Efficient computational model of the in-flow capturing of magnetic nanoparticles by a cylindrical magnet for cancer nanomedicine.

Magnetic nanoparticles have emerged as a promising approach to improving cancer treatment. However, many nanoparticle designs fail in clinical trials due to a lack of understanding of how to overcome the in vivo transport barriers. To address this shortcoming, we develop a computational model aimed at the study of magnetic nanoparticles in vitro and in vivo. In this paper, we present an important building block for this overall goal, namely an efficient computational model of the in-flow capture of magnetic nanoparticles by a cylindrical permanent magnet in an idealized test setup. We use a continuum approach based on the Smoluchowski advection-diffusion equation, combined with a simple approach to consider the capture at an impenetrable boundary, and derive an analytical expression for the magnetic force of a cylindrical magnet of finite length on the nanoparticles. This provides a simple and numerically efficient way to study different magnet configurations and their influence on the nanoparticle distribution in three dimensions. Such an in silico model can increase insight into the underlying physics, help to design prototypes, and serve as a precursor to more complex systems in vivo and in silico.

Adaptive integration of history variables in constrained mixture models for organ-scale growth and remodeling.

In the last decades, many computational models have been developed to predict soft tissue growth and remodeling (G&R). The constrained mixture theory describes fundamental mechanobiological processes in soft tissue G&R and has been widely adopted in cardiovascular models of G&R. However, even after two decades of work, large organ-scale models are rare, mainly due to high computational costs (model evaluation and memory consumption), especially in long-range simulations. We propose two strategies to adaptively integrate history variables in constrained mixture models to enable large organ-scale simulations of G&R. Both strategies exploit that the influence of deposited tissue on the current mixture decreases over time through degradation. One strategy is independent of external loading, allowing the estimation of the computational resources ahead of the simulation. The other adapts the history snapshots based on the local mechanobiological environment so that the additional integration errors can be controlled and kept negligibly small, even in G&R scenarios with severe perturbations. We analyze the adaptively integrated constrained mixture model on a tissue patch for a parameter study and show the performance under different G&R scenarios. To confirm that adaptive strategies enable large organ-scale examples, we show simulations of different hypertension conditions with a real-world example of a biventricular heart discretized with a finite element mesh. In our example, adaptive integrations sped up simulations by a factor of three and reduced memory requirements to one-sixth. The reduction of the computational costs gets even more pronounced for simulations over longer periods. Adaptive integration of the history variables allows studying more finely resolved models and longer G&R periods while computational costs are drastically reduced and largely constant in time.

Pressure- and time-dependent alveolar recruitment/derecruitment in a spatially resolved patient-specific computational model for injured human lungs.

We present a novel computational model for the dynamics of alveolar recruitment/derecruitment (RD), which reproduces the underlying characteristics typically observed in injured lungs. The basic idea is a pressure- and time-dependent variation of the stress-free reference volume in reduced dimensional viscoelastic elements representing the acinar tissue. We choose a variable reference volume triggered by critical opening and closing pressures in a time-dependent manner from a straightforward mechanical point of view. In the case of (partially and progressively) collapsing alveolar structures, the volume available for expansion during breathing reduces and vice versa, eventually enabling consideration of alveolar collapse and reopening in our model. We further introduce a method for patient-specific determination of the underlying critical parameters of the new alveolar RD dynamics when integrated into the tissue elements, referred to as terminal units, of a spatially resolved physics-based lung model that simulates the human respiratory system in an anatomically correct manner. Relevant patient-specific parameters of the terminal units are herein determined based on medical image data and the macromechanical behavior of the lung during artificial ventilation. We test the whole modeling approach for a real-life scenario by applying it to the clinical data of a mechanically ventilated patient. The generated lung model is capable of reproducing clinical measurements such as tidal volume and pleural pressure during various ventilation maneuvers. We conclude that this new model is an important step toward personalized treatment of ARDS patients by considering potentially harmful mechanisms-such as cyclic RD and overdistension-and might help in the development of relevant protective ventilation strategies to reduce ventilator-induced lung injury (VILI).

