Robust morris screening method (RMSM) for complex physiological models.

BACKGROUND AND OBJECTIVES: Morris screening sensitivity analysis (MSM) comes forth as the method needing the minimum number of model simulations to qualify the impact of input parameter variations on outputs of complex, nonlinear and overparametrized models. However, the reliability of MSM indices (mean and standard deviation) and the reproducibility of their results are rarely explored despite the input parameter tuning/identification needs. In fact, these models, such those used in medical applications as digital twins, often lie in this category and need efficient and robust tools to assess both sensitivity and reliability of the outputs to numerous input model parameters. METHODS: In this study, a new Robust Morris Screening Method (RMSM) is proposed and based on new indices: the absolute median (χ*) and the median absolute deviation (ρ). The proposed RMSM approach is evaluated on a complex multi-scales neuromuscular electrophysiological model simulating HD-sEMG (high density surface electromyography) signals at the skin surface. The reliability and stability of new RMSM indicators are evaluated at different trajectories within the parameter space and compared to classical MSM results. For this purpose, We propose a new methodology for parameter screening based on the ratio ρ/χ* as a graphic indicator of (non)linearity and (non)monotonicity of parameter effects. RESULTS: Firstly, the results demonstrated that the computed elementary effects (EE) of inputs are not normally distributed using MSM indices contrary to the proposed RMSM indices. Secondly, the ranking stability of RMSM indices was earlier obtained from 20 trajectories (T=20), while MSM ranking remained unstable until T = 100. Thirdly, The screening separation between influential and negligible input model parameters was more distinct and interpretable with RMSM than MSM. CONCLUSION: The proposed RMSM approach ensures a fast, reliable and stable ranking of parameters for complex and overparametrized models compared to classical MSM. this allows a more precise exploration of the model parameter influence space for future application in parameter tuning and identification.

High-density Surface Electromyography as Biomarker of Muscle Aging.

Sarcopenia is a muscle disease with adverse changes that increase throughout the lifetime but with different chronological scales between individuals. Addressing "early muscle aging" is becoming a critical issue for prevention. Through the CHRONOS study, we demonstrated the ability of the high-density surface electromyography (HD-sEMG), a noninvasive, wireless, portable technology, to detect both healthy muscle aging and accelerated muscle aging related to a sedentary lifestyle, one of the risk factors of sarcopenia. The HD-sEMG signals were analyzed in 91 healthy young, middle-aged, and old subjects (25-75 years) distributed according to their physical activity status (82 active and 9 sedentary; International Physical Activity Questionnaire) and compared with current methods for muscle evaluation, including muscle mass (dual-energy X-ray absorptiometry [DXA], ultrasonography), handgrip strength, and physical performance. The HD-sEMG signals were recorded from the rectus femoris during sit-to-stand trials, and 2 indexes were analyzed: muscular contraction intensity and muscle contraction dynamics. The clinical parameters did not differ significantly across the aging and physical activity levels. Inversely, the HD-sEMG indexes were correlated to age and were different significantly through the age categories of the 82 active subjects. They were significantly different between sedentary subjects aged 45-54 years and active ones at the same age. The HD-sEMG indexes of sedentary subjects were not significantly different from those of older active subjects (≥55 years). The muscle thicknesses evaluated using ultrasonography were significantly different between the 5 age decades but did not show a significant difference with physical activity. The HD-sEMG technique can assess muscle aging and physical inactivity-related "early aging," outperforming clinical and DXA parameters.

Statistical shape analysis of gravid uteri throughout pregnancy by a ray description technique.

In order to study the anatomical variability of the uterus induced by pregnancy, a parametrization of gravid uterine geometry based on principal component analysis (PCA) is proposed. Corresponding meshes used for PCA are created by a ray description technique applied to a reference mesh. A smoothed voxel-based methodology is applied to determine the reference mesh from a database of 11 real shapes produced by the FEMONUM project. The ray-based correspondence technique is compared to two existing methods (He, Giessen) as well as a proposed mixed method. Principal component analysis results are based on a database of 11 existing shapes. Results of the parametrization show that 90% of the total variance of the database can be represented with four new shape parameters and that a wide spectrum of shapes can be generated. Graphical Abstract Proposed correspondence technique compared to existing methods.

Multiscale Hill-type modeling of the mechanical muscle behavior driven by the neural drive in isometric conditions.

