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The lymphatics maintain fluid balance by returning interstitial fluid to veins via contraction/compression of vessel segments with check valves. Disruption of lymphatic pumping can result in a condition called lymphedema with interstitial fluid accumulation. Lymphedema treatments are often ineffective, which is partially attributable to insufficient understanding of specialized lymphatic muscle lining the vessels. This muscle exhibits cardiac-like phasic contractions and smooth muscle-like tonic contractions to generate and regulate flow. To understand the relationship between this sub-cellular contractile machinery and organ-level pumping, we have developed a multiscale computational model of phasic and tonic contractions in lymphatic muscle and coupled it to a lymphangion pumping model. Our model uses the sliding filament model (Huxley in Prog Biophys Biophys Chem 7:255–318, 1957) and its adaptation for smooth muscle (Mijailovich in Biophys J 79(5):2667–2681, 2000). Multiple structural arrangements of contractile components and viscoelastic elements were trialed but only one provided physiologic results. We then coupled this model with our previous lumped parameter model of the lymphangion to relate results to experiments. We show that the model produces similar pressure, diameter, and flow tracings to experiments on rat mesenteric lymphatics. This model provides the first estimates of lymphatic muscle contraction energetics and the ability to assess the potential effects of sub-cellular level phenomena such as calcium oscillations on lymphangion outflow. The maximum efficiency value predicted (40%) is at the upper end of estimates for other muscle types. Spontaneous calcium oscillations during diastole were found to increase outflow up to approximately 50% in the range of frequencies and amplitudes tested. Supplementary Information The online version contains supplementary material available at 10.1007/s10237-021-01501-0.

Heart diseases are one of the leading causes of death worldwide, and a dysfunction of the cardiac electrical mechanisms is responsible for a significant portion of these deaths. One of these mechanisms, the mechano-electric feedback (MEF), is the electrical response of the heart to local mechanical changes in the environment. This electrical response, in turn, leads to macroscopic changes in heart function. In this paper, we demonstrate that the MEF plays a crucial role in mechanical generation and recovery from arrhythmia which has been observed in experimental studies. To this end, we investigate the cardiac response to a mechanical stimulation using a minimal, multiscale model of the heart which couples the organ level dynamics (left ventricular pressure and volume) and contractile dynamics. By including a mechanical stimulation into the model as a (short, sudden) impulse in the muscle microscale stress, we investigate how the timing, amplitude and duration of the impulse affect the cardiac cycle. In particular, when introduced in the diastolic period of the cardiac cycle, the pulse rate can be stabilised, and ectopic beats and bifurcation can be eliminated, either temporarily or permanently. The stimulation amplitude is a key indicator to this response. We find an optimal value of the impulse amplitude above or below which the impulse maximises the stabilisation. As a result a dysfunction of the MEF can be helped using a mechanical stimulation, by allowing the heart to recover its pumping power. On the other hand, when the mechanical stimulation is introduced towards the end of systole, arrhythmia can be generated.

Angiogenesis, a formation of blood vessels from an existing vasculature, plays a key role in tumor growth and its progression into cancer. The lining of blood vessels consists of endothelial cells (ECs) which proliferate and migrate, allowing the capillaries to sprout towards the tumor to deliver the needed oxygen. Various treatments aiming to suppress or even inhibit angiogenesis have been explored. Mesenchymal stem cells (MSCs) have recently been undergoing development in cell-based therapy for cancer due to their ability to migrate towards the capillaries and induce the apoptosis of the ECs, causing capillary degeneration. However, further investigations in this direction are needed as it is usually difficult to preclinically assess the efficacy of such therapy. We develop a hybrid multiscale model that integrates molecular, cellular, tissue and extracellular components of tumor system to investigate angiogenesis and tumor growth under MSC-mediated therapy. Our simulations produce angiogenesis and vascular tumor growth profiles as observed in the experiments. Furthermore, the simulations show that the effectiveness of MSCs in inducing EC apoptosis is density dependent and its full effect is reached within several days after MSCs application. Quantitative agreements with experimental data indicate the predictive potential of our model for evaluating the efficacy of cell-based therapies targeting angiogenesis.