An in silico model of the capturing of magnetic nanoparticles in tumour spheroids in the presence of flow.

One of the main challenges in improving the efficacy of conventional chemotherapeutic drugs is that they do not reach the cancer cells at sufficiently high doses while at the same time affecting healthy tissue and causing significant side effects and suffering in cancer patients. To overcome this deficiency, magnetic nanoparticles as transporter systems have emerged as a promising approach to achieve more specific tumour targeting. Drug-loaded magnetic nanoparticles can be directed to the target tissue by applying an external magnetic field. However, the magnetic forces exerted on the nanoparticles fall off rapidly with distance, making the tumour targeting challenging, even more so in the presence of flowing blood or interstitial fluid. We therefore present a computational model of the capturing of magnetic nanoparticles in a test setup: our model includes the flow around the tumour, the magnetic forces that guide the nanoparticles, and the transport within the tumour. We show how a model for the transport of magnetic nanoparticles in an external magnetic field can be integrated with a multiphase tumour model based on the theory of porous media. Our approach based on the underlying physical mechanisms can provide crucial insights into mechanisms that cannot be studied conclusively in experimental research alone. Such a computational model enables an efficient and systematic exploration of the nanoparticle design space, first in a controlled test setup and then in more complex in vivo scenarios. As an effective tool for minimising costly trial-and-error design methods, it expedites translation into clinical practice to improve therapeutic outcomes and limit adverse effects for cancer patients.

A homogenized constrained mixture model of cardiac growth and remodeling: analyzing mechanobiological stability and reversal.

Cardiac growth and remodeling (G&R) patterns change ventricular size, shape, and function both globally and locally. Biomechanical, neurohormonal, and genetic stimuli drive these patterns through changes in myocyte dimension and fibrosis. We propose a novel microstructure-motivated model that predicts organ-scale G&R in the heart based on the homogenized constrained mixture theory. Previous models, based on the kinematic growth theory, reproduced consequences of G&R in bulk myocardial tissue by prescribing the direction and extent of growth but neglected underlying cellular mechanisms. In our model, the direction and extent of G&R emerge naturally from intra- and extracellular turnover processes in myocardial tissue constituents and their preferred homeostatic stretch state. We additionally propose a method to obtain a mechanobiologically equilibrated reference configuration. We test our model on an idealized 3D left ventricular geometry and demonstrate that our model aims to maintain tensional homeostasis in hypertension conditions. In a stability map, we identify regions of stable and unstable G&R from an identical parameter set with varying systolic pressures and growth factors. Furthermore, we show the extent of G&R reversal after returning the systolic pressure to baseline following stage 1 and 2 hypertension. A realistic model of organ-scale cardiac G&R has the potential to identify patients at risk of heart failure, enable personalized cardiac therapies, and facilitate the optimal design of medical devices.

An approach to study recruitment/derecruitment dynamics in a patient-specific computational model of an injured human lung.

We present a new approach for physics-based computational modeling of diseased human lungs. Our main object is the development of a model that takes the novel step of incorporating the dynamics of airway recruitment/derecruitment into an anatomically accurate, spatially resolved model of respiratory system mechanics, and the relation of these dynamics to airway dimensions and the biophysical properties of the lining fluid. The importance of our approach is that it potentially allows for more accurate predictions of where mechanical stress foci arise in the lungs, since it is at these locations that injury is thought to arise and propagate from. We match the model to data from a patient with acute respiratory distress syndrome (ARDS) to demonstrate the potential of the model for revealing the underlying derangements in ARDS in a patient-specific manner. To achieve this, the specific geometry of the lung and its heterogeneous pattern of injury are extracted from medical CT images. The mechanical behavior of the model is tailored to the patient's respiratory mechanics using measured ventilation data. In retrospective simulations of various clinically performed, pressure-driven ventilation profiles, the model adequately reproduces clinical quantities measured in the patient such as tidal volume and change in pleural pressure. The model also exhibits physiologically reasonable lung recruitment dynamics and has the spatial resolution to allow the study of local mechanical quantities such as alveolar strains. This modeling approach advances our ability to perform patient-specific studies in silico, opening the way to personalized therapies that will optimize patient outcomes.

