Quantifying uncertainties in the microvascular transport of nanoparticles

In silico modeling of patient-specific blood rheology in type 2 diabetes mellitus

Increased blood viscosity in type 2 diabetes mellitus (T2DM) is a risk factor for the development of insulin resistance and diabetes-related vascular complications; however, individuals with T2DM exhibit heterogeneous hemorheological properties, including cell deformation and aggregation. Using a multiscale red blood cell (RBC) model with key parameters derived from patient-specific data, we present a computational study of the rheological properties of blood from individual patients with T2DM. Specifically, one key model parameter, which determines the shear stiffness of the RBC membrane (μ) is informed by the high-shear-rate blood viscosity of patients with T2DM. At the same time, the other, which contributes to the strength of the RBC aggregation interaction (D0), is derived from the low-shear-rate blood viscosity of patients with T2DM. The T2DM RBC suspensions are simulated at different shear rates, and the predicted blood viscosity is compared with clinical laboratory-measured data. The results show that the blood viscosity obtained from clinical laboratories and computational simulations are in agreement at both low and high shear rates. These quantitative simulation results demonstrate that the patient-specific model has truly learned the rheological behavior of T2DM blood by unifying the mechanical and aggregation factors of the RBCs, which provides an effective way to extract quantitative predictions of the rheological properties of the blood of individual patients with T2DM.

Predictive Design and Analysis of Drug Transport by Multiscale Computational Models Under Uncertainty

Computational modeling of drug delivery is becoming an indispensable tool for advancing drug development pipeline, particularly in nanomedicine where a rational design strategy is ultimately sought. While numerous in silico models have been developed that can accurately describe nanoparticle interactions with the bioenvironment within prescribed length and time scales, predictive design of these drug carriers, dosages and treatment schemes will require advanced models that can simulate transport processes across multiple length and time scales from genomic to population levels. In order to address this problem, multiscale modeling efforts that integrate existing discrete and continuum modeling strategies have recently emerged. These multiscale approaches provide a promising direction for bottom-up in silico pipelines of drug design for delivery. However, there are remaining challenges in terms of model parametrization and validation in the presence of variability, introduced by multiple levels of heterogeneities in disease state. Parametrization based on physiologically relevant in vitro data from microphysiological systems as well as widespread adoption of uncertainty quantification and sensitivity analysis will help address these challenges.

Deep-learning-based porous media microstructure quantitative characterization and reconstruction method

Microstructure characterization and reconstruction (MCR) is one of the most important components of discovering processing-structure-property relations of porous media behavior and inverse porous media design in computational materials science. Since the algorithms for describing and controlling the geometric configuration of microstructures need to solve a large number of variables and involve multiobjective conditions, the existing MCR methods have difficulty in gaining a perfect trade-off among the quantitative generation and characterization capability and the reconstruction quality. In this work, an improved 3D Porous Media Microstructure (3DPmmGAN) generative adversarial network based on deep-learning algorithm is demonstrated for high-quality microstructures generation with high controllability and high prediction accuracy. The proposed 3DPmmGAN allows the model to utilize unlabeled data for complex high-randomness microstructures end-to-end training within an acceptable time consumption. Further analysis shows that the trained network has good adaptivity for microstructures with different random geometric configurations, and can quantitatively control the generated structure according to semantic conditions, and can also quantitatively predict complex microstructure features. The key results suggest the proposed 3DPmmGAN is a powerful tool to accelerate the preparation and the initial characterization of 3D porous media, and potentially maximize the design efficiency for porous media.

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.