There has been a growing interest in the non-invasive stimulation of specific brain tissues, while reducing unintended stimulation in surrounding regions, for the medical treatment of brain disorders. Traditional methods for non-invasive brain stimulation, such as transcranial direct current stimulation (tDCS) or transcranial magnetic stimulation (TMS), can stimulate brain regions, but they also simultaneously stimulate the brain and non-brain regions that lie between the target and the stimulation site of the source. Temporal interference (TI) stimulation has been suggested to selectively stimulate brain regions by superposing two alternating currents with slightly different frequencies injected through electrodes attached to the scalp. Previous studies have reported promising results for TI applied to the motor area in mice, but the mechanisms are yet to be clarified. As computational techniques can help reveal different aspects of TI, in this study, we computationally investigated TI stimulation using a multiscale model that computes the generated interference current pattern effects in a neural cortical model of a mouse head. The results indicated that the threshold increased with the carrier frequency and that the beat frequency did not influence the threshold. It was also found that the intensity ratio between the alternating currents changed the location of the responding nerve, which is in agreement with previous experiments. Moreover, particular characteristics of the envelope were investigated to predict the stimulation region intuitively. It was found that regions with high modulation depth (| maximum| − | minimum| values of the envelope) and low minimum envelope (near zero) corresponded with the activation region obtained via neural computation.

International audience; Germinal centers play a key role in the adaptive immune system since they are able to produce memory B cells and plasma cells that produce high affinity antibodies for an effective immune protection. The mechanisms underlying cell-fate decisions are not well understood but asymmetric division of antigen, B-cell receptor affinity, interactions between B-cells and T follicular helper cells (triggering CD40 signaling), and regulatory interactions of transcription factors have all been proposed to play a role. In addition, a temporal switch from memory B-cell to plasma cell differentiation during the germinal center reaction has been shown. To investigate if antigen affinity-based Tfh cell help recapitulates the temporal switch we implemented a multiscale model that integrates cellular interactions with a core gene regulatory network comprising BCL6, IRF4, and BLIMP1. Using this model we show that affinity-based CD40 signaling in combination with asymmetric division of B-cells result in switch from memory B-cell to plasma cell generation during the course of the germinal center reaction. We also show that cell fate division is unlikely to be (solely) based on asymmetric division of Ag but that BLIMP1 is a more important factor. Altogether, our model enables to test the influence of molecular modulations of the CD40 signaling pathway on the production of germinal center output cells.

Clinically, fractional flow reserve (FFR)-guided coronary artery bypass grafting (CABG) is more effective than CABG guided by coronary angiography alone. However, no scholars have explained the mechanism from the perspective of hemodynamics. Two patients were clinically selected; their angiography showed 70% coronary stenosis, and the FFRs were 0.7 (patient 1) and 0.95 (patient 2). The FFR non-invasive computational model of the two patients was constructed by a 0–3D coupled multiscaled model, in order to verify that the model can accurately calculate the FFR results. Virtual bypass surgery was performed on these two stenoses, and a CABG multiscaled model was constructed. The flow rate of the graft and the stenosis coronary artery, as well as the wall shear stress (WSS) and the oscillatory shear index (OSI) in the graft were calculated. The non-invasive calculation results of FFR are 0.67 and 0.91, which are close to the clinical results, which proves that our model is accurate. According to the CABG model, the flow ratios of the stenosis coronary artery to the graft of patient 1 and patient 2 were 0.12 and 0.42, respectively. The time-average wall shear stress (TAWSS) results of patient 1 and patient 2 grafts were 2.09 and 2.16 Pa, respectively, and WSS showed uniform distribution on the grafts. The OSI results of patients 1 and 2 grafts were 0.0375 and 0.1264, respectively, and a significantly high OSI region appeared at the anastomosis of patient 2. The FFR value of the stenosis should be considered when performing bypass surgery. When the stenosis of high FFR values is grafted, a high OSI region is created at the graft, especially at the anastomosis. In the long term, this can cause anastomotic blockage and graft failure.

Mathematical modeling studies are useful for an improved understanding of the dynamics of human immunodeficiency virus type 1 (HIV-1) infection dynamics. Mutations are considered to facilitate the escape of HIV-1 from the immune system and anti-HIV-1 drugs. Thus, quasispecies, populations of closely related virus variants, are important in HIV-1 infection. Recently, a multiscale model incorporating both intracellular viral genome replication and extracellular viral infection was developed to study viral dynamics. A multiscale model has also been developed for analyzing HIV-1 infection. However, the multiscale model could not reveal high quasispecies diversity. Herein, I present a new quasi-steady-state multiscale model of HIV-1 infection that incorporates a quasi-steady state among the virion, uninfected cell, and virion–uninfected cell complex similar to that among the enzyme, substrate, and enzyme–substrate complex in enzyme kinetics. This new model can reveal stable quasispecies better than the previously described multiscale model. The model and the strategy to calculate the model might be useful in the field of demographics where multiscale models are used. For HIV-1 infection, the model might be useful for analyzing and predicting the breakthrough of drug-resistant mutants in the future.