Tumour growth: An approach to calibrate parameters of a multiphase porous media model based on in vitro observations of Neuroblastoma spheroid growth in a hydrogel microenvironment.

To unravel processes that lead to the growth of solid tumours, it is necessary to link knowledge of cancer biology with the physical properties of the tumour and its interaction with the surrounding microenvironment. Our understanding of the underlying mechanisms is however still imprecise. We therefore developed computational physics-based models, which incorporate the interaction of the tumour with its surroundings based on the theory of porous media. However, the experimental validation of such models represents a challenge to its clinical use as a prognostic tool. This study combines a physics-based model with in vitro experiments based on microfluidic devices used to mimic a three-dimensional tumour microenvironment. By conducting a global sensitivity analysis, we identify the most influential input parameters and infer their posterior distribution based on Bayesian calibration. The resulting probability density is in agreement with the scattering of the experimental data and thus validates the proposed workflow. This study demonstrates the huge challenges associated with determining precise parameters with usually only limited data for such complex processes and models, but also demonstrates in general how to indirectly characterise the mechanical properties of neuroblastoma spheroids that cannot feasibly be measured experimentally.

Global sensitivity analysis based on Gaussian-process metamodelling for complex biomechanical problems.

Biomechanical models often need to describe very complex systems, organs or diseases, and hence also include a large number of parameters. One of the attractive features of physics-based models is that in those models (most) parameters have a clear physical meaning. Nevertheless, the determination of these parameters is often very elaborate and costly and shows a large scatter within the population. Hence, it is essential to identify the most important parameters (worth the effort) for a particular problem at hand. In order to distinguish parameters which have a significant influence on a specific model output from non-influential parameters, we use sensitivity analysis, in particular the Sobol method as a global variance-based method. However, the Sobol method requires a large number of model evaluations, which is prohibitive for computationally expensive models. We therefore employ Gaussian processes as a metamodel for the underlying full model. Metamodelling introduces further uncertainty, which we also quantify. We demonstrate the approach by applying it to two different problems: nanoparticle-mediated drug delivery in a complex, multiphase tumour-growth model, and arterial growth and remodelling. Even relatively small numbers of evaluations of the full model suffice to identify the influential parameters in both cases and to separate them from non-influential parameters. The approach also allows the quantification of higher-order interaction effects. We thus show that a variance-based global sensitivity analysis is feasible for complex, computationally expensive biomechanical models. Different aspects of sensitivity analysis are covered including a transparent declaration of the uncertainties involved in the estimation process. Such a global sensitivity analysis not only helps to massively reduce costs for experimental determination of parameters but is also highly beneficial for inverse analysis of such complex models.

In silico numerical simulation of ventilator settings during high-frequency ventilation in preterm infants.

OBJECTIVE: Despite the routine use of antenatal steroids, exogenous surfactants, and different noninvasive ventilation methods, many extremely low gestational age neonates, preterm, and term infants eventually require invasive ventilation. In addition to prematurity, mechanical ventilation itself can induce ventilator-induced lung injury leading to lifelong pulmonary sequelae. Besides conventional mechanical ventilation, high-frequency oscillatory ventilation (HFOV) with tidal volumes below dead space and high ventilation frequencies is used either as a primary or rescue therapy in severe neonatal respiratory failure. METHODS AND RESULTS: Applying a high-resolution computational lung modeling technique in a preterm infant, we studied three different high-frequency ventilation settings as well as conventional ventilation (CV) settings. Evaluating the computed oxygen delivery (OD) and lung mechanics (LM) we outline for the first time how changing ventilator settings from CV to HFOV lead to significant improvements in OD and LM. CONCLUSION: This personalized "digital twin" strategy advances our general knowledge of protective ventilation strategies in neonatal care and can support decisions on various modes of ventilatory therapy at high frequencies.

Validation and parameter optimization of a hybrid embedded/homogenized solid tumor perfusion model.

