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

Comprehensive analysis of lung cancer pathology images to discover tumor shape and boundary features that predict survival outcome

Pathology images capture tumor histomorphological details in high resolution. However, manual detection and characterization of tumor regions in pathology images is labor intensive and subjective. Using a deep convolutional neural network (CNN), we developed an automated tumor region recognition system for lung cancer pathology images. From the identified tumor regions, we extracted 22 well-defined shape and boundary features and found that 15 of them were significantly associated with patient survival outcome in lung adenocarcinoma patients from the National Lung Screening Trial. A tumor region shape-based prognostic model was developed and validated in an independent patient cohort (n = 389). The predicted high-risk group had significantly worse survival than the low-risk group (p value = 0.0029). Predicted risk group serves as an independent prognostic factor (high-risk vs. low-risk, hazard ratio = 2.25, 95% CI 1.34–3.77, p value = 0.0022) after adjusting for age, gender, smoking status, and stage. This study provides new insights into the relationship between tumor shape and patient prognosis.

Computational modelling of drug delivery to solid tumour: Understanding the interplay between chemotherapeutics and biological system for optimised delivery systems

Drug delivery to solid tumour involves multiple physiological, biochemical and biophysical processes taking place across a wide range of length and time scales. The therapeutic efficacy of anticancer drugs is influenced by the complex interplays among the intrinsic properties of tumours, biophysical aspects of drug transport and cellular uptake. Mathematical and computational modelling allows for a well-controlled study on the individual and combined effects of a wide range of parameters on drug transport and therapeutic efficacy, which would not be possible or economically viable through experimental means. A wide spectrum of mathematical models has been developed for the simulation of drug transport and delivery in solid tumours, including PK/PD-based compartmental models, microscopic and macroscopic transport models, and molecular dynamics drug loading and release models. These models have been used as a tool to identify the limiting factors and for optimal design of efficient drug delivery systems. This article gives an overview of the currently available computational models for drug transport in solid tumours, together with their applications to novel drug delivery systems, such as nanoparticle-mediated drug delivery and convection-enhanced delivery.

Investigation of Biotransport in a Tumor With Uncertain Material Properties Using a Nonintrusive Spectral Uncertainty Quantification Method

In this study, statistical models are developed for modeling uncertain heterogeneous permeability and porosity in tumors, and the resulting uncertainties in pressure and velocity fields during an intratumoral injection are quantified using a nonintrusive spectral uncertainty quantification (UQ) method. Specifically, the uncertain permeability is modeled as a log-Gaussian random field, represented using a truncated Karhunen-Lòeve (KL) expansion, and the uncertain porosity is modeled as a log-normal random variable. The efficacy of the developed statistical models is validated by simulating the concentration fields with permeability and porosity of different uncertainty levels. The irregularity in the concentration field bears reasonable visual agreement with that in MicroCT images from experiments. The pressure and velocity fields are represented using polynomial chaos (PC) expansions to enable efficient computation of their statistical properties. The coefficients in the PC expansion are computed using a nonintrusive spectral projection method with the Smolyak sparse quadrature. The developed UQ approach is then used to quantify the uncertainties in the random pressure and velocity fields. A global sensitivity analysis is also performed to assess the contribution of individual KL modes of the log-permeability field to the total variance of the pressure field. It is demonstrated that the developed UQ approach can effectively quantify the flow uncertainties induced by uncertain material properties of the tumor.

The effect of tumour size on drug transport and uptake in 3-D tumour models reconstructed from magnetic resonance images

Drug transport and its uptake by tumour cells are strongly dependent on tumour properties, which vary in different types of solid tumours. By simulating the key physical and biochemical processes, a numerical study has been carried out to investigate the transport of anti-cancer drugs in 3-D tumour models of different sizes. The therapeutic efficacy for each tumour is evaluated by using a pharmacodynamics model based on the predicted intracellular drug concentration. Simulation results demonstrate that interstitial fluid pressure and interstitial fluid loss vary non-linearly with tumour size. Transvascular drug exchange, driven by the concentration gradient of unbound drug between blood and interstitial fluid, is more efficient in small tumours, owing to the low spatial-mean interstitial fluid pressure and dense microvasculature. However, this has a detrimental effect on therapeutic efficacy over longer periods as a result of enhanced reverse diffusion of drug to the blood circulation after the cessation of drug infusion, causing more rapid loss of drug in small tumours.