Multi-objective optimization of tumor response to drug release from vasculature-bound nanoparticles

The pharmacokinetics of nanoparticle-borne drugs targeting tumors depends critically on nanoparticle design. Empirical approaches to evaluate such designs in order to maximize treatment efficacy are time- and cost-intensive. We have recently proposed the use of computational modeling of nanoparticle-mediated drug delivery targeting tumor vasculature coupled with numerical optimization to pursue optimal nanoparticle targeting and tumor uptake. Here, we build upon these studies to evaluate the effect of tumor size on optimal nanoparticle design by considering a cohort of heterogeneously-sized tumor lesions, as would be clinically expected. The results indicate that smaller nanoparticles yield higher tumor targeting and lesion regression for larger-sized tumors. We then augment the nanoparticle design optimization problem by considering drug diffusivity, which yields a two-fold tumor size decrease compared to optimizing nanoparticles without this consideration. We quantify the tradeoff between tumor targeting and size decrease using bi-objective optimization, and generate five Pareto-optimal nanoparticle designs. The results provide a spectrum of treatment outcomes - considering tumor targeting vs. antitumor effect - with the goal to enable therapy customization based on clinical need. This approach could be extended to other nanoparticle-based cancer therapies, and support the development of personalized nanomedicine in the longer term.

Hybrid modeling frameworks of tumor development and treatment

Tumors are complex multicellular heterogeneous systems comprised of components that interact with and modify one another. Tumor development depends on multiple factors: intrinsic, such as genetic mutations, altered signaling pathways, or variable receptor expression; and extrinsic, such as differences in nutrient supply, crosstalk with stromal or immune cells, or variable composition of the surrounding extracellular matrix. Tumors are also characterized by high cellular heterogeneity and dynamically changing tumor microenvironments. The complexity increases when this multiscale, multicomponent system is perturbed by anticancer treatments. Modeling such complex systems and predicting how tumors will respond to therapies require mathematical models that can handle various types of information and combine diverse theoretical methods on multiple temporal and spatial scales, that is, hybrid models. In this update, we discuss the progress that has been achieved during the last 10 years in the area of the hybrid modeling of tumors. The classical definition of hybrid models refers to the coupling of discrete descriptions of cells with continuous descriptions of microenvironmental factors. To reflect on the direction that the modeling field has taken, we propose extending the definition of hybrid models to include of coupling two or more different mathematical frameworks. Thus, in addition to discussing recent advances in discrete/continuous modeling, we also discuss how these two mathematical descriptions can be coupled with theoretical frameworks of optimal control, optimization, fluid dynamics, game theory, and machine learning. All these methods will be illustrated with applications to tumor development and various anticancer treatments.

This article is characterized under:

Analytical and Computational Methods > Computational Methods

Translational, Genomic, and Systems Medicine > Therapeutic Methods

Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models

Particle morphology: an important factor affecting drug delivery by nanocarriers into solid tumors

INTRODUCTION

Efficient delivery of drugs by nanoparticles deep into solid tumors is the precondition of valid cancer therapy. Despite profound understanding of the delivery of spherical nanoparticles into solid tumor attained, insufficient attention was paid to anisotropic particles. Actually, owing to their structural asymmetry, some non-spherical particles exhibit significant advantages over their spherical counterparts.

AREAS COVERED

This review will focus on particles with different shapes (discoidal particle, nanorod, filamentous particle, single-walled carbon nanotube) and the influence of their morphological characteristics (size, aspect ratio, rigidity) on the process of drug delivery to solid tumor in view of systemic circulation, transport from circulation system to tumor tissue, intratumoral transport and uptake by tumor cells, on the basis of introduction of challenges for drug delivery to solid tumor. In addition, the morphological characteristics will be briefly introduced to provide an understanding of anisotropic particle morphology.

EXPERT OPINION

Anisotropic particles exhibit desirable properties such as enhanced circulation time and efficient tumor penetration that could serve as an enlightenment in the exploitation of novel non-spherical nanocarriers to clinical therapy. Yet, current understanding of how anisotropic particles interact with organism is insufficient, which restricts the biomedical application of anisotropic particles. Further work is desired for the development of practical fabrication of anisotropic particles, quantitative analysis of particle morphology, as well as profound understanding of new targeting mechanism and intratumoral penetration of anisotropic particles.