Objective This study retrospectively examined the health and social determinants of the COVID-19 outbreak in 175 countries from a spatial epidemiological approach. Methods We used spatial analysis to examine the cross-national determinants of confirmed cases of COVID-19 based on the World Health Organization official COVID-19 data and the World Bank Indicators of Interest to the COVID-19 outbreak. All models controlled for COVID-19 government measures. Results The percentage of the population age between 15-64 years (Age15-64), percentage smokers (SmokTot.), and out-of-pocket expenditure (OOPExp) significantly explained global variation in the current COVID-19 outbreak in 175 countries. The percentage population age group 15-64 and out of pocket expenditure were positively associated with COVID-19. Conversely, the percentage of the total population who smoke was inversely associated with COVID-19 at the global level. Conclusions This study is timely and could serve as a potential geospatial guide to developing public health and epidemiological surveillance programs for the outbreak in multiple countries. Removal of catastrophic medical expenditure, smoking cessation, and observing public health guidelines will not only reduce illness related to COVID-19 but also prevent unecessary deaths.

Background: Peripheral Artery Disease (PAD) is an atherosclerotic disorder that leads to impaired lumen patency through intimal hyperplasia and the build-up of plaques, mainly localized in areas of disturbed flow. Computational models can provide valuable insights in the pathogenesis of atherosclerosis and act as a predictive tool to optimize current interventional techniques. Our hypothesis is that a reliable predictive model must include the atherosclerosis development history. Accordingly, we developed a multiscale modeling framework of atherosclerosis that replicates the hemodynamic-driven arterial wall remodeling and plaque formation. Methods: The framework was based on the coupling of Computational Fluid Dynamics (CFD) simulations with an Agent-Based Model (ABM). The CFD simulation computed the hemodynamics in a 3D artery model, while 2D ABMs simulated cell, Extracellular Matrix (ECM) and lipid dynamics in multiple vessel cross-sections. A sensitivity analysis was also performed to evaluate the oscillation of the ABM output to variations in the inputs and to identify the most influencing ABM parameters. Results: Our multiscale model qualitatively replicated both the physiologic and pathologic arterial configuration, capturing histological-like features. The ABM outputs were mostly driven by cell and ECM dynamics, largely affecting the lumen area. A subset of parameters was found to affect the final lipid core size, without influencing cell/ECM or lumen area trends. Conclusion: The fully coupled CFD-ABM framework described atherosclerotic morphological and compositional changes triggered by a disturbed hemodynamics.

Osteoporotic hip fractures are a major healthcare problem. Fall severity and bone strength are important risk factors of hip fracture. This study aims to obtain a mechanistic explanation for fracture risk in dependence of these risk factors. A novel modelling approach is developed that combines models at different scales to overcome the challenge of a large space–time domain of interest and considers the variability of impact forces between potential falls in a subject. The multiscale model and its component models are verified with respect to numerical approximations made therein, the propagation of measurement uncertainties of model inputs is quantified, and model predictions are validated against experimental and clinical data. The main results are model predicted absolute risk of current fracture (ARF0) that ranged from 1.93 to 81.6% (median 36.1%) for subjects in a retrospective cohort of 98 postmenopausal British women (49 fracture cases and 49 controls); ARF0 was computed up to a precision of 1.92 percentage points (pp) due to numerical approximations made in the model; ARF0 possessed an uncertainty of 4.00pp due to uncertainties in measuring model inputs; ARF0 classified observed fracture status in the above cohort with AUC = 0.852 (95% CI 0.753–0.918), 77.6% specificity (95% CI 63.4–86.5%) and 81.6% sensitivity (95% CI 68.3–91.1%). These results demonstrate that ARF0 can be computed using the model with sufficient precision to distinguish between subjects and that the novel mechanism of fracture risk determination based on fall dynamics, hip impact and bone strength can be considered validated.

Quantification of elastic stiffness and thermal conductivity of fired clay bricks is still often limited to empirical rules and laboratory testing, which becomes progressively more challenging given the large variety of raw materials used to optimize the properties of modern brick products. Applying a continuum micromechanics multiscale approach, we herein aim at upscaling of microstructural features to quantify the bricks’ macroscopic properties. Microstructural features such as assemblage and morphometry of mineral phases (quartz, feldspar, and micas), of pores, and of the binding matrix phase, respectively, as well as thermoelastic phase properties are provided by recently published results from extensive microscopic testing including electron microscopy imaging, mercury intrusion porosimetry, nanoindentation, and scanning thermal microscopy. These results are incorporated into the micromechanics model by introducing spheroidal phases with characteristic orientation distribution at two observation scales. The homogenized macroscopic stiffness and conductivity agree very well with independent results from novel macroscopic tests for all seven studied brick compositions. This corroborates the microstructure-informed multiscale model approach and its assumptions: the linear increase of the binding matrix properties with the material’s carbonate content, and the inability of large quartz with interface cracks to take over any mechanical loads.

