-with and without normal healthy cells. The tumor growth rate increases considerably as closed vessel loops (anastomoses) form around the tumor cells resulting from tumor induced vascularization. When taking into account the host tissue around the tumor, the results show that competition between normal cells and cancer cells leads to the formation of a hypoxic tumor core within a relatively short period of time. Moreover, a dense intratumoral vascular network is formed throughout the entire lesion as a sign of a high malignancy grade, which is consistent with reported experimental data for several types of solid carcinomas. In comparison with other mathematical models of tumor development, in this work we introduce a multiscale simulation that models the cellular interactions and cell behavior as a consequence of the activation of oncogenes and deactivation of gene signaling pathways within each cell. Simulating a therapy that blocks relevant signaling pathways results in the prevention of further tumor growth and leads to an expressive decrease in its size (82% in the simulation).

Enhancing Clinical Translation of Cancer Using Nanoinformatics

Application of drugs in high doses has been required due to the limitations of no specificity, short circulation half-lives, as well as low bioavailability and solubility. Higher toxicity is the result of high dosage administration of drug molecules that increase the side effects of the drugs. Recently, nanomedicine, that is the utilization of nanotechnology in healthcare with clinical applications, has made many advancements in the areas of cancer diagnosis and therapy. To overcome the challenge of patient-specificity as well as time- and dose-dependency of drug administration, artificial intelligence (AI) can be significantly beneficial for optimization of nanomedicine and combinatorial nanotherapy. AI has become a tool for researchers to manage complicated and big data, ranging from achieving complementary results to routine statistical analyses. AI enhances the prediction precision of treatment impact in cancer patients and specify estimation outcomes. Application of AI in nanotechnology leads to a new field of study, i.e., nanoinformatics. Besides, AI can be coupled with nanorobots, as an emerging technology, to develop targeted drug delivery systems. Furthermore, by the advancements in the nanomedicine field, AI-based combination therapy can facilitate the understanding of diagnosis and therapy of the cancer patients. The main objectives of this review are to discuss the current developments, possibilities, and future visions in naoinformatics, for providing more effective treatment for cancer patients.

A Mathematical Model to Estimate Chemotherapy Concentration at the Tumor-Site and Predict Therapy Response in Colorectal Cancer Patients with Liver Metastases

Simple Summary

It is known that drug transport barriers in the tumor determine drug concentration at the tumor site, causing disparity from the systemic (plasma) drug concentration. However, current clinical standard of care still bases dosage and treatment optimization on the systemic concentration of drugs. Here, we present a proof of concept observational cohort study to accurately estimate drug concentration at the tumor site from mathematical modeling using biologic, clinical, and imaging/perfusion data, and correlate it with outcome in colorectal cancer liver metastases. We demonstrate that drug concentration at the tumor site, not in systemic circulation, can be used as a credible biomarker for predicting chemotherapy outcome, and thus our mathematical modeling approach can be applied prospectively in the clinic to personalize treatment design to optimize outcome.

Abstract

Chemotherapy remains a primary treatment for metastatic cancer, with tumor response being the benchmark outcome marker. However, therapeutic response in cancer is unpredictable due to heterogeneity in drug delivery from systemic circulation to solid tumors. In this proof-of-concept study, we evaluated chemotherapy concentration at the tumor-site and its association with therapy response by applying a mathematical model. By using pre-treatment imaging, clinical and biologic variables, and chemotherapy regimen to inform the model, we estimated tumor-site chemotherapy concentration in patients with colorectal cancer liver metastases, who received treatment prior to surgical hepatic resection with curative-intent. The differential response to therapy in resected specimens, measured with the gold-standard Tumor Regression Grade (TRG; from 1, complete response to 5, no response) was examined, relative to the model predicted systemic and tumor-site chemotherapy concentrations. We found that the average calculated plasma concentration of the cytotoxic drug was essentially equivalent across patients exhibiting different TRGs, while the estimated tumor-site chemotherapeutic concentration (eTSCC) showed a quadratic decline from TRG = 1 to TRG = 5 (p < 0.001). The eTSCC was significantly lower than the observed plasma concentration and dropped by a factor of ~5 between patients with complete response (TRG = 1) and those with no response (TRG = 5), while the plasma concentration remained stable across TRG groups. TRG variations were driven and predicted by differences in tumor perfusion and eTSCC. If confirmed in carefully planned prospective studies, these findings will form the basis of a paradigm shift in the care of patients with potentially curable colorectal cancer and liver metastases.