Effect of fractional blood flow on plasma skimming in the microvasculature

Although redistribution of red blood cells at bifurcated vessels is highly dependent on flow rate, it is still challenging to quantitatively express the dependence of flow rate in plasma skimming due to nonlinear cellular interactions. We suggest a plasma skimming model that can involve the effect of fractional blood flow at each bifurcation point. To validate the model, it is compared with in vivo data at single bifurcation points, as well as microvascular network systems. In the simulation results, the exponential decay of the plasma skimming parameter M along fractional flow rate shows the best performance in both cases.

Predicting different adhesive regimens of circulating particles at blood capillary walls

A fundamental step in the rational design of vascular targeted particles is the firm adhesion at the blood vessel walls. Here, a combined lattice Boltzmann-immersed boundary model is presented for predicting the near-wall dynamics of circulating particles. A moving least squares algorithm is used to reconstruct the forcing term accounting for the immersed particle, whereas ligand-receptor binding at the particle-wall interface is described via forward and reverse probability distributions. First, it is demonstrated that the model predicts with good accuracy the rolling velocity of tumor cells over an endothelial layer in a microfluidic channel. Then, particle-wall interactions are systematically analyzed in terms of particle geometries (circular, elliptical with aspect ratios 2 and 3), surface ligand densities (0.3, 0.5, 0.7 and 0.9), ligand-receptor bond strengths (1 and 2) and Reynolds numbers (Re = 0.01, 0.1 and 1.0). Depending on these conditions, four different particle-wall interaction regimens are identified, namely not adhering, rolling, sliding and firmly adhering particles. The proposed computational strategy can be efficiently used for predicting the near-wall dynamics of particles with arbitrary geometries and surface properties and represents a fundamental tool in the rational design of particles for the specific delivery of therapeutic and imaging agents.

Generalized plasma skimming model for cells and drug carriers in the microvasculature

In microvascular transport, where both blood and drug carriers are involved, plasma skimming has a key role on changing hematocrit level and drug carrier concentration in capillary beds after continuous vessel bifurcation in the microvasculature. While there have been numerous studies on modeling the plasma skimming of blood, previous works lacked in consideration of its interaction with drug carriers. In this paper, a generalized plasma skimming model is suggested to predict the redistributions of both the cells and drug carriers at each bifurcation. In order to examine its applicability, this new model was applied on a single bifurcation system to predict the redistribution of red blood cells and drug carriers. Furthermore, this model was tested at microvascular network level under different plasma skimming conditions for predicting the concentration of drug carriers. Based on these results, the applicability of this generalized plasma skimming model is fully discussed and future works along with the model's limitations are summarized.

Cell and nanoparticle transport in tumour microvasculature: the role of size, shape and surface functionality of nanoparticles

Through nanomedicine, game-changing methods are emerging to deliver drug molecules directly to diseased areas. One of the most promising of these is the targeted delivery of drugs and imaging agents via drug carrier-based platforms. Such drug delivery systems can now be synthesized from a wide range of different materials, made in a number of different shapes, and coated with an array of different organic molecules, including ligands. If optimized, these systems can enhance the efficacy and specificity of delivery compared with those of non-targeted systems. Emerging integrated multiscale experiments, models and simulations have opened the door for endless medical applications. Current bottlenecks in design of the drug-carrying particles are the lack of knowledge about the dispersion of these particles in the microvasculature and of their subsequent internalization by diseased cells (Bao et al. 2014 J. R. Soc. Interface 11, 20140301 (doi:10.1098/rsif.2014.0301)). We describe multiscale modelling techniques that study how drug carriers disperse within the microvasculature. The immersed molecular finite-element method is adopted to simulate whole blood including blood plasma, red blood cells and nanoparticles. With a novel dissipative particle dynamics method, the beginning stages of receptor-driven endocytosis of nanoparticles can be understood in detail. Using this multiscale modelling method, we elucidate how the size, shape and surface functionality of nanoparticles will affect their dispersion in the microvasculature and subsequent internalization by targeted cells.