In this study, we present a new model describing the mechanical behavior of the skeletal muscle during isometric contraction. This model is based on a former Hill-inspired model detailing the electromechanical behavior of the muscle based on the Huxley formulation. However, in this new multiscale model the muscle is represented at the Motor Unit (MU) scale. The proposed model is driven by a physiological input describing the firing moments of the activated MUs. Definition of both voluntary and evoked MU recruitment schemes are described, enabling the study of both contractions in isometric conditions. During this type of contraction, there is no movement of the joints and the tendon-muscle complex remains at the same length. Moreover, some well-established macroscopic relationships such as force-length or force-velocity properties are considered. A comparison with a twitch model using the same input definition is provided with both recruitment schemes exhibiting limitations of twitch type models. Finally, the proposed model is validated with a comparison between simulated and recorded force profiles following eight electrical stimulations pulses in isometric conditions. The simulated muscle force was generated to mimic the one recorded from the quadriceps of a patient implanted with a functional electrical stimulation neuroprosthesis. This validation demonstrates the ability of the proposed model to reproduce realistically the skeletal muscle contractions and to take into account subject-specific parameters.

Model based optimal multipolar stimulation without a priori knowledge of nerve structure: application to vagus nerve stimulation.

OBJECTIVE: Multipolar cuff electrode can selectively stimulate areas of peripheral nerves and therefore enable to control independent functions. However, the branching and fascicularization are known for a limited set of nerves and the specific organization remains subject-dependent. This paper presents general modeling and optimization methods in the context of multipolar stimulation using a cuff electrode without a priori knowledge of the nerve structure. Vagus nerve stimulation experiments based on the optimization results were then investigated. APPROACH: The model consisted of two independent components: a lead field matrix representing the transfer function from the applied current to the extracellular voltage present on the nodes of Ranvier along each axon, and a linear activation model. The optimization process consisted in finding the best current repartition (ratios) to reach activation of a targeted area depending on three criteria: selectivity, efficiency and robustness. MAIN RESULTS: The results showed that state-of-the-art configurations (tripolar transverse, tripolar longitudinal) were part of the optimized solutions but new ones could emerge depending on the trade-off between the three criteria and the targeted area. Besides, the choice of appropriate current ratios was more important than the choice of the stimulation amplitude for a stimulation without a priori knowledge of the nerve structure. We successfully assessed the solutions in vivo to selectively induce a decrease in cardiac rhythm through vagus nerve stimulation while limiting side effects. Compared to the standard whole ring configuration, a selective solution found by simulation provided on average 2.6 less adverse effects. SIGNIFICANCE: The preliminary results showed the rightness of the simulation, using a generic nerve geometry. It suggested that this approach will have broader applications that would benefit from multicontact cuff electrodes to elicit selective responses. In the context of the vagus nerve stimulation for heart failure therapy, we show that the simulation results were confirmed and improved the therapy while decreasing the side effects.

Speedup computation of HD-sEMG signals using a motor unit-specific electrical source model.

Nowadays, bio-reliable modeling of muscle contraction is becoming more accurate and complex. This increasing complexity induces a significant increase in computation time which prevents the possibility of using this model in certain applications and studies. Accordingly, the aim of this work is to significantly reduce the computation time of high-density surface electromyogram (HD-sEMG) generation. This will be done through a new model of motor unit (MU)-specific electrical source based on the fibers composing the MU. In order to assess the efficiency of this approach, we computed the normalized root mean square error (NRMSE) between several simulations on single generated MU action potential (MUAP) using the usual fiber electrical sources and the MU-specific electrical source. This NRMSE was computed for five different simulation sets wherein hundreds of MUAPs are generated and summed into HD-sEMG signals. The obtained results display less than 2% error on the generated signals compared to the same signals generated with fiber electrical sources. Moreover, the computation time of the HD-sEMG signal generation model is reduced to about 90% compared to the fiber electrical source model. Using this model with MU electrical sources, we can simulate HD-sEMG signals of a physiological muscle (hundreds of MU) in less than an hour on a classical workstation. Graphical Abstract Overview of the simulation of HD-sEMG signals using the fiber scale and the MU scale. Upscaling the electrical source to the MU scale reduces the computation time by 90% inducing only small deviation of the same simulated HD-sEMG signals.

Multi-scale and multi-physics model of the uterine smooth muscle with mechanotransduction.