Hypoplastic left heart syndrome is a complex congenital heart disease characterised by the underdevelopment of the left ventricle normally treated with a three-stage surgical repair. In this study, a multiscale closed-loop cardio-circulatory model is created to reproduce the pre-operative condition of a patient suffering from such pathology and virtual surgery is performed. Firstly, cardio-circulatory parameters are estimated using a fully closed-loop cardio-circulatory lumped parameter model. Secondly, a 3D standalone FEA model is build up to obtain active and passive ventricular characteristics and unloaded reference state. Lastly, the 3D model of the single ventricle is coupled to the lumped parameter model of the circulation obtaining a multiscale closed-loop pre-operative model. Lacking any information on the fibre orientation, two cases were simulated: (i) fibre distributed as in the physiological right ventricle and (ii) fibre as in the physiological left ventricle. Once the pre-operative condition is satisfactorily simulated for the two cases, virtual surgery is performed. The post-operative results in the two cases highlighted similar hemodynamic behaviour but different local mechanics. This finding suggests that the knowledge of the patient-specific fibre arrangement is important to correctly estimate the single ventricle's working condition and consequently can be valuable to support clinical decision.

Many biological processes are triggered or driven by mechanical forces in the cytoskeletal network, but these transducing forces have rarely been assessed. Striated muscle, with its well-organized structure provides an opportunity to assess intracellular forces using small-angle X-ray fiber diffraction. We present a new methodology using Monte Carlo simulations of muscle contraction in an explicit 3D sarcomere lattice to predict the fiber deformations and length changes along thin filaments during contraction. Comparison of predicted diffraction patterns to experimental meridional X-ray reflection profiles allows assessment of the stepwise changes in intermonomer spacings and forces in the myofilaments within living muscle cells. These changes along the filament length reflect the effect of forces from randomly attached crossbridges. This approach enables correlation of the molecular events, such as the current number of attached crossbridges and the distributions of crossbridge forces to macroscopic measurements of force and length changes during muscle contraction. In addition, assessments of fluctuations in local forces in the myofilaments may reveal how variations in the filament forces acting on signaling proteins in the sarcomere M-bands and Z-discs modulate gene expression, protein synthesis and degradation, and as well to mechanisms of adaptation of muscle in response to changes in mechanical loading.

Bone is a complex material showing a hierarchical and porous structure but also a natural ability to remodel thanks to cells sensitive to fluid flows. Based on these characteristics, a multiscale numerical model has been developed in order to represent the bone response under mechanical solicitation. It relies on the homogenization technique, simulating bone as a homogeneous structure having a porous microstructure saturated with bone fluid. The numerical modeling of the loading of a finite volume of bone enables the determination of an equivalent poroelastic stiffness. Focusing on two extreme fluid boundary conditions, the study of the corresponding structural response provides an overview of the fluid contribution to the poroelastic behavior, impacting the stiffness of the considered material. This parameter is either reduced (when the fluid can flow out of the structure) or increased (when the fluid is kept inside the structure) and quantified through this model. The presented poroelastic numerical model is here developed in the perspective of providing a bio-reliable model of bones, to determine the critical parameters that might impact bone remodeling.

Computational models have been widely used to predict the efficacy of surgical interventions in response to Peripheral Occlusive Diseases. However, most of them lack a multiscale description of the development of the disease, which, in our hypothesis, is the key to develop an effective predictive model. Accordingly, in this work we present a multiscale computational framework that simulates the generation of atherosclerotic arterial occlusions. Starting from a healthy artery in homeostatic conditions, the perturbation of specific cellular and extracellular dynamics led to the development of the pathology, with the final output being a diseased artery. The presented model was developed on an idealized portion of a Superficial Femoral Artery (SFA), where an Agent-Based Model (ABM), locally replicating the plaque development, was coupled to Computational Fluid Dynamics (CFD) simulations that define the Wall Shear Stress (WSS) profile at the lumen interface. The ABM was qualitatively validated on histological images and a preliminary analysis on the coupling method was conducted. Once optimized the coupling method, the presented model can serve as a predictive platform to improve the outcome of surgical interventions such as angioplasty and stent deployment.

