For the sake of computational efficiency and for theoretical purposes, in mathematical modelling, the DiracDelta distributions are often utilized as a replacement for cells or vesicles, since the... Show moreFor the sake of computational efficiency and for theoretical purposes, in mathematical modelling, the DiracDelta distributions are often utilized as a replacement for cells or vesicles, since the size of cells or vesicles is much smaller than the size of the surrounding tissues. Here, we consider the scenario that the cell or the vesicle releases the diffusive compounds to the immediate environment, which is modelled by the diffusion equation. Typically, one separates the intracellular and extracellular environment and uses homogeneous Neumann boundary condition for the cell boundary (so-called spatial exclusion model), while the point source model neglects the intracellular environment. We show that extra conditions are needed such that the solutions to the two models are consistent. We prove a necessary and sufficient condition for the consistency. Suggested by the numerical results, we conclude that an initial condition in the form of Gaussian kernel in the point source model compensates for a time-delay discrepancy between the solutions to the two models in the numerical solutions. Various approaches determining optimal amplitude and variance of the Gaussian kernel have been discussed. Show less
Cancer cell migration between different body parts is the driving force behind cancer metastasis, which is the main cause of mortality of patients. Migration of cancer cells often proceeds by... Show moreCancer cell migration between different body parts is the driving force behind cancer metastasis, which is the main cause of mortality of patients. Migration of cancer cells often proceeds by penetration through narrow cavities in locally stiff, yet flexible tissues. In our previous work, we developed a model for cell geometry evolution during invasion, which we extend here to investigate whether leader and follower (cancer) cells that only interact mechanically can benefit from sequential transmigration through narrow micro-channels and cavities. We consider two cases of cells sequentially migrating through a flexible channel: leader and follower cells being closely adjacent or distant. Using Wilcoxon’s signed-rank test on the data collected from Monte Carlo simulations, we conclude that the modelled transmigration speed for the follower cell is significantly larger than for the leader cell when cells are distant, i.e. follower cells transmigrate after the leader has completed the crossing. Furthermore, it appears that there exists an optimum with respect to the width of the channel such that cell moves fastest. On the other hand, in the case of closely adjacent cells, effectively performing collective migration, the leader cell moves 12% faster since the follower cell pushes it. This work shows that mechanical interactions between cells can increase the net transmigration speed of cancer cells, resulting in increased invasiveness. In other words, interaction between cancer cells can accelerate metastatic invasion. Show less
Skin contraction is an important biophysical process that takes place during and after recovery of deep tissue injury. This process is mainly caused by fibroblasts (skin cells) and myofibroblasts ... Show moreSkin contraction is an important biophysical process that takes place during and after recovery of deep tissue injury. This process is mainly caused by fibroblasts (skin cells) and myofibroblasts (differentiated fibroblasts which exert larger pulling forces and produce larger amounts of collagen) that both exert pulling forces on the surrounding extracellular matrix (ECM). Modelling is done in multiple scales: agent-based modelling on the microscale and continuum-based modelling on the macroscale. In this manuscript we present some results from our study of the connection between these scales. For the one-dimensional case, we managed to rigorously establish the link between the two modelling approaches for both closed-form solutions and finite-element approximations. For the multi-dimensional case, we computationally evidence the connection between the agent-based and continuum-based modelling approaches. Show less
Deep dermal wounds induce skin contraction as a result of the traction forcing exerted by (myo)fibroblasts on their immediate environment. These (myo)fibroblasts are skin cells that are responsible... Show moreDeep dermal wounds induce skin contraction as a result of the traction forcing exerted by (myo)fibroblasts on their immediate environment. These (myo)fibroblasts are skin cells that are responsible for the regeneration of collagen that is necessary for the integrity of skin We consider several mathematical issues regarding models that simulate traction forces exerted by (myo)fibroblasts. Since the size of cells (e.g. (myo)fibroblasts) is much smaller than the size of the domain of computation, one often considers point forces, modelled by Dirac Delta distributions on boundary segments of cells to simulate the traction forces exerted by the skin cells. In the current paper, we treat the forces that are directed normal to the cell boundary and toward the cell centre. Since it can be shown that there exists no smooth solution, at least not in H1 for solutions to the governing momentum balance equation, we analyse the convergence and quality of approximation. Furthermore, the expected finite element problems that we get necessitate to scrutinize alternative model formulations, such as the use of smoothed Dirac Delta distributions, or the so-called smoothed particle approach as well as the so-called 'hole' approach where cellular forces are modelled through the use of (natural) boundary conditions. In this paper, we investigate and attempt to quantify the conditions for consistency between the various approaches. This has resulted into error analyses in the L2-norm of the numerical solution based on Galerkin principles that entail Lagrangian basis functions. The paper also addresses well-posedness in terms of existence and uniqueness. The current analysis has been performed for the linear steady-state (hence neglecting inertia and damping) momentum equations under the assumption of Hooke's law. (C) 2022 The Author(s). Published by Elsevier B.V. on behalf of International Association for Mathematics and Computers in Simulation (IMACS). Show less
