Mathematical investigation of normal and abnormal wound healing dynamics: local and non-local models.

The movement of cells during (normal and abnormal) wound healing is the result of biomechanical interactions that combine cell responses with growth factors as well as cell-cell and cell-matrix interactions (adhesion and remodelling). It is known that cells can communicate and interact locally and non-locally with other cells inside the tissues through mechanical forces that act locally and at a distance, as well as through long non-conventional cell protrusions. In this study, we consider a non-local partial differential equation model for the interactions between fibroblasts, macrophages and the extracellular matrix (ECM) via a growth factor (TGF-$ \beta $) in the context of wound healing. For the non-local interactions, we consider two types of kernels (i.e., a Gaussian kernel and a cone-shaped kernel), two types of cell-ECM adhesion functions (i.e., adhesion only to higher-density ECM vs. adhesion to higher-/lower-density ECM) and two types of cell proliferation terms (i.e., with and without decay due to overcrowding). We investigate numerically the dynamics of this non-local model, as well as the dynamics of the localised versions of this model (i.e., those obtained when the cell perception radius decreases to 0). The results suggest the following: (ⅰ) local models explain normal wound healing and non-local models could also explain abnormal wound healing (although the results are parameter-dependent); (ⅱ) the models can explain two types of wound healing, i.e., by primary intention, when the wound margins come together from the side, and by secondary intention when the wound heals from the bottom up.

Modelling Keloids Dynamics: A Brief Review and New Mathematical Perspectives.

Keloids are fibroproliferative disorders described by excessive growth of fibrotic tissue, which also invades adjacent areas (beyond the original wound borders). Since these disorders are specific to humans (no other animal species naturally develop keloid-like tissue), experimental in vivo/in vitro research has not led to significant advances in this field. One possible approach could be to combine in vitro human models with calibrated in silico mathematical approaches (i.e., models and simulations) to generate new testable biological hypotheses related to biological mechanisms and improved treatments. Because these combined approaches do not really exist for keloid disorders, in this brief review we start by summarising the biology of these disorders, then present various types of mathematical and computational approaches used for related disorders (i.e., wound healing and solid tumours), followed by a discussion of the very few mathematical and computational models published so far to study various inflammatory and mechanical aspects of keloids. We conclude this review by discussing some open problems and mathematical opportunities offered in the context of keloid disorders by such combined in vitro/in silico approaches, and the need for multi-disciplinary research to enable clinical progress.

A data-driven reduced-order surrogate model for entire elastoplastic simulations applied to representative volume elements.

This contribution discusses surrogate models that emulate the solution field(s) in the entire simulation domain. The surrogate uses the most characteristic modes of the solution field(s), in combination with neural networks to emulate the coefficients of each mode. This type of surrogate is well known to rapidly emulate flow simulations, but rather new for simulations of elastoplastic solids. The surrogate avoids the iterative process of constructing and solving the linearized governing equations of rate-independent elastoplasticity, as necessary for direct numerical simulations or (hyper-)reduced-order-models. Instead, the new plastic variables are computed only once per increment, resulting in substantial time savings. The surrogate uses a recurrent neural network to treat the path dependency of rate-independent elastoplasticity within the neural network itself. Because only a few of these surrogates have been developed for elastoplastic simulations, their potential and limitations are not yet well studied. The aim of this contribution is to shed more light on their numerical capabilities in the context of elastoplasticity. Although more widely applicable, the investigation focuses on a representative volume element, because these surrogates have the ability to both emulate the macroscale stress-deformation relation (which drives the multiscale simulation), as well as to recover all microstructural quantities within each representative volume element.

Anisotropic mechanical characterization of human skin by in vivo multi-axial ring suction test.