In this paper, we review multiscale modeling for cancer treatment with the incorporation of drug effects from an applied system's pharmacology perspective. Both the classical pharmacology and systems biology are inherently quantitative; however, systems biology focuses more on networks and multifactorial controls over biological processes rather than on drugs and targets in isolation, whereas systems pharmacology has a strong focus on studying drugs with regard to the pharmacokinetic (PK) and pharmacodynamic (PD) relations accompanying drug interactions with multiscale physiology as well as the prediction of dosage-exposure responses and economic potentials of drugs. Thus, it requires multiscale methods to address the need for integrating models from the molecular levels to the cellular, tissue, and organism levels. It is a common belief that tumorigenesis and tumor growth can be best understood and tackled by employing and integrating a multifaceted approach that includes in vivo and in vitro experiments, in silico models, multiscale tumor modeling, continuous/discrete modeling, agent-based modeling, and multiscale modeling with PK/PD drug effect inputs. We provide an example application of multiscale modeling employing stochastic hybrid system for a colon cancer cell line HCT-116 with the application of Lapatinib drug. It is observed that the simulation results are similar to those observed from the setup of the wet-lab experiments at the Translational Genomics Research Institute.

Cardiac contractile dysfunction (CD) is a multifactorial syndrome caused by different acute or progressive diseases which hamper assessing the role of the underlying mechanisms characterizing a defined pathological condition. Mathematical modeling can help to understand the processes involved in CD and analyze their relative impact in the overall response. The aim of this study was thus to use a myocyte-based multiscale model of the circulatory system to simulate the effects of halothane, a volatile anesthetic which at high doses elicits significant acute CD both in isolated myocytes and intact animals. Ventricular chambers built using a human myocyte model were incorporated into a whole circulatory system represented by resistances and capacitances. Halothane-induced decreased sarco(endo)plasmic reticulum Ca2+ (SERCA2a) reuptake pump, transient outward K+ (Ito), Na+-Ca2+ exchanger (INCX) and L-type Ca2+ channel (ICaL) currents, together with ryanodine receptor (RyR2) increased open probability (Po) and reduced myofilament Ca2+ sensitivity, reproduced equivalent decreased action potential duration at 90% repolarization and intracellular Ca2+ concentration at the myocyte level reported in the literature. In the whole circulatory system, model reduction in mean arterial pressure, cardiac output and regional wall thickening fraction was similar to experimental results in open-chest sheep subjected to acute halothane overdose. Effective model performance indicates that the model structure could be used to study other changes in myocyte targets eliciting CD. Fil: Lascano, Elena C.. Universidad Favaloro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Medicina Traslacional, Trasplante y Bioingeniería. Fundación Favaloro. Instituto de Medicina Traslacional, Trasplante y Bioingeniería; Argentina Fil: Felice, Juan Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Centro de Investigaciones Cardiovasculares "Dr. Horacio Eugenio Cingolani". Universidad Nacional de La Plata. Facultad de Ciencias Médicas. Centro de Investigaciones Cardiovasculares "Dr. Horacio Eugenio Cingolani"; Argentina Fil: Wray, Sandra. Universidad Favaloro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Medicina Traslacional, Trasplante y Bioingeniería. Fundación Favaloro. Instituto de Medicina Traslacional, Trasplante y Bioingeniería; Argentina Fil: Kosta, Sara. Université de Liège; Bélgica Fil: Dauby, Pierre. Université de Liège; Bélgica Fil: Cabrera Fischer, Edmundo Ignacio. Universidad Favaloro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Medicina Traslacional, Trasplante y Bioingeniería. Fundación Favaloro. Instituto de Medicina Traslacional, Trasplante y Bioingeniería; Argentina Fil: Negroni, Jorge Antonio. Universidad Favaloro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Medicina Traslacional, Trasplante y Bioingeniería. Fundación Favaloro. Instituto de Medicina Traslacional, Trasplante y Bioingeniería; Argentina

The multiscale model of hepatitis C virus (HCV) dynamics, which includes intracellular viral RNA (vRNA) replication, has been formulated in recent years in order to provide a new conceptual framework for understanding the mechanism of action of a variety of agents for the treatment of HCV. We present a robust and efficient numerical method that belongs to the family of adaptive stepsize methods and is implicit, a Rosenbrock type method that is highly suited to solve this problem. We provide a Graphical User Interface that applies this method and is useful for simulating viral dynamics during treatment with anti-HCV agents that act against HCV on the molecular level.

We introduce in this work a new method of retrieving the reference state of the breast in a stress-free configuration and estimating at the same time the elasticity of the breast tissues by combining MRI and surface imaging data and using finite element analysis. This reference state of the breast is particularly useful in predicting the cosmetic outcome and the healing process of breast cancer surgery, and breast conserving therapy in particular.