Plastic (permanent) deformations were earlier, modeled by a phenomenological model in Peng and Vermolen (Biomech Model Mechanobiol 19(6):2525-2551, 2020). In this manusctipt, we consider a more... Show morePlastic (permanent) deformations were earlier, modeled by a phenomenological model in Peng and Vermolen (Biomech Model Mechanobiol 19(6):2525-2551, 2020). In this manusctipt, we consider a more physics-based formulation that is based on morphoelasticity. We firstly introduce the morphoelasticity approach and investigate the impact of various input variables on the output parameters by sensitivity analysis. A comparison of both model formulations shows that both models give similar computational results. Furthermore, we carry out Monte Carlo simulations of the skin contraction model containing the morphoelasticity approach. Most statistical correlations from the two models are similar, however, the impact of the collagen density on the severeness of contraction is larger for the morphoelasticity model than for the phenomenological model. Show less
Kato, Y.; Kizer, J.R.; Ostovaneh, M.R.; Lazar, J.; Peng, Q.; Geest, R.J. van der; ... ; Ambale-Venkatesh, B. 2021
Background Quantification of non-ischemic myocardial scar remains a challenge due to the patchy diffuse nature of fibrosis. Extracellular volume (ECV) to guide late gadolinium enhancement (LGE)... Show moreBackground Quantification of non-ischemic myocardial scar remains a challenge due to the patchy diffuse nature of fibrosis. Extracellular volume (ECV) to guide late gadolinium enhancement (LGE) analysis may achieve a robust scar assessment. Methods Three cohorts of 80 non-ischemic-training, 20 non-ischemic-validation, and 10 ischemic-validation were prospectively enrolled and underwent 3.0 Tesla cardiac MRI. An ECV cutoff to differentiate LGE scar from non-scar was identified in the training cohort from the receiver-operating characteristic curve analysis, by comparing the ECV value against the visually-determined presence/absence of the LGE scar at the highest signal intensity (SI) area of the mid-left ventricle (LV) LGE. Based on the ECV cutoff, an LGE semi-automatic threshold of n-times of standard-deviation (n-SD) above the remote-myocardium SI was optimized in the individual cases ensuring correspondence between LGE and ECV images. The inter-method agreement of scar amount in comparison with manual (for non-ischemic) or full-width half-maximum (FWHM, for ischemic) was assessed. Intra- and inter-observer reproducibility were investigated in a randomly chosen subset of 40 non-ischemic and 10 ischemic cases. Results The non-ischemic groups were all female with the HIV positive rate of 73.8% (training) and 80% (validation). The ischemic group was all male with reduced LV function. An ECV cutoff of 31.5% achieved optimum performance (sensitivity: 90%, specificity: 86.7% in training; sensitivity: 100%, specificity: 81.8% in validation dataset). The identified n-SD threshold varied widely (range 3 SD-18 SD), and was independent of scar amount (beta = -0.01, p = 0.92). In the non-ischemic cohorts, results suggested that the manual LGE assessment overestimated scar (%) in comparison to ECV-guided analysis [training: 4.5 (3.2-6.4) vs. 0.92 (0.1-2.1); validation: 2.5 (1.2-3.7) vs. 0.2 (0-1.6); P < 0.01 for both]. Intra- and inter-observer analyses of global scar (%) showed higher reproducibility in ECV-guided than manual analysis with CCC = 0.94 and 0.78 versus CCC = 0.86 and 0.73, respectively (P < 0.01 for all). In ischemic validation, the ECV-guided LGE analysis showed a comparable scar amount and reproducibility with the FWHM. Conclusions ECV-guided LGE analysis is a robust scar quantification method for a non-ischemic cohort. Trial registration ClinicalTrials.gov; NCT00000797, retrospectively-registered 2 November 1999; NCT02501811, registered 15 July 2015. Show less
This study reports a high-resolution MRI approach to image basal blood flow and hypercapnia-induced blood-flow changes in the unanesthetized human retina on a 3-T MRI scanner. Pseudo-continuous... Show moreThis study reports a high-resolution MRI approach to image basal blood flow and hypercapnia-induced blood-flow changes in the unanesthetized human retina on a 3-T MRI scanner. Pseudo-continuous arterial spin labeling technique with static tissue suppression was implemented to minimize movement artifacts and improve blood-flow sensitivity. Turbo spin-echo acquisition was used to achieve high spatial resolution free of susceptibility artifacts. The size, shape, and position of a custom-made receive radiofrequency coil were optimized for sensitivity in the posterior retina. Synchronized eye blink and respiration to the end of each data readout minimized eye movement and physiological fluctuation. Robust high-contrast blood-flow MRI of the unanesthetized human retina was obtained at 500 X 800 mu m(2) in-plane resolution. Blood flow in the posterior retina was 93 +/- 31 mL/(100 mL min) (mean +/- standard deviation, N = 5). Hypercapnic inhalation (5% CO2) increased blood flow by 12 +/- 4% relative to air (P < 0.01, N = 5). This study demonstrates the feasibility of blood-flow MRI of the retina of unanesthetized human. Because blood flow is tightly coupled to metabolic function under normal conditions and it is often perturbed in diseases, this approach could provide unique insights into retinal physiology and serve as an objective imaging biomarker for disease staging and testing of novel therapeutic strategies. This approach could open up new avenue of retinal research. Magn Reson Med 65:1768-1775, 2011. (C)2011 Wiley-Liss, Inc. Show less
