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Inaccuracies of deterministic finite-element models of human middle ear revealed by stochastic modelling.

ABSTRACT: For over 40 years, finite-element models of the mechanics of the middle ear have been mostly deterministic in nature. Deterministic models do not take into account the effects of inter-individual variabilities on middle-ear parameters. We present a stochastic finite-element model of the human middle ear that uses variability in the model parameters to investigate the uncertainty in the model outputs (umbo, stapes, and tympanic-membrane displacements). We demonstrate: (1) uncertainties in the model parameters can be magnified by more than three times in the umbo and stapes footplate responses at frequencies above 2 kHz; (2) middle-ear models are biased and they distort the output distributions; and (3) with increased frequency, the highly-uncertain regions spatially spread out on the tympanic membrane surface. Our results assert that we should be mindful when using deterministic finite-element middle-ear models for critical tasks such as novel device developments and diagnosis.

SUBMITTER: Ebrahimian A

PROVIDER: S-EPMC10163043 | biostudies-literature | 2023 May

REPOSITORIES: biostudies-literature

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Inaccuracies of deterministic finite-element models of human middle ear revealed by stochastic modelling.

Ebrahimian Arash A Mohammadi Hossein H Rosowski John J JJ Cheng Jeffrey Tao JT Maftoon Nima N

Scientific reports 20230505 1

For over 40 years, finite-element models of the mechanics of the middle ear have been mostly deterministic in nature. Deterministic models do not take into account the effects of inter-individual variabilities on middle-ear parameters. We present a stochastic finite-element model of the human middle ear that uses variability in the model parameters to investigate the uncertainty in the model outputs (umbo, stapes, and tympanic-membrane displacements). We demonstrate: (1) uncertainties in the mod ...[more]

PMID: 37147426

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Project description:Computational models, particularly finite-element (FE) models, are essential for interpreting experimental data and predicting system behavior, especially when direct measurements are limited. A major challenge in tuning these models is the large number of parameters involved. Traditional methods, such as one-by-one sensitivity analyses, are time-consuming, subjective, and often return only a single set of parameter values, focusing on reproducing averaged data rather than capturing the full variability of experimental measurements. In this study, we applied simulation-based inference (SBI) using neural posterior estimation (NPE) to tune an FE model of the human middle ear. The training dataset consisted of 10,000 FE simulations of stapes velocity, ear-canal (EC) input impedance, and absorbance, paired with seven FE parameter values randomly sampled within plausible ranges. The neural network learned the association between parameters and simulation outcomes, returning the probability distribution of parameter values that can reproduce experimental data. Our approach successfully identified parameter sets that reproduced three experimental datasets simultaneously. By accounting for experimental noise and variability during training, the method provided a probability distribution of parameters, representing all valid combinations that could fit the data, rather than tuning to averaged values. The network demonstrated robustness to noise and exhibited an efficient learning curve due to the large training dataset. SBI offers an objective alternative to laborious sensitivity analyses, providing probability distributions for each parameter and uncovering interactions between them. This method can be applied to any biological FE model, and we demonstrated its effectiveness using a middle-ear model. Importantly, it holds promise for objective differential diagnosis of conductive hearing loss by providing insight into the mechanical properties of the middle ear.

Project description:Experimental studies of the flowering of Arabidopsis thaliana have shown that a large complex gene regulatory network (GRN) is responsible for its regulation. This process has been mathematically modelled with deterministic differential equations by considering the interactions between gene activators and inhibitors (Valentim et al. in PLoS ONE 10(2):e0116973, 2015; van Mourik et al. in BMC Syst Biol 4(1):1, 2010). However, due to complexity of the model, the properties of the network and the roles of the individual genes cannot be deducted from the numerical solution the published work offers. Here, we propose simplifications of the model, based on decoupling of the original GRN to motifs, described with three and two differential equations. A stable solution of the original model is sought by linearisation of the original model which contributes to further investigation of the role of the individual genes to the flowering. Furthermore, we study the role of noise by introducing and investigating two types of stochastic elements into the model. The deterministic and stochastic nonlinear dynamic models of Arabidopsis flowering time are considered by following the deterministic delayed model introduced in Valentim et al. (2015). Steady-state regimes and stability of the deterministic original model are investigated analytically and numerically. By decoupling some concentrations, the system was reduced to emphasise the role played by the transcription factor Suppressor of Overexpression of Constants1 ([Formula: see text]) and the important floral meristem identity genes, Leafy ([Formula: see text]) and Apetala1 ([Formula: see text]). Two-dimensional motifs, based on the dynamics of [Formula: see text] and [Formula: see text], are obtained from the reduced network and parameter ranges ensuring flowering are determined. Their stability analysis shows that [Formula: see text] and [Formula: see text] are regulating each other for flowering, matching experimental findings. New sufficient conditions of mean square stability in the stochastic model are obtained using a stochastic Lyapunov approach. Our numerical simulations demonstrate that the reduced models of Arabidopsis flowering time, describing specific motifs of the GRN, can capture the essential behaviour of the full system and also introduce the conditions of flowering initiation. Additionally, they show that stochastic effects can change the behaviour of the stability region through a stability switch. This study thus contributes to a better understanding of the role of [Formula: see text] and [Formula: see text] in Arabidopsis flowering.

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Inaccuracies of deterministic finite-element models of human middle ear revealed by stochastic modelling.

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Inaccuracies of deterministic finite-element models of human middle ear revealed by stochastic modelling.

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