Numerical modeling of nanodrug distribution in tumors with heterogeneous vasculature

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 [...].

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.

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.

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

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

Multiscale Modelling of Nanoparticle Distribution in a Realistic Tumour Geometry Following Local Injection

Radiosensitizers have proven to be an effective method of improving radiotherapy outcomes, with the distribution of particles being a crucial element to delivering optimal treatment outcomes due to the short range of effect of these particles. Here we present a computational model for the transport of nanoparticles within the tumour, whereby the fluid velocity and particle deposition are obtained and used as input into the convection-diffusion equation to calculate the spatio-temporal concentration of the nanoparticles. The effect of particle surface charge and injection locations on the distribution of nanoparticle concentration within the interstitial fluid and deposited onto cell surfaces is assessed. The computational results demonstrate that negatively charged particles can achieve a more uniform distribution throughout the tumour as compared to uncharged or positively charged particles, with particle volume within the fluid being 100% of tumour volume and deposited particle volume 44.5%. In addition, varying the injection location from the end to the middle of the tumour caused a reduction in particle volume of almost 20% for negatively charged particles. In conclusion, radiosensitizing particles should be negatively charged to maximise their spread and penetration within the tumour. Choosing an appropriate injection location can further improve the distribution of these particles.

Modelling of Nanoparticle Distribution in a Spherical Tumour during and Following Local Injection

Radio-sensitizing nanoparticles are a potential method to increase the damage caused to cancerous cells during the course of radiotherapy. The distribution of these particles in a given targeted tumour is a relevant factor in determining the efficacy of nanoparticle-enhanced treatment. In this study, a three-part mathematical model is shown to predict the distribution of nanoparticles after direct injection into a tumour. In contrast with previous studies, here, a higher value of diffusivity for charged particles was used and the concentration profile of deposited particles was studied. Simulation results for particle concentrations both in the interstitial fluid and deposited onto cells are compared for different values of particle surface charges during and after injection. Our results show that particles with a negative surface charge can spread farther from the injection location as compared to uncharged particles with charged particles occupying 100% of the tumour volume compared to 8.8% for uncharged particles. This has implications for the future development of radiosensitizers and any associated trials.

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.

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.

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.

Nanomaterials to Fight Cancer: An Overview on Their Multifunctional Exploitability

In recent years the worldwide research community has highlighted innumerable benefits of nanomaterials in cancer detection and therapy. Nevertheless, the development of cancer nanomedicines and other bionanotechnology requires a huge amount of considerations about the interactions of nanomaterials and biological systems, since long-term effects are not yet fully known. Open issues remain the determination of the nanoparticles distributions patterns and the internalization rate into the tumor while avoiding their accumulation in internal organs or other healthy tissues. The purpose of this work is to provide a standard overview of the most recent advances in nanomaterials to fight cancer and to collect trends and future directions to follow according to some critical aspects still present in this field. Complementary to the very recent review of Wolfram and Ferrari which discusses and classifies successful clinically-approved cancer nanodrugs as well as promising candidates in the pipeline, this work embraces part of their proposed classification system based on the exploitation of multifunctionality and extends the review to peer-reviewed journal articles published in the last 3 years identified through international databases.

Evaluation of retinal vascular structure after epiretinal membrane surgery by optical coherence tomography angiography

PURPOSE

To evaluate the retinal vascular structure before and after the epiretinal membrane (ERM) surgery by optical coherence tomography angiography (OCTA).

METHODS

Twenty-two eyes with ERM (study eyes) had been evaluated by OCTA for superficial capillary plexus (SCP) and deep capillary plexus (DCP) vessel density (VD) at foveal and parafoveal regions and foveal avascular zone (FAZ) before and after ERM removal surgery. Twenty-two fellow eyes were selected as control group.