Numerical study of microwave induced thermoacoustic imaging for initial detection of cancer of breast on anatomically realistic breast phantom

BACKGROUND AND OBJECTIVE

Microwave-induced thermoacoustic imaging (MITAI) represents an innovative imaging approach for detection of breast cancer at initial phases by integrating the benefits provided by procedures of microwave and ultrasound imaging. The present investigation examines an innovative three-dimensional numerical modeling of MITAI as a problem with multi-physics nature.

METHODS

Simulations are performed by the use of COMSOL software. An anatomically realistic breast phantom representing various parts of a real breast, such as three different types of tissue, fibro-connective/glandular, transitional; and fatty, is taken into consideration along with a tumor. This breast phantom with a tumor is irradiated by a 2.45 GHz pulsed rectangular waveguide. The temperature increase and its consequent pressure caused by electromagnetic absorption are analyzed.

RESULTS

More temperature increase occurs in the tumor area than in the other parts of the breast, the fact which results in further increase in the pressure in the tumor area than other parts. This makes the tumor distinguishable. The ability of the MITAI process regarding the tumor size, shape (both geometrical shape and spatial orientation), location, the irradiation power level, and the pulse width is also investigated. It is demonstrated that tumor size does not have a significant impact on the efficiency of detection. In fact, very small tumors in the early stages of cancer development (with a radius of 0.25 cm) are also detectable by employing the MITAI technique. The geometrical shape of the tumor does not considerably affect the detecting performance just by itself. The spatial orientation of the tumor actually has a great impact on it. The location of the tumor is an essential factor involved in detection efficiency of MITAI. Tumors located in the fatty tissues would be much easier to be detected than those in the glandular tissues. Moreover, results denote that with augmentation of the irradiation power level or increasing the pulse width, stronger acoustic waves would be produced to make tumor detection easier.

CONCLUSION

These modeling and techniques may be applied aiming for determination of the amount of the generated pressure differences and acoustic pressure magnitude, and can be utilized as an effective prognosticator in practical tests.

Controlled anti-cancer drug release through advanced nano-drug delivery systems: Static and dynamic targeting strategies

Advances in nanomedicine, including early cancer detection, targeted drug delivery, and personalized approaches to cancer treatment are on the rise. For example, targeted drug delivery systems can improve intracellular delivery because of their multifunctionality. Novel endogenous-based and exogenous-based stimulus-responsive drug delivery systems have been proposed to prevent the cancer progression with proper drug delivery. To control effective dose loading and sustained release, targeted permeability and individual variability can now be described in more-complex ways, such as by combining internal and external stimuli. Despite these advances in release control, certain challenges remain and are identified in this research, which emphasizes the control of drug release and applications of nanoparticle-based drug delivery systems. Using a multiscale and multidisciplinary approach, this study investigates and analyzes drug delivery and release strategies in the nanoparticle-based treatment of cancer, both mathematically and clinically.

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.

Evaluation of inverse methods for estimation of mechanical parameters in solid tumors

To treat cancer, knowledge of mechanical parameters can be essential. This study proposes a new approach for estimating hydraulic conductivity (k) and hydraulic conductivity ratio (α) of a living tissue, based on inverse methods, allowing tissue parameter estimation using only a limited set of measurements. First, two population-based algorithms (Levenberg-Marquardt (LM) method and conjugate gradient (CG) method) and two gradient-based algorithms (genetic algorithm (GA) and particle swarm optimization (PSO) algorithm) are considered, and a comparative study between these different inverse methods is performed to determine which methods have a good performance in terms of convergence rate and stability. CG method is shown to perform well in the case of noise-free input data; however, in the case of noisy input data, it fails to converge. The other three methods (LM, GA, and PSO) converge with estimation errors <10% in both noise-free and noisy input data, suggesting their utility to tackle this problem. In the second part, the effectiveness and good accuracy of these robust algorithms (LM, GA, and PSO) are validated with experimental results. The hydraulic conductivity and hydraulic conductivity ratio of a specific living tumor tissue are then estimated for mammary adenocarcinoma (R3230AC). Moreover, assuming measurement of only one-point interstitial pressure inside the tumor, the effect of the location of this one-point on estimation accuracy of hydraulic conductivity is investigated. We show that estimation errors for points measured near the surface and center of the tumor are greater than at other points.