Preterm labor is an important public health problem. However, the efficiency of the uterine muscle during labor is complex and still poorly understood. This work is a first step towards a model of the uterine muscle, including its electrical and mechanical components, to reach a better understanding of the uterus synchronization. This model is proposed to investigate, by simulation, the possible role of mechanotransduction for the global synchronization of the uterus. The electrical diffusion indeed explains the local propagation of contractile activity, while the tissue stretching may play a role in the synchronization of distant parts of the uterine muscle. This work proposes a multi-physics (electrical, mechanical) and multi-scales (cell, tissue, whole uterus) model, which is applied to a realistic uterus 3D mesh. This model includes electrical components at different scales: generation of action potentials at the cell level, electrical diffusion at the tissue level. It then links these electrical events to the mechanical behavior, at the cellular level (via the intracellular calcium concentration), by simulating the force generated by each active cell. It thus computes an estimation of the intra uterine pressure (IUP) by integrating the forces generated by each active cell at the whole uterine level, as well as the stretching of the tissue (by using a viscoelastic law for the behavior of the tissue). It finally includes at the cellular level stretch activated channels (SACs) that permit to create a loop between the mechanical and the electrical behavior (mechanotransduction). The simulation of different activated regions of the uterus, which in this first "proof of concept" case are electrically isolated, permits the activation of inactive regions through the stretching (induced by the electrically active regions) computed at the whole organ scale. This permits us to evidence the role of the mechanotransduction in the global synchronization of the uterus. The results also permit us to evidence the effect on IUP of this enhanced synchronization induced by the presence of SACs. This proposed simplified model will be further improved in order to permit a better understanding of the global uterine synchronization occurring during efficient labor contractions.

Investigation of the HD-sEMG probability density function shapes with varying muscle force using data fusion and shape descriptors.

This work presents an evaluation of the High Density surface Electromyogram (HD-sEMG) Probability Density Function (PDF) shape variation according to contraction level. On that account, using PDF shape descriptors: High Order Statistics (HOS) and Shape Distances (SD), we try to address the absence of a consensus for the sEMG non-Gaussianity evolution with force variation. This is motivated by the fact that PDF shape information are relevant in physiological assessment of the muscle architecture and function, such as contraction level classification, in complement to classical amplitude parameters. Accordingly, both experimental and simulation studies are presented in this work. For data fusion, the watershed image processing technique was used. This technique allowed us to find the dominant PDF shape variation profiles from the 64 signals. The experimental protocol consisted of three isometric isotonic contractions of 30, 50 and 70% of the Maximum Voluntary Contraction (MVC). This protocol was performed by six subjects and recorded using an 8 × 8 HD-sEMG grid. For the simulation study, the muscle modeling was done using a fast computing cylindrical HD-sEMG generation model. This model was personalized by morphological parameters obtained by sonography. Moreover, a set of the model parameter configurations were compared as a focused sensitivity analysis of the PDF shape variation. Further, monopolar, bipolar and Laplacian electrode configurations were investigated in both experimental and simulation studies. Results indicated that sEMG PDF shape variations according to force increase are mainly dependent on the Motor Unit (MU) spatial recruitment strategy, the MU type distribution within the muscle, and the used electrode arrangement. Consequently, these statistics can give us an insight into non measurable parameters and specifications of the studied muscle primarily the MU type distribution.

Analysis of the sEMG/force relationship using HD-sEMG technique and data fusion: A simulation study.

The relationship between the surface Electromyogram (sEMG) signal and the force of an individual muscle is still ambiguous due to the complexity of experimental evaluation. However, understanding this relationship should be useful for the assessment of neuromuscular system in healthy and pathological contexts. In this study, we present a global investigation of the factors governing the shape of this relationship. Accordingly, we conducted a focused sensitivity analysis of the sEMG/force relationship form with respect to neural, functional and physiological parameters variation. For this purpose, we used a fast generation cylindrical model for the simulation of an 8×8 High Density-sEMG (HD-sEMG) grid and a twitch based force model for the muscle force generation. The HD-sEMG signals as well as the corresponding force signals were simulated in isometric non-fatiguing conditions and were based on the Biceps Brachii (BB) muscle properties. A total of 10 isometric constant contractions of 5s were simulated for each configuration of parameters. The Root Mean Squared (RMS) value was computed in order to quantify the sEMG amplitude. Then, an image segmentation method was used for data fusion of the 8×8 RMS maps. In addition, a comparative study between recent modeling propositions and the model proposed in this study is presented. The evaluation was made by computing the Normalized Root Mean Squared Error (NRMSE) of their fitting to the simulated relationship functions. Our results indicated that the relationship between the RMS (mV) and muscle force (N) can be modeled using a 3rd degree polynomial equation. Moreover, it appears that the obtained coefficients are patient-specific and dependent on physiological, anatomical and neural parameters.