Human skin is a soft tissue behaving as an anisotropic material. The anisotropy emerges from the alignment of collagen fibers in the dermis, which causes the skin to exhibit greater stiffness in a certain direction, known as Langer's line. The importance of determining this anisotropy axis lies in assisting surgeons in making incisions that do not produce undesirable scars. In this paper, we introduce an open-source numerical framework, MARSAC (Multi-Axial Ring Suction for Anisotropy Characterization: https://github.com/aflahelouneg/MARSAC), adapted to a commercial device CutiScan CS 100® that applies a suction load on an annular section, causing a multi-axial stretch in the central zone, where in-plane displacements are captured by a camera. The presented framework receives inputs from a video file and converts them into displacement fields through Digital Image Correlation (DIC) technique. From the latter and based on an analytical model, the method assesses the anisotropic material parameters of human skin: Langer's line ϕ, and the elastic moduli E1 and E2 along the principal axes, providing that the Poisson's ratio is fixed. The pipeline was applied to a public data repository, https://search-data.ubfc.fr/femto/FR-18008901306731-2021-08-25_In-vivo-skin-anisotropy-dataset-for-a-young-man.html, containing 30 test series performed on a forearm of a Caucasian subject. As a result, the identified parameter averages, ϕˆ=40.9±8.2∘ and the anisotropy ratio E1ˆ/E2ˆ=3.14±1.60, were in accordance with the literature. The intra-subject analysis showed a reliable assessment of ϕ and E2. As skin anisotropy varies from site to site and from subject to subject, the novelty of the method consists in (i) an optimal utilization of CutiScan CS 100® probe to measure the Langer's line accurately and rapidly on small areas with a minimum diameter of 14mm, (ii) validation of an analytical model based on deformation ellipticity.

Digital Volume Correlation for large deformations of soft tissues: Pipeline and proof of concept for the application to breast ex vivo deformations.

Being able to reposition tumors from prone imaging to supine surgery stances is key for bypassing current invasive marking used for conservative breast surgery. This study aims to demonstrate the feasibility of using Digital Volume Correlation (DVC) to measure the deformation of a female quarter thorax between two different body positioning when subjected to gravity. A segmented multipart mesh (bones, cartilage and tissue) was constructed and a three-step FE-based DVC procedure with heterogeneous elastic regularization was implemented. With the proposed framework, the large displacement field of a hard/soft breast sample was recovered with low registration residuals and small error between the measured and manually determined deformations of phase interfaces. The present study showed the capacity of FE-based DVC to faithfully capture large deformations of hard/soft tissues.

An open source pipeline for design of experiments for hyperelastic models of the skin with applications to keloids.

The aim of this work is to characterize the mechanical parameters governing the in-plane behavior of human skin and, in particular, of a keloid-scar. We consider 2D hyperelastic bi-material model of a keloid and the surrounding healthy skin. The problem of finding the optimal model parameters that minimize the misfit between the model observations and the in vivo experimental measurements is solved using our in-house developed inverse solver that is based on the FEniCS finite element computational platform. The paper focuses on the model parameter sensitivity quantification with respect to the experimental measurements, such as the displacement field and reaction force measurements. The developed tools quantify the significance of different measurements on different model parameters and, in turn, give insight into a given model's ability to capture experimental measurements. Finally, an a priori estimate for the model parameter sensitivity is proposed that is independent of the actual measurements and that is defined in the whole computational domain. This estimate is primarily useful for the design of experiments, specifically, in localizing the optimal displacement field measurement sites for the maximum impact on model parameter inference.

A partitioned model order reduction approach to rationalise computational expenses in nonlinear fracture mechanics.

We propose in this paper a reduced order modelling technique based on domain partitioning for parametric problems of fracture. We show that coupling domain decomposition and projection-based model order reduction permits to focus the numerical effort where it is most needed: around the zones where damage propagates. No a priori knowledge of the damage pattern is required, the extraction of the corresponding spatial regions being based solely on algebra. The efficiency of the proposed approach is demonstrated numerically with an example relevant to engineering fracture.

Extraction of process zones and low-dimensional attractive subspaces in stochastic fracture mechanics.

We propose to identify process zones in heterogeneous materials by tailored statistical tools. The process zone is redefined as the part of the structure where the random process cannot be correctly approximated in a low-dimensional deterministic space. Such a low-dimensional space is obtained by a spectral analysis performed on pre-computed solution samples. A greedy algorithm is proposed to identify both process zone and low-dimensional representative subspace for the solution in the complementary region. In addition to the novelty of the tools proposed in this paper for the analysis of localised phenomena, we show that the reduced space generated by the method is a valid basis for the construction of a reduced order model.

Bridging Proper Orthogonal Decomposition methods and augmented Newton-Krylov algorithms: an adaptive model order reduction for highly nonlinear mechanical problems.

This article describes a bridge between POD-based model order reduction techniques and the classical Newton/Krylov solvers. This bridge is used to derive an efficient algorithm to correct, "on-the-fly", the reduced order modelling of highly nonlinear problems undergoing strong topological changes. Damage initiation problems are addressed and tackle via a corrected hyperreduction method. It is shown that the relevancy of reduced order model can be significantly improved with reasonable additional costs when using this algorithm, even when strong topological changes are involved.