Engineering approaches in siRNA delivery

siRNAs are very potent drug molecules, able to silence genes involved in pathologies development. siRNAs have virtually an unlimited therapeutic potential, particularly for the treatment of inflammatory diseases. However, their use in clinical practice is limited because of their unfavorable properties to interact and not to degrade in physiological environments. In particular they are large macromolecules, negatively charged, which undergo rapid degradation by plasmatic enzymes, are subject to fast renal clearance/hepatic sequestration, and can hardly cross cellular membranes. These aspects seriously impair siRNAs as therapeutics. As in all the other fields of science, siRNAs management can be advantaged by physical-mathematical descriptions (modeling) in order to clarify the involved phenomena from the preparative step of dosage systems to the description of drug-body interactions, which allows improving the design of delivery systems/processes/therapies. This review analyzes a few mathematical modeling approaches currently adopted to describe the siRNAs delivery, the main procedures in siRNAs vectors' production processes and siRNAs vectors' release from hydrogels, and the modeling of pharmacokinetics of siRNAs vectors. Furthermore, the use of physical models to study the siRNAs vectors' fate in blood stream and in the tissues is presented. The general view depicts a framework maybe not yet usable in therapeutics, but with promising possibilities for forthcoming applications.

A Validated Multiscale In-Silico Model for Mechano-sensitive Tumour Angiogenesis and Growth

Vascularisation is a key feature of cancer growth, invasion and metastasis. To better understand the governing biophysical processes and their relative importance, it is instructive to develop physiologically representative mathematical models with which to compare to experimental data. Previous studies have successfully applied this approach to test the effect of various biochemical factors on tumour growth and angiogenesis. However, these models do not account for the experimentally observed dependency of angiogenic network evolution on growth-induced solid stresses. This work introduces two novel features: the effects of hapto- and mechanotaxis on vessel sprouting, and mechano-sensitive dynamic vascular remodelling. The proposed three-dimensional, multiscale, in-silico model of dynamically coupled angiogenic tumour growth is specified to in-vivo and in-vitro data, chosen, where possible, to provide a physiologically consistent description. The model is then validated against in-vivo data from murine mammary carcinomas, with particular focus placed on identifying the influence of mechanical factors. Crucially, we find that it is necessary to include hapto- and mechanotaxis to recapitulate observed time-varying spatial distributions of angiogenic vasculature.

Spatiotemporal distribution modeling of PET tracer uptake in solid tumors

OBJECTIVE

Distribution of PET tracer uptake is elaborately modeled via a general equation used for solute transport modeling. This model can be used to incorporate various transport parameters of a solid tumor such as hydraulic conductivity of the microvessel wall, transvascular permeability as well as interstitial space parameters. This is especially significant because tracer delivery and drug delivery to solid tumors are determined by similar underlying tumor transport phenomena, and quantifying the former can enable enhanced prediction of the latter.

METHODS

We focused on the commonly utilized FDG PET tracer. First, based on a mathematical model of angiogenesis, the capillary network of a solid tumor and normal tissues around it were generated. The coupling mathematical method, which simultaneously solves for blood flow in the capillary network as well as fluid flow in the interstitium, is used to calculate pressure and velocity distributions. Subsequently, a comprehensive spatiotemporal distribution model (SDM) is applied to accurately model distribution of PET tracer uptake, specifically FDG in this work, within solid tumors.

RESULTS

The different transport mechanisms, namely convention and diffusion from vessel to tissue and in tissue, are elaborately calculated across the domain of interest and effect of each parameter on tracer distribution is investigated. The results show the convection terms to have negligible effect on tracer transport and the SDM can be solved after eliminating these terms.

CONCLUSION

The proposed framework of spatiotemporal modeling for PET tracers can be utilized to comprehensively assess the impact of various parameters on the spatiotemporal distribution of PET tracers.

Drug-Specific Design of Telodendrimer Architecture for Effective Doxorubicin Encapsulation

Designing a versatile nanocarrier platform that can be tailored to deliver specific drug payloads is challenging. In general, effective drug encapsulation, high drug-loading capacity, uniform shape and size distribution, and enhanced stability are among the fundamental attributes of a successful nanocarrier design. These physiochemical features of the nanocarriers are intimately tied to the specific drug payload that they are tasked to deliver. The molecular architecture of the nanocarrier's scaffold often needs to be tuned for each drug, especially if the target drugs are structurally and chemically distinct as in the case of doxorubicin (DOX) and paclitaxel (PTX). Starting from our previously reported telodendrimeric block copolymer platform optimized for PTX, we analyze three generations of telodendrimer architectures to arrive at the design that is capable of encapsulating another important chemotherapeutic drug, DOX. Multiple long-time-scale self-assembly simulations were performed both in atomistic and coarse-grained resolutions to generate equilibrated DOX-encapsulated nanocarriers. The results show how subtle changes in the molecular architecture of the telodendrimer head groups have profound effects on the nanocarrier size, morphology, and asphericity. The simulation results are in agreement with the experimental data for DOX-encapsulated nanocarriers. This work emphasizes the increasing role of molecular simulations in the rational design of nanocarriers, thereby eliminating the trial and error method that has been prevalent in experimental synthesis. The molecular-level insights gained from the simulations will be used to design the next generation of drug-specific nanocarriers.