The cerebral circulation is unique in its ability to maintain blood flow to the brain under widely varying physiologic conditions. Incorporating this autoregulatory response is necessary for cerebral blood flow (CBF) modeling, as well as investigations into pathological conditions. We discuss a one-dimensional (1D) nonlinear model of blood flow in the cerebral arteries coupled to autoregulatory lumped-parameter (LP) networks. The LP networks incorporate intracranial pressure (ICP), cerebrospinal fluid (CSF), and cortical collateral blood flow models. The overall model is used to evaluate changes in CBF due to occlusions in the middle cerebral artery (MCA) and common carotid artery (CCA). Velocity waveforms at the CCA and internal carotid artery (ICA) were examined prior and post MCA occlusion. Evident waveform changes due to the occlusion were observed, providing insight into cerebral vasospasm monitoring by morphological changes of the velocity or pressure waveforms. The role of modeling of collateral blood flows through cortical pathways and communicating arteries was also studied. When the MCA was occluded, the cortical collateral flow had an important compensatory role, whereas the communicating arteries in the circle of Willis (CoW) became more important when the CCA was occluded. To validate the model, simulations were conducted to reproduce a clinical test to assess dynamic autoregulatory function, and results demonstrated agreement with published measurements.

Angiogenesis, the formation of new blood vessel networks from existing capillary or post-capillary venules, is an intrinsically multiscale process occurring in several physio-pathological conditions. In particular, hypoxic tissue cells activate downstream cascades culminating in the secretion of a wide range of angiogenic factors, including VEGF isoforms. Such diffusive chemicals activate the endothelial cells (ECs) forming the external walls of the nearby vessels that chemotactically migrate toward the hypoxic areas of the tissue as multicellular sprouts. A functional network eventually emerges by further branching and anastomosis processes. We here propose a CPM-based approach reproducing selected features of the angiogenic progression necessary for the reoxygenation of a hypoxic tissue. Our model is able to span the different scale involved in the angiogenic progression as it incorporates reaction-diffusion equations for the description of the evolution of microenvironmental variables in a discrete mesoscopic cellular Potts model (CPM) that reproduces the dynamics of the vascular cells. A key feature of this work is the explicit phenotypic differentiation of the ECs themselves, distinguished in quiescent, stalk and tip. The simulation results allow identifying a set of key mechanisms underlying tissue vascularization. Further, we provide evidence that the nascent pattern is characterized by precise topological properties. Finally, we link abnormal sprouting angiogenesis with alteration in selected cell behavior. HighlightsAn in vivo angiogenic process is modeled by a suitable version of the Cellular Potts Model.Vascular cells undergo phenotypic differentiations (i.e., from quiescent to stalk or tip).A fundamental mechanism is the chemotactic movement of tip cells.Stalk cells are characterized by a directionally preferential mitosis.The size of the hypoxic tissue only affects the duration of the process.

The scientific community continues to accrue evidence that blood flow alterations and ischemic conditions in the retina play an important role in the pathogenesis of ocular diseases. Many factors influence retinal hemodynamics and tissue oxygenation, including blood pressure, blood rheology, oxygen arterial permeability and tissue metabolic demand. Since the influence of these factors on the retinal circulation is difficult to isolate in vivo, we propose here a novel mathematical and computational model describing the coupling between blood flow mechanics and oxygen ([Formula: see text]) transport in the retina. Albeit in a simplified manner, the model accounts for the three-dimensional anatomical structure of the retina, consisting in a layered tissue nourished by an arteriolar/venular network laying on the surface proximal to the vitreous. Capillary plexi, originating from terminal arterioles and converging into smaller venules, are embedded in two distinct tissue layers. Arteriolar and venular networks are represented by fractal trees, whereas capillary plexi are represented using a simplified lumped description. In the model, [Formula: see text] is transported along the vasculature and delivered to the tissue at a rate that depends on the metabolic demand of the various tissue layers. First, the model is validated against available experimental results to identify baseline conditions. Then, a sensitivity analysis is performed to quantify the influence of blood pressure, blood rheology, oxygen arterial permeability and tissue oxygen demand on the [Formula: see text] distribution within the blood vessels and in the tissue. This analysis shows that: (1) systemic arterial blood pressure has a strong influence on the [Formula: see text] profiles in both blood and tissue; (2) plasma viscosity and metabolic consumption rates have a strong influence on the [Formula: see text] tension at the level of the retinal ganglion cells; and (3) arterial [Formula: see text] permeability has a strong influence on the [Formula: see text] saturation in the retinal arterioles.