RESULTS

Preoperative VD of SCP and DCP were significantly lower in ERM eyes than in controls in both foveal and parafoveal areas (p < 0.05, for all). The difference regressed in SCP (fovea: 18.04 ± 3.1 vs 19.98 ± 18 p = 0.002 and parafovea: 47.33 ± 3.54 vs 49.71 ± 28 p = 0.001), but persisted in DCP (fovea: 17.25 ± 3.52 vs 17.57 ± 4.01 p = 0.856 and parafovea: 50.12 ± 4.35 vs 50.93 ± 3.24 p = 0.791) in study eyes, postoperatively. Superficial and deep FAZ areas were significantly smaller in study eyes than controls. Postoperatively, superficial FAZ area enlarged (0.288 ± 0.10 vs 0.307 ± 0.08 p = 0.012), whereas deep FAZ area did not (0.324 ± 0.09 vs 0.338 ± 0.07 p = 0.435). FAZ area was correlated with the best-corrected visual acuity in ERM eyes.

CONCLUSION

Vascular damage in SCP and DCP was demonstrated by OCTA in eyes with ERM. ERM removal surgery mainly improves superficial changes caused by ERM. Changes in deep retinal flow may be associated with visual outcomes after ERM removal surgery.

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.

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.

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.

Validation of MRI quantitative susceptibility mapping of superparamagnetic iron oxide nanoparticles for hyperthermia applications in live subjects

The use of magnetic fluid hyperthermia (MFH) for cancer therapy has shown promise but lacks suitable methods for quantifying exogenous irons such as superparamagnetic iron oxide (SPIO) nanoparticles as a source of heat generation under an alternating magnetic field (AMF). Application of quantitative susceptibility mapping (QSM) technique to prediction of SPIO in preclinical models has been challenging due to a large variation of susceptibility values, chemical shift from tissue fat, and noisier data arising from the higher resolution required to visualize the anatomy of small animals. In this study, we developed a robust QSM for the SPIO ferumoxytol in live mice to examine its potential application in MFH for cancer therapy. We demonstrated that QSM was able to simultaneously detect high level ferumoxytol accumulation in the liver and low level localization near the periphery of tumors. Detection of ferumoxytol distribution in the body by QSM, however, required imaging prior to and post ferumoxytol injection to discriminate exogenous iron susceptibility from other endogenous sources. Intratumoral injection of ferumoxytol combined with AMF produced a ferumoxytol-dose dependent tumor killing. Histology of tumor sections corroborated QSM visualization of ferumoxytol distribution near the tumor periphery, and confirmed the spatial correlation of cell death with ferumoxytol distribution. Due to the dissipation of SPIOs from the injection site, quantitative mapping of SPIO distribution will aid in estimating a change in temperature in tissues, thereby maximizing MFH effects on tumors and minimizing side-effects by avoiding unwanted tissue heating.

Mixture theory modeling for characterizing solute transport in breast tumor tissues

Background

Tumor numerical models have been used to quantify solute transport with a single capillary embedded in an infinite tumor expanse, but measurements from different mammalian tumors suggest that a tissue containing a single capillary with an infinite intercapillary distance assumption is not physiological. The present study aims to investigate the limits of the intercapillary distance within which nanoparticle transport resembles solute extravasation in a breast tumor model as a function of the solute size, the intercapillary separation, and the flow direction in microvessels.

Methods

Solute transport is modeled in a breast tumor for different vascular configurations using mixture theory. A comparison of a single capillary configuration (SBC) with two parallel cylindrical blood vessels (2 BC) and a lymph vessel parallel to a blood vessel (BC_LC) embedded in the tissue cylinder is performed for five solute molecular weights between 0.1 kDa and 70 kDa. The effects of counter flow (CN) versus co-current flow (CO) on the solute accumulation were also investigated and the scaling of solute accumulation-decay time and concentration was explored.

Results

We found that the presence of a second capillary reduces the extravascular concentration compared to a single capillary and this reduction is enhanced by the presence of a lymph vessel. Varying the intercapillary distance with respect to vessel diameter shows a deviation of 10-30% concentration for 2 BC and 45-60% concentration for BC_LC configuration compared to the reference SBC configuration. Finally, we introduce a non-dimensional time scale that captures the concentration as a function of the transport and geometric parameters. We find that the peak solute concentration in the tissue space occurs at a non-dimensional time, T peak ∗ = 0.027 ± 0.018, irrespective of the solute size, tissue architecture, and microvessel flow direction.

Conclusions

This work suggests that the knowledge of such a unique non-dimensional time would allow estimation of the time window at which solute concentration in tissue peaks. Hence this can aid in the design of future therapeutic efficacy studies as an example for triggering drug release or laser excitation in the case of photothermal therapies.

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

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