Mutagenicity testing of benomyl, methyl-2-benzimidazole carbamate, streptozotocin and N-methyl-N'-nitro-N-nitrosoguanidine in Salmonella typhimurium in vitro and in rodent host-mediated assays.

The fungicide benomyl and its commercial preparations Fundazol 50WP and Benlate 50WP and the benomyl metabolite methyl-2-benzimidazole carbamate and its commercial preparation MBC 50WP were tested for mutagenicity in in vitro spot tests, in microsomal plate assay, in liquid-culture treatments, or in rodent host-mediated assay. The base-pair substitution Salmonella typhimurium mutant hisG46 and the hisG46-bearing uvrB excision-repair-deficient mutants TA100, TA1530, TA1535 or TA1950 were used as test organisms. Complete genotypic information of these mutants is given in Ames et al. [2]. Captain 50WP, streptozotocin (SZN), N-methyl-N'-nitro-N-nitrosoguanidine (MNNG), 2-aminopurine and N-acetylaminofluorene were used as positive control compounds. In nonoverlay spot tests Benlate 50WP was not mutagenic over a dose range of 50-5000 microgram/spot in hisG46 and TA1535. In overlay spot tests 50 or 100 microgram/spot Benomyl, MBC, Fundazol 50WP, Benlate 50WP and MBC 50WP were tested in hisG46, TA1530 or TA1950. Only a non-commercial MBC sample at 100 microgram/spot showed weak mutagenic activity in hisG46. In microsomal activation plate assay MBC, benomyl, Fundazol 50WP and Benlate 50WP were tested in TA100 over a dose range of 50-2000 microgram/plate. None of the compounds showed mutagenicity. In a 20-h liquid-culture treatment 10, 100, 1000 and 10 000 microgram/ml Fundazol 50WP were not mutagenic in TA 30. In 1-h liquid-culture treatments benomyl, Benlate 50WP or Fundazol 50WP failed to induce mutations in hisG46, TA100 or TA1950 over a dose range of 0.25-1000 microgram/ml. Appropriate positive controls were mutagenic in each experiment. The consistently negative results in this study with commercial MBC and benomyl preparations are contrary to positive results reported earlier with similar methods and similar commercial preparations. Possible reasons to explain the different results are presented. The alkylating agents SZN and MNNG induced fewer mutations in TA1530 and TA1950 uvrB excision-repair-deficient strains than in the hisG46 excision-proficient strain, indicating that with these mutagens excision-repair is also a mutation-prone process. In rodent host-mediated assays with Fundazol 50WP in mice 3 consecutive subcutaneous hourly doses of 500 mg/kg in hisG46 and TA1950 and in rats or mice an oral dose of 4000 mg/kg in TA1950 were not mutagenic. The positive control SZN was mutagenic.

Mammalian host- and fluid-mediated mutagenicity assays of captan and streptozotocin in Salmonella typhimurium.

The mutagenicity of captan and of streptozotocin was tested in vivo by reversion of hisG46 base-pair substitution histidine auxotrophs of Salmonella typhimurium in the peritoneal cavity or in blood, plasma or urine of rats or mice. Genetic response was determined by the frequency of revertants (quantitative test) or by the number of revertants per plate (semiquantitative test). In quantitative HMA captan gave negative results following 3 hourly 500 mg/kg s.c. doses or 1000 mg/kg oral dose in mice with the hisG46 mutant or 2000 mg/kg oral dose in rats with the hisG46, uvrB (TA1950) mutant. The positive control SZN induced many reversions at 0.5 mg/kg i.p. or 10 or 100 mg/kg oral doses. In semiquantitative in vivo blood or urine assays captan gave negative results after a 250 mg/kg oral dose with hisG46. SZN in the same experiment gave positive results in both semiquantitative and quantitative in vivo blood assays following 1000 mg/kg i.p. or 2000 mg/kg oral doses in the rat with TA1950. Rat blood mixed with captan for 45 min before adding TA1950 cells inactivated 1000 mug captan/ml but not 5000 mg/ml in the semiquantitative test. Corresponding figures in the quantitative test were 500 mu/ml and 1000 mug/ml. Rat plasma inactivated the mutagenicity of about 10 times less captan than rat blood. Human blood inactivated about as much captan as rat blood. The mutagenicity of captan was inactivated more efficiently than of SZN by blood. The results of the experiments suggested that captan's mutagenicity is probably inactivated by glutathione of the erythrocytes. Rat S-9 liver microsomal fraction also strongly decreased captan's mutagenicity in a semiquantitative test with the R factor, uvrB, hisG46 (TA100) mutant.