Cancer research is not only a fast growing field involving many branches of science, but also an intricate and diversified field rife with anomalies. One such anomaly is the consistent reliance of cancer cells on glucose metabolism for energy production even in a normoxic environment. Glycolysis is an inefficient pathway for energy production and normally is used during hypoxic conditions. Since cancer cells have a high demand for energy (e.g. for proliferation) it is somehow paradoxical for them to rely on such a mechanism. An emerging conjecture aiming to explain this behavior is that cancer cells preserve this aerobic glycolytic phenotype for its use in invasion and metastasis (see, e.g., Gatenby and Gillies (2004) [1] , Racker (1976) [2] ). We follow this hypothesis and propose a new model for cancer invasion, depending on the dynamics of extra- and intracellular protons, by building upon the existing ones. We incorporate random perturbations in the intracellular proton dynamics to account for uncertainties affecting the cellular machinery. Finally, we address the well-posedness of our setting and use numerical simulations to illustrate the model predictions.

Invasion is a key property of tumour cells for building metastasis. A class of functionally related proteins called heat shock proteins (HSPs), the expression of which is increased when cells are exposed to elevated temperatures or other stress, play an important role in the invasion. In this paper we develop a mathematical model focusing on the effect of HSPs on the tumour cell migration. The resulting multiscale setting accounts both for the microscopic, intracellular level on which these proteins are acting and for the macroscopic level of the cell population. We prove the local existence of a unique positive solution and perform numerical simulations in order to illustrate the behaviour of cancer cells w.r.t. the fibre density of the tissue and the matrix degrading enzymes, along with the effect of HSPs. © 2013 Elsevier Ltd.

MOCHA Investigators: Andrew Taylor, MD, Alessandro Giardini, MD, Sachin Khambadkone, MD, Silvia Schievano, PhD, Marc de Leval, MD, and T.-Y. Hsia, MD (Institute of Child Health, London, United Kingdom); Edward Bove, MD, and Adam Dorfman, MD (University of Michigan, Ann Arbor, MI); G. Hamilton Baker, MD, and Anthony Hlavacek (Medical University of South Carolina, Charleston, SC); Francesco Migliavacca, PhD, Giancarlo Pennati, PhD, and Gabriele Dubini, PhD (Politecnico di Milano, Milan, Italy); Alison Marsden, PhD (University of California, San Diego, CA); Jeffrey Feinstein, MD (Stanford University, Stanford, CA) Irene Vignon-Clementel (National Institute of Research in Informatics and Automation, Paris, France); Richard Figliola, PhD, and John McGregor, PhD (Clemson University, Clemson, SC).; International audience; Single ventricle malformations are complex congenital heart defects which require a three-stage surgical treatment, starting from the very first days of life, to separate the systemic and pulmonary circulations, and restore the serial circuit occurring in normal patients. The final surgery results in a total cavopulmonary connection (TCPC), where both the superior and the inferior vena cava are connected to the right pulmonary artery. Several clinical and computational studies have been done to optimize the geometry of the TCPC, with the aim of minimizing energy losses and improving surgical outcomes. To date, only few modeling studies have taken into account respiration and exercise as important factors to quantify the performance of a Fontan geometry. The objective of this work is to test the dependence of fluid dynamic variables and energy efficiency on respiration in patient-specific models of Fontan circulation, when subjected to exercise tests.|A closed-loop multiscale approach was used, including a simple respiration model that modulates the extravascular pressures in the thoracic and abdominal cavities, to generate physiologic time-varying flow conditions. A lumped parameter network (LPN) representing the whole circulation was coupled to a patient-specific 3D finite volume model of the preoperative bidirectional cavo-pulmonary anastomosis (BCPA) with detailed pulmonary anatomy. Subsequently, three virtual TCPC alternatives were coupled to the LPN and investigated in terms of both local and global hemodynamics. In particular, a T-junction of the venae cavae to the pulmonary arteries, a design with an offset between the venae cavae and a Y-graft design were compared under exercise conditions.|Results showed that the BCPA model is able to realistically capture oscillations due to both cardiac and respiratory effects, when compared to the venous Doppler velocity tracings acquired preoperatively on the patient.|The differences in hemodynamics between the three investigated TCPC options were minimal and similar to those obtained without inclusion of respiratory effects. Hence, the three surgical options result to be equivalent according to the analyzed parameters. Moreover, although the simulation of the Fontan circulation with a respiratory model requires a longer computational time, the developed framework allows for a more physiologic method to incorporate respiratory effects that was not possible using other methods.