The goal of this paper is to investigate the validity of a hybrid embedded/homogenized in-silico approach for modeling perfusion through solid tumors. The rationale behind this novel idea is that only the larger blood vessels have to be explicitly resolved while the smaller scales of the vasculature are homogenized. As opposed to typical discrete or fully resolved 1D-3D models, the required data can be obtained with in-vivo imaging techniques since the morphology of the smaller vessels is not necessary. By contrast, the larger vessels, whose topology and structure is attainable noninvasively, are resolved and embedded as one-dimensional inclusions into the three-dimensional tissue domain which is modeled as a porous medium. A sound mortar-type formulation is employed to couple the two representations of the vasculature. We validate the hybrid model and optimize its parameters by comparing its results to a corresponding fully resolved model based on several well-defined metrics. These tests are performed on a complex data set of three different tumor types with heterogeneous vascular architectures. The correspondence of the hybrid model in terms of mean representative elementary volume blood and interstitial fluid pressures is excellent with relative errors of less than 4%. Larger, but less important and explicable errors are present in terms of blood flow in the smaller, homogenized vessels. We finally discuss and demonstrate how the hybrid model can be further improved to apply it for studies on tumor perfusion and the efficacy of drug delivery.

What do cells regulate in soft tissues on short time scales?

Cells within living soft biological tissues seem to promote the maintenance of a mechanical state within a defined range near a so-called set-point. This mechanobiological process is often referred to as mechanical homeostasis. During this process, cells interact with the fibers of the surrounding extracellular matrix (ECM). It remains poorly understood, however, what individual cells actually regulate during these interactions, and how these micromechanical regulations are translated to the tissue-level to lead to what we observe as biomaterial properties. Herein, we examine this question by a combination of experiments, theoretical analysis, and computational modeling. We demonstrate that on short time scales (hours) - during which deposition and degradation of ECM fibers can largely be neglected - cells appear to not regulate the stress / strain in the ECM or their own shape, but rather only the contractile forces that they exert on the surrounding ECM. STATEMENT OF SIGNIFICANCE: Cells in soft biological tissues sense and regulate the mechanical state of the extracellular matrix to ensure structural integrity and functionality. This so-called mechanical homeostasis plays an important role in the natural history of various diseases such as aneurysms in the cardiovascular system or cancer. Yet, it remains poorly understood to date which target quantity cells regulate on the mircroscale and how it translates to the macroscale. In this paper, we combine experiments, computer simulations, and theoretical analysis to compare different hypotheses about this target quantity. This allows us to identify a likely candidate for it at least on short time scales and in the simplified environment of tissue equivalents.

A computational framework for modeling cell-matrix interactions in soft biological tissues.

Living soft tissues appear to promote the development and maintenance of a preferred mechanical state within a defined tolerance around a so-called set point. This phenomenon is often referred to as mechanical homeostasis. In contradiction to the prominent role of mechanical homeostasis in various (patho)physiological processes, its underlying micromechanical mechanisms acting on the level of individual cells and fibers remain poorly understood, especially how these mechanisms on the microscale lead to what we macroscopically call mechanical homeostasis. Here, we present a novel computational framework based on the finite element method that is constructed bottom up, that is, it models key mechanobiological mechanisms such as actin cytoskeleton contraction and molecular clutch behavior of individual cells interacting with a reconstructed three-dimensional extracellular fiber matrix. The framework reproduces many experimental observations regarding mechanical homeostasis on short time scales (hours), in which the deposition and degradation of extracellular matrix can largely be neglected. This model can serve as a systematic tool for future in silico studies of the origin of the numerous still unexplained experimental observations about mechanical homeostasis.

Topological defects produce kinks in biopolymer filament bundles.

Bundles of stiff filaments are ubiquitous in the living world, found both in the cytoskeleton and in the extracellular medium. These bundles are typically held together by smaller cross-linking molecules. We demonstrate, analytically, numerically, and experimentally, that such bundles can be kinked, that is, have localized regions of high curvature that are long-lived metastable states. We propose three possible mechanisms of kink stabilization: a difference in trapped length of the filament segments between two cross-links, a dislocation where the endpoint of a filament occurs within the bundle, and the braiding of the filaments in the bundle. At a high concentration of cross-links, the last two effects lead to the topologically protected kinked states. Finally, we explore, numerically and analytically, the transition of the metastable kinked state to the stable straight bundle.

