Computational modeling of drug delivery to solid tumors: A pilot study based on a real image

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.

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.

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.

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

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

Computational Modeling of 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.

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.

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.