An electro-mechanical multiscale model of uterine pregnancy contraction.

Detecting preterm labor as early as possible is important because tocolytic drugs are much more likely to delay preterm delivery if administered early. Having good information on the real risk of premature labor also leads to fewer women who do not need aggressive treatment for premature labor threat. Currently, one of the most promising ways to diagnose preterm labor threat is the analysis of the electrohysterogram (EHG). Its characteristics have been related to preterm labor risk but they have not proven to be sufficiently accurate to use in clinical routine. One of the reasons for this is that the physiology of the pregnant uterus is insufficiently understood. Models already exist in literature that simulate either the electrical or the mechanical component of the uterine smooth muscle. Few include both components in a co-simulation of electrical and mechanical aspects. A model that can represent realistically both the electrical and the mechanical behavior of the uterine muscle could be useful for better understanding the EHG and therefore for preterm labor detection. Processing the EHG considers only the electrical component of the uterus but the electrical activity does not seem to explain by itself the synchronization of the uterine muscle that occurs during labor and not at other times. Recent studies have demonstrated that the mechanical behavior of the uterine muscle seems to play an important role in uterus synchronization during labor. The aim of the proposed study is to link three different models of the uterine smooth muscle behavior by using co-simulation. The models go from the electrical activity generated at the cellular level to the mechanical force generated by the muscle and from there to the deformation of the tissue. The results show the feasibility of combining these three models to model a whole uterus contraction on 3D realistic uterus model.

Fast generation model of high density surface EMG signals in a cylindrical conductor volume.

In the course of the last decade, fast and qualitative computing power developments have undoubtedly permitted for a better and more realistic modeling of complex physiological processes. Due to this favorable environment, a fast, generic and reliable model for high density surface electromyographic (HD-sEMG) signal generation with a multilayered cylindrical description of the volume conductor is presented in this study. Its main peculiarity lies in the generation of a high resolution potential map over the skin related to active Motor Units (MUs). Indeed, the analytical calculus is fully performed in the frequency domain. HD-sEMG signals are obtained by surfacic numerical integration of the generated high resolution potential map following a variety of electrode shapes. The suggested model is implemented using parallel computing techniques as well as by using an object-oriented approach which is comprehensive enough to be fairly quickly understood, used and potentially upgraded. To illustrate the model abilities, several simulation analyses are put forward in the results section. These simulations have been performed on the same muscle anatomy while varying the number of processes in order to show significant speed improvement. Accuracy of the numerical integration method, illustrating electrode shape diversity, is also investigated in comparison to analytical transfer functions definition. An additional section provides an insight on the volume detection of a circular electrode according to its radius. Furthermore, a large scale simulation is introduced with 300MUs in the muscle and a HD-sEMG electrode grid composed of 16×16 electrodes for three constant isometric contractions in 12s. Finally, advantages and limitations of the proposed model are discussed with a focus on perspective works.

Realistic motor unit placement in a cylindrical HD-sEMG generation model.

The aim of this work is to assess an automatic optimized algorithm for the positioning of the Motor Units (MUs) within a multilayered cylindrical High Density surface EMG (HD-sEMG) generation model representing a skeletal muscle. The multilayered cylinder is composed of three layers: muscle, adipose and skin tissues. For this purpose, two different algorithms will be compared: an unconstrained random and a Mitchell's Best Candidate (MBC) placements, both with uniform distribution for the MUs positions. These algorithms will then be compared by their fiber density within the muscle and by using a classical amplitude descriptor, the Root-Mean-Square (RMS) amplitude value obtained from 64 HD-sEMG signals recorded by an 8×8 electrode grid of circular electrode during one contraction at 70% Maximum Voluntary Contraction (MVC) in both simulation and experimental conditions for the Biceps Brachii (BB) muscle. The obtained results clearly exposed the necessity to use a specific algorithm to place the MUs within the muscle representation volume in agreement with physiology.

Preliminary global sensitivity analysis of a uterine electrical activity model.

A comprehensive multiscale model of the uterine muscle electrical activity would permit understanding the important link between the genesis and evolution of the action potential at the cell level and the process leading to labor. Understanding this link can open the way to more effective tools for the prediction of labor and prevention of preterm delivery.

A multiscale model of the electrohysterogram the BioModUE_PTL project.

The electrohysterogram (EHG) is a promising means of monitoring pregnancy and of detecting a risk of preterm labor. To improve