MRI contrast agent concentration and tumor interstitial fluid pressure

The present work describes the relationship between tumor interstitial fluid pressure (TIFP) and the concentration of contrast agent for dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI). We predict the spatial distribution of TIFP based on that of contrast agent concentration. We also discuss the cases for estimating tumor interstitial volume fraction (void fraction or porosity of porous medium), ve, and contrast volume transfer constant, K(trans), by measuring the ratio of contrast agent concentration in tissue to that in plasma. A linear fluid velocity distribution may reflect a quadratic function of TIFP distribution and lead to a practical method for TIFP estimation. To calculate TIFP, the parameters or variables should preferably be measured along the direction of the linear fluid velocity (this is in the same direction as the gray value distribution of the image, which is also linear). This method may simplify the calculation for estimating TIFP.

Computer Simulations of the Tumor Vasculature: Applications to Interstitial Fluid Flow, Drug Delivery, and Oxygen Supply

Tumor vasculature, the blood vessel network supplying a growing tumor with nutrients such as oxygen or glucose, is in many respects different from the hierarchically organized arterio-venous blood vessel network in normal tissues. Angiogenesis (the formation of new blood vessels), vessel cooption (the integration of existing blood vessels into the tumor vasculature), and vessel regression remodel the healthy vascular network into a tumor-specific vasculature. Integrative models, based on detailed experimental data and physical laws, implement, in silico, the complex interplay of molecular pathways, cell proliferation, migration, and death, tissue microenvironment, mechanical and hydrodynamic forces, and the fine structure of the host tissue vasculature. With the help of computer simulations high-precision information about blood flow patterns, interstitial fluid flow, drug distribution, oxygen and nutrient distribution can be obtained and a plethora of therapeutic protocols can be tested before clinical trials. This chapter provides an overview over the current status of computer simulations of vascular remodeling during tumor growth including interstitial fluid flow, drug delivery, and oxygen supply within the tumor. The model predictions are compared with experimental and clinical data and a number of longstanding physiological paradigms about tumor vasculature and intratumoral solute transport are critically scrutinized.

Multistep, effective drug distribution within solid tumors

The distribution of drugs within solid tumors presents a long-standing barrier for efficient cancer therapies. Tumors are highly resistant to diffusion, and the lack of blood and lymphatic flows suppresses convection. Prolonged, continuous intratumoral drug delivery from a miniature drug source offers an alternative to both systemic delivery and intratumoral injection. Presented here is a model of drug distribution from such a source, in a multistep process. At delivery onset the drug mainly affects the closest surroundings. Such 'priming' enables drug penetration to successive cell layers. Tumor 'void volume' (volume not occupied by cells) increases, facilitating lymphatic perfusion. The drug is then transported by hydraulic convection downstream along interstitial fluid pressure (IFP) gradients, away from the tumor core. After a week tumor cell death occurs throughout the entire tumor and IFP gradients are flattened. Then, the drug is transported mainly by 'mixing', powered by physiological bulk body movements. Steady state is achieved and the drug covers the entire tumor over several months. Supporting measurements are provided from the LODER system, releasing siRNA against mutated KRAS over months in pancreatic cancer in-vivo models. LODER was also successfully employed in a recent Phase 1/2 clinical trial with pancreatic cancer patients.

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

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

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

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

Numerical modeling of drug delivery in a dynamic solid tumor microvasculature

The complicated capillary network induced by angiogenesis is one of the main reasons of unsuccessful cancer therapy. A multi-scale mathematical method which simulates drug transport to a solid tumor is used in this study to investigate how capillary network structure affects drug delivery. The mathematical method involves processes such as blood flow through vessels, solute and fluid diffusion, convective transport in extracellular matrix, and extravasation from blood vessels. The effect of heterogeneous dynamic network on interstitial fluid flow and drug delivery is investigated by this multi-scale method. The sprouting angiogenesis model is used for generating capillary network and then fluid flow governing equations are implemented to calculate blood flow through the tumor-induced capillary network and fluid flow in normal and tumor tissues. Finally, convection-diffusion equation is used to simulate drug delivery. Three approaches are used to simulate drug transport based on the developed mathematical method: without a vascular network, using a static vascular network, and a dynamic vascular network. The avascular approach predicts more uniform and higher drug concentration than vascular approaches since the simplified assumptions are implemented in this method. The dynamic network which uses more realistic assumptions predicts more irregular blood vessels, high interstitial pressure, and more heterogeneity in drug distribution than other two approaches.