Transport of nanoparticles in magnetic targeting: Comparison of magnetic, diffusive and convective forces and fluxes in the microvasculature, through vascular pores and across the interstitium

Magnetic nanoparticle targeting in tumor areas is examined by an integrated consideration of the transport steps from the microcirculation to the vascular walls, through their pores and into the interstitium. Brownian, flow- and magnetically induced forces and fluxes are compared on the basis of order-of-magnitude estimates and numerical simulations. The main resistance to nanoparticle transport is found to be within the interstitium, since fluxes there are much smaller than the extravasation fluxes, and the latter are much smaller than the convective-diffusive ones within the microvasculature. For typical nanoparticle sizes, magnetic properties and strengths of magnetic fields as in MRI equipment, magnetic targeting is rather unlikely to play a significant role in directing nanoparticles towards vascular walls or through vascular pores. However, magnetic drift can have an effect within the interstitium and a tangible overall outcome, despite the fact that typical magnetic forces are smaller than Brownian ones or interstitial flow convective forces. The reason behind such an effect has to do with the much larger length scales involved in interstitial transport. Magnetic drift creates a front of large nanoparticle concentrations, flooding the inadequately perfused and poorly accessible tumor area. On the basis of time-scale estimates, it is suggested that sequential cycles of magnetic nanoparticle dosage may help in more efficient access of cell layers ever closer to the tumor center. The present results may assist in the quest for optimal parameters and conditions, given the conflicting requirements for particles small enough to evade hydrodynamic and steric hindrances in vascular pores and the interstitium, yet large enough to bear a substantial magnetic load.

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.

Estimation of drug and tumor properties using novel hybrid meta-heuristic methods

One of the major drawbacks in mathematical modeling of the drug delivery in living species is application of a common value for a specific property such as diffusion coefficient of drug in tissue, while this property is unique for each person or species. Therefore, knowledge on the species-specific values of these properties can improve the process of drug delivery and treatment. Inverse problem methods can achieve these unique properties for each specimen. Estimation of the individual-specific drug and tumor parameters requires the evaluation of the drug concentration (the concentration of medical images) within the tumor tissue. Accordingly, in this paper, first, the drug transport equation in tumor is determined. Then, the sensitivity analysis is conducted to determine the appropriate area for selecting the drug concentration to estimate the drug and tumor parameters. Finally, the parameters estimated by meta-heuristic and hybrid meta-heuristic methods are compared. To enhance the validity of the methods, two different drug transport models are examined. The results indicate that the hybrid methods gave rise to more precise estimations, especially the hybrid particle swarm optimization (PSO) method with whale optimization algorithm (WOA) which offer more appropriate responses in the parameters estimation of two models.

Numerical modeling of high-intensity focused ultrasound-mediated intraperitoneal delivery of thermosensitive liposomal doxorubicin for cancer chemotherapy

Although intraperitoneal chemotherapy (IPC) has been suggested as a promising method for the management of peritoneal dissemination (PD) of ovarian or colorectal cancers, the actual clinical use of this method has been restricted due to such problems as poor drug penetration into the tumor and high side effects. It is, therefore, necessary to develop new strategies to improve the efficacy of this approach. In the present work, a new strategy is proposed based on intraperitoneal (IP) injection of thermosensitive liposomal doxorubicin (TSL-Dox) with triggered release by mild hyperthermia induced by high intensity focused ultrasound (HIFU). A computational model is developed to evaluate the proposed drug delivery system. Results show an order of magnitude increase in drug penetration depth into the tumor compared to the conventional IP delivery. Furthermore, the effects of thermal conditions applied to the tumor, TSL size, tumor vessel permeability, and tumor size are investigated. Results indicate an improved efficiency of the drug delivery by expanding the heated region, yet, it increases the risk of unintentional TSL drug load release in the peritoneal cavity. Results also indicate that smaller TSLs have better treatment outcome. However, there is a significant reduction in treatment efficacy for TSLs with sizes smaller than the vessel wall pore size. Thus, tuning the size of TSL should be based on the tumor microvascular permeability. The simulation results suggest that the TSL-Dox delivery system in smaller tumors is far advantageous than larger ones. Results of our model can be used as guidelines for future preclinical studies.