Directed force propagation in semiflexible networks.

We consider the propagation of tension along specific filaments of a semiflexible filament network in response to the application of a point force using a combination of numerical simulations and analytic theory. We find the distribution of force within the network is highly heterogeneous, with a small number of fibers supporting a significant fraction of the applied load over distances of multiple mesh sizes surrounding the point of force application. We suggest that these structures may be thought of as tensile force chains, whose structure we explore via simulation. We develop self-consistent calculations of the point-force response function and introduce a transfer matrix approach to explore the decay of tension (into bending) energy and the branching of tensile force chains in the network.

Repulsive Backbone-Backbone Interactions Modulate Access to Specific and Unspecific Binding Sites on Surface-Bound Mucins.

Mucin glycoproteins are the matrix-forming key components of mucus, the innate protective barrier protecting us from pathogenic attack. However, this barrier is constantly challenged by mucin-degrading enzymes, which tend to target anionic glycan chains such as sulfate groups and sialic acid residues. Here, we demonstrate that the efficiency of both unspecific and specific binding of small molecules to mucins is reduced when sulfate groups are enzymatically removed from mucins; this is unexpected because neither of the specific mucin-binding partners tested here targets these sulfate motifs on the mucin glycoprotein. Based on simulation results obtained from a numerical model of the mucin macromolecule, we propose that anionic motifs along the mucin chain establish intramolecular repulsion forces which maintain an elongated mucin conformation. In the absence of these repulsive forces, the mucin seems to adopt a more compacted structure, in which the accessibility of several binding sites is restricted. Our results contribute to a better understanding on how different glycans contribute to the broad spectrum of functions mucin glycoproteins have.

Extension of a multiphase tumour growth model to study nanoparticle delivery to solid tumours.

One of the main challenges in increasing the efficacy of conventional chemotherapeutics is the fact that they do not reach cancerous cells at a sufficiently high dosage. In order to remedy this deficiency, nanoparticle-based drugs have evolved as a promising novel approach to more specific tumour targeting. Nevertheless, several biophysical phenomena prevent the sufficient penetration of nanoparticles in order to target the entire tumour. We therefore extend our vascular multiphase tumour growth model, enabling it to investigate the influence of different biophysical factors on the distribution of nanoparticles in the tumour microenvironment. The novel model permits the examination of the interplay between the size of vessel-wall pores, the permeability of the blood-vessel endothelium and the lymphatic drainage on the delivery of particles of different sizes. Solid tumours develop a non-perfused core and increased interstitial pressure. Our model confirms that those two typical features of solid tumours limit nanoparticle delivery. Only in case of small nanoparticles is the transport dominated by diffusion, and particles can reach the entire tumour. The size of the vessel-wall pores and the permeability of the blood-vessel endothelium have a major impact on the amount of delivered nanoparticles. This extended in-silico tumour growth model permits the examination of the characteristics and of the limitations of nanoparticle delivery to solid tumours, which currently complicate the translation of nanoparticle therapy to a clinical stage.

An approach for vascular tumor growth based on a hybrid embedded/homogenized treatment of the vasculature within a multiphase porous medium model.

The aim of this work is to develop a novel computational approach to facilitate the modeling of angiogenesis during tumor growth. The preexisting vasculature is modeled as a 1D inclusion and embedded into the 3D tissue through a suitable coupling method, which allows for nonmatching meshes in 1D and 3D domain. The neovasculature, which is formed during angiogenesis, is represented in a homogenized way as a phase in our multiphase porous medium system. This splitting of models is motivated by the highly complex morphology, physiology, and flow patterns in the neovasculature, which are challenging and computationally expensive to resolve with a discrete, 1D angiogenesis and blood flow model. Moreover, it is questionable if a discrete representation generates any useful additional insight. By contrast, our model may be classified as a hybrid vascular multiphase tumor growth model in the sense that a discrete, 1D representation of the preexisting vasculature is coupled with a continuum model describing angiogenesis. It is based on an originally avascular model which has been derived via the thermodynamically constrained averaging theory. The new model enables us to study mass transport from the preexisting vasculature into the neovasculature and tumor tissue. We show by means of several illustrative examples that it is indeed capable of reproducing important aspects of vascular tumor growth phenomenologically.