Soft Discoidal Polymeric Nanoconstructs Resist Macrophage Uptake and Enhance Vascular Targeting in Tumors

Most nanoparticles for biomedical applications originate from the self-assembling of individual constituents through molecular interactions and possess limited geometry control and stability. Here, 1000 × 400 nm discoidal polymeric nanoconstructs (DPNs) are demonstrated by mixing hydrophobic and hydrophilic polymers with lipid chains and curing the resulting paste directly within silicon templates. By changing the paste composition, soft- and rigid-DPNs (s- and r-DPNs) are synthesized exhibiting the same geometry, a moderately negative surface electrostatic charge (-14 mV), and different mechanical stiffness (∼1.3 and 15 kPa, respectively). Upon injection in mice bearing nonorthotopic brain or skin cancers, s-DPNs exhibit ∼24 h circulation half-life and accumulate up to ∼20% of the injected dose per gram tumor, detecting malignant masses as small as ∼0.1% the animal weight via PET imaging. This unprecedented behavior is ascribed to the unique combination of geometry, surface properties, and mechanical stiffness which minimizes s-DPN sequestration by the mononuclear phagocyte system. Our results could boost the interest in using less conventional delivery systems for cancer theranosis.

USNCTAM perspectives on mechanics in medicine

Over decades, the theoretical and applied mechanics community has developed sophisticated approaches for analysing the behaviour of complex engineering systems. Most of these approaches have targeted systems in the transportation, materials, defence and energy industries. Applying and further developing engineering approaches for understanding, predicting and modulating the response of complicated biomedical processes not only holds great promise in meeting societal needs, but also poses serious challenges. This report, prepared for the US National Committee on Theoretical and Applied Mechanics, aims to identify the most pressing challenges in biological sciences and medicine that can be tackled within the broad field of mechanics. This echoes and complements a number of national and international initiatives aiming at fostering interdisciplinary biomedical research. This report also comments on cultural/educational challenges. Specifically, this report focuses on three major thrusts in which we believe mechanics has and will continue to have a substantial impact. (i) Rationally engineering injectable nano/microdevices for imaging and therapy of disease. Within this context, we discuss nanoparticle carrier design, vascular transport and adhesion, endocytosis and tumour growth in response to therapy, as well as uncertainty quantification techniques to better connect models and experiments. (ii) Design of biomedical devices, including point-of-care diagnostic systems, model organ and multi-organ microdevices, and pulsatile ventricular assistant devices. (iii) Mechanics of cellular processes, including mechanosensing and mechanotransduction, improved characterization of cellular constitutive behaviour, and microfluidic systems for single-cell studies.

A Bayesian hierarchical model for maximizing the vascular adhesion of nanoparticles

The complex vascular dynamics and wall deposition of systemically injected nanoparticles is regulated by their geometrical properties (size, shape) and biophysical parameters (ligand-receptor bond type and surface density, local shear rates). Although sophisticated computational models have been developed to capture the vascular behavior of nanoparticles, it is increasingly recognized that purely deterministic approaches, where the governing parameters are known a priori and conclusively describe behaviors based on physical characteristics, may be too restrictive to accurately reflect natural processes. Here, a novel computational framework is proposed by coupling the physics dictating the vascular adhesion of nanoparticles with a stochastic model. In particular, two governing parameters (i.e. the ligand-receptor bond length and the ligand surface density on the nanoparticle) are treated as two stochastic quantities, whose values are not fixed a priori but would rather range in defined intervals with a certain probability. This approach is used to predict the deposition of spherical nanoparticles with different radii, ranging from 750 to 6,000 nm, in a parallel plate flow chamber under different flow conditions, with a shear rate ranging from 50 to 90 sec^-1. It is demonstrated that the resulting stochastic model can predict the experimental data more accurately than the original deterministic model. This approach allows one to increase the predictive power of mathematical models of any natural process by accounting for the experimental and intrinsic biological uncertainties.