Stability of a one-dimensional morphoelastic model for post-burn contraction

Desmoulière

Biomech Model Mechanobiol

et al. 2022

Self Cite

We consider a two-dimensional biomorphoelastic model describing post-burn scar contraction. This model describes skin displacement and the development of the effective Eulerian strain in the tissue. Besides these mechanical components, signaling molecules, fibroblasts, myofibroblasts, and collagen also play a significant role in the model. We perform a sensitivity analysis for the independent parameters of the model and focus on the effects on features of the relative surface area and the total strain energy density. We conclude that the most sensitive parameters are the Poisson’s ratio, the equilibrium collagen concentration, the contraction inhibitor constant, and the myofibroblast apoptosis rate. Next to these insights, we perform a sensitivity analysis where the proliferation rates of fibroblasts and myofibroblasts are not the same. The impact of this model adaptation is significant.

“…We note that decreasing growth factor secretion and increasing decay increase the stability of the chemical part of the model (Egberts et al. 2021 ).…”

Section: Conclusion and Discussionmentioning

confidence: 73%

“…That is: , a criterion that was found in Egberts et al. ( 2021 ). If the secretion rate is high, and the decay rate and collagen equilibrium are low, these values are closer to the stability bound, explaining why remeshing is necessary.…”

Section: Sensitivity Analysis For the Original Modelmentioning

confidence: 86%

Sensitivity of a two-dimensional biomorphoelastic model for post-burn contraction

Desmoulière

Biomech Model Mechanobiol

et al. 2022

Self Cite

“…We draw parameter samples from uniform statistical distributions based on the ranges. The model's stability condition [20] k c < δ c ρ a II c defines acceptable samples. We use a domain of 10 cm 2 with a uniform triangulation with 968 nodes.…”

Section: Datamentioning

confidence: 99%

High-speed predictions of post-burn contraction using a neural network trained on 2D-finite element simulations

Front. Appl. Math. Stat.

Zuijlen

2023

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Severe burn injuries often lead to skin contraction, leading to stresses in and around the damaged skin region. If this contraction leads to impaired joint mobility, one speaks of contracture. To optimize treatment, a mathematical model, that is based on finite element methods, is developed. Since the finite element-based simulation of skin contraction can be expensive from a computational point of view, we use machine learning to replace these simulations such that we have a cheap alternative. The current study deals with a feed-forward neural network that we trained with 2D finite element simulations based on morphoelasticity. We focus on the evolution of the scar shape, wound area, and total strain energy, a measure of discomfort, over time. The results show average goodness of fit (R2) of 0.9979 and a tremendous speedup of 1815000X. Further, we illustrate the applicability of the neural network in an online medical app that takes the patient's age into account.

“…For the time integration, we apply the backward Euler method, using a monolithic approach with inner Picard iterations to account for nonlinearity. For a complete overview of the model (including parameters), initial and boundary conditions, and further derivations of the numerical methods, we refer to our earlier study [ 11 ], as they are not essential for this study.…”

Section: The Mathematical Modelmentioning

confidence: 99%

“…Based on the ranges, we define uniform statistical distributions from which we draw parameter samples. We accept samples that satisfy , a stability condition of the mathematical model [ 11 ]. Tables S1 and S2 in File S1 show the values for the varied parameters and the fixed parameters.…”

Section: A Neural Network For Post-burn Scar Contractionmentioning

confidence: 99%

A Bayesian finite-element trained machine learning approach for predicting post-burn contraction

Schaaphok

et al. 2022

Neural Comput & Applic

Self Cite

Burn injuries can decrease the quality of life of a patient tremendously, because of esthetic reasons and because of contractions that result from them. In severe case, skin contraction takes place at such a large extent that joint mobility of a patient is significantly inhibited. In these cases, one refers to a contracture. In order to predict the evolution of post-wounding skin, several mathematical model frameworks have been set up. These frameworks are based on complicated systems of partial differential equations that need finite element-like discretizations for the approximation of the solution. Since these computational frameworks can be expensive in terms of computation time and resources, we study the applicability of neural networks to reproduce the finite element results. Our neural network is able to simulate the evolution of skin in terms of contraction for over one year. The simulations are based on 25 input parameters that are characteristic for the patient and the injury. One of such input parameters is the stiffness of the skin. The neural network results have yielded an average goodness of fit ($$R^2$$ R 2 ) of 0.9928 (± 0.0013). Further, a tremendous speed-up of 19354X was obtained with the neural network. We illustrate the applicability by an online medical App that takes into account the age of the patient and the length of the burn.