Modern discontinuous Galerkin methods for the simulation of transitional and turbulent flows in biomedical engineering: A comprehensive LES study of the FDA benchmark nozzle model.

This work uses high-order discontinuous Galerkin discretization techniques to simulate transitional and turbulent flows through medical devices. Flows through medical devices are characterized by moderate Reynolds numbers and typically involve different flow regimes such as laminar, transitional, and turbulent flows. Previous studies for the FDA benchmark nozzle model revealed limitations of Reynolds-averaged Navier-Stokes turbulence models when applied to more complex flow scenarios. Recent works based on large-eddy simulation approaches indicate that these limitations can be overcome but also highlight potential limitations due to a high sensitivity with respect to numerical parameters. The methodology presented in this work introduces two novel ingredients compared with previous studies. Firstly, we use high-order discontinuous Galerkin methods for discretization in space. The inherent dissipation and dispersion properties of high-order discontinuous Galerkin discretizations are expected to render this approach well suited for transitional and turbulent flow simulations. Secondly, to mimic blinded CFD studies, we propose to use a precursor simulation approach in order to predict the inflow boundary condition for laminar, transitional, and turbulent flow regimes instead of prescribing analytical velocity profiles at the inflow. We investigate the whole range of Reynolds numbers as suggested by the FDA benchmark nozzle problem and compare the numerical results to experimental data obtained by particle image velocimetry in order to critically assess the predictive capabilities of the solver on the one hand and the suitability of the FDA nozzle problem as a benchmark in computational fluid dynamics on the other hand.

Conformation of a semiflexible filament in a quenched random potential.

Motivated by the observation of the storage of excess elastic free energy, prestress, in cross-linked semiflexible networks, we consider the problem of the conformational statistics of a single semiflexible polymer in a quenched random potential. The random potential, which represents the effect of cross-linking to other filaments, is assumed to have a finite correlation length ξ and mean strength V_{0}. We examine statistical distribution of curvature in filament with thermal persistence length ℓ_{P} and length L_{0} in the limit in which ℓ_{P}≫L_{0}. We compare our theoretical predictions to finite-element Brownian dynamics simulations. Finally, we comment on the validity of replica field techniques in addressing these questions.

Constituent-specific material behavior of soft biological tissue: experimental quantification and numerical identification for lung parenchyma.

In this study, we present a method to experimentally quantify and numerically identify the constituent-specific material behavior of soft biological tissues. This allows the clear identification of the individual contributions of major load-bearing constituents and their interactions in the constitutive law. While the overall approach is applicable for many tissues, here it will be presented for the identification of a sophisticated constituent-specific material model of viable lung parenchyma. This material model will help to better model the effects of various lung diseases that feature altered fiber content in the lungs, such as emphysema or fibrosis. To experimentally quantify the mechanical properties of collagen, elastin, collagen-elastin-fiber interactions, and ground substance, we examined 18 collagenase and elastase treated rat lung parenchymal slices. The mechanical contributions of the collagen and elastin fibers in the living tissue were inferred from uniaxial tension tests comparing the behavior before and after the selective digestion of the respective fibers. In order to also obtain the mechanical influence of the ground substance, we consecutively treated the samples with both proteases. Collagen and elastin fibers are morphologically interconnected. Thus, a mechanical interaction between these fibers appears likely, but has not yet been experimentally verified. In this paper, we propose an experimental method to quantitatively assess the mechanical behavior of these collagen-elastin-fiber interactions. Based on our experiments, we have identified individual material models within a nonlinear continuum mechanics framework for each load-bearing component via an inverse analysis. The proposed constituent-specific material law can be incorporated into computational models of the respiratory system to simulate and even predict the behavior and alteration of the individual constituents and their effect on the whole respiratory system during normal and artificial breathing, in particular in the case of diseases that alter the fibers in the tissue.