Elderly frequently present variable degrees of osteopenia, sarcopenia, and neuromotor control degradation. Severely osteoporotic patients sometime fracture their femoral neck when falling. Is it possible that such fractures might occur without any fall, but rather spontaneously while the patient is performing normal movements such as level walking? The aim of this study was to verify if such spontaneous fractures are biomechanically possible, and in such case, which conditions of osteoporosis, sarcopenia, and neuromotor degradation could produce them. To the purpose, a probabilistic multiscale body-organ model validated against controlled experiments was used to predict the risk of spontaneous fractures in a population of 80-years old women, with normal weight and musculoskeletal anatomy, and variable degree of osteopenia, sarcopenia, and neuromotor control degradation. A multi-body inverse dynamics sub-model, coupled to a probabilistic neuromuscular sub-model, and to a femur finite element sub-model, formed the multiscale model, which was run within a Monte Carlo stochastic scheme, where the various parameters were varied randomly according to well defined distributions. The model predicted that neither extreme osteoporosis, nor extreme neuromotor degradation alone are sufficient to predict spontaneous fractures. However, when the two factors are combined an incidence of 0.4% of spontaneous fractures is predicted for the simulated population, which is consistent with clinical reports. When the model represented only severely osteoporotic patients, the incidence of spontaneous fractures increased to 29%. Thus, is biomechanically possible that spontaneous femoral neck fractures occur during level walking, due to a combination of severe osteoporosis and severe neuromotor degradation.

International audience; The objective of this work is to perform a virtual planning of surgical repairs in patients with congenital heart diseases--to test the predictive capability of a closed-loop multi-scale model. As a first step, we reproduced the pre-operative state of a specific patient with a univentricular circulation and a bidirectional cavopulmonary anastomosis (BCPA), starting from the patient's clinical data. Namely, by adopting a closed-loop multi-scale approach, the boundary conditions at the inlet and outlet sections of the three-dimensional model were automatically calculated by a lumped parameter network. Successively, we simulated three alternative surgical designs of the total cavopulmonary connection (TCPC). In particular, a T-junction of the venae cavae to the pulmonary arteries (T-TCPC), a design with an offset between the venae cavae (O-TCPC) and a Y-graft design (Y-TCPC) were compared. A multi-scale closed-loop model consisting of a lumped parameter network representing the whole circulation and a patient-specific three-dimensional finite volume model of the BCPA with detailed pulmonary anatomy was built. The three TCPC alternatives were investigated in terms of energetics and haemodynamics. Effects of exercise were also investigated. Results showed that the pre-operative caval flows should not be used as boundary conditions in post-operative simulations owing to changes in the flow waveforms post-operatively. The multi-scale approach is a possible solution to overcome this incongruence. Power losses of the Y-TCPC were lower than all other TCPC models both at rest and under exercise conditions and it distributed the inferior vena cava flow evenly to both lungs. Further work is needed to correlate results from these simulations with clinical outcomes.

International audience; In this paper, we present a two-level physiological model that is able to reflect morphology and function of vascular networks, in clinical images. Our approach results from the combination of a macroscopic model, providing simulation of the growth and pathological modifications of vascular network, and a microvascular model, based on compartmental approach, which simulates blood and contrast medium transfer through capillary walls. The two-level model is applied to generate biphasic computed tomography of hepatocellular carcinoma. A contrast-enhanced sequence of simulated images is acquired, and enhancement curves extracted from normal and tumoral regions are compared to curves obtained from in vivo images. The model offers the potential of finding early indicators of disease in clinical vascular images.

Colorectal cancer (CRC) is one of the major causes of death in the developed world and forms a canonical example of tumorigenesis. CRC arises from a string of mutations of individual cells in the colorectal crypt, making it particularly suited for multiscale multicellular modeling, where mutations of individual cells can be clearly represented and their effects readily tracked. In this paper, we present a multicellular model of the onset of colorectal cancer, utilizing the cellular Potts model (CPM). We use the model to investigate how, through the modification of their mechanical properties, mutant cells colonize the crypt. Moreover, we study the influence of mutations on the shape of cells in the crypt, suggesting possible cell- and tissue-level indicators for identifying early-stage cancerous crypts. Crucially, we discuss the effect that the motility parameters of the model (key factors in the behavior of the CPM) have on the distribution of cells within a homeostatic crypt, resulting in an optimal parameter regime that accurately reflects biological assumptions. In summary, the key results of this paper are 1) how to couple the CPM with processes occurring on other spatial scales, using the example of the crypt to motivate suitable motility parameters; 2) modeling mutant cells with the CPM; 3) and investigating how mutations influence the shape of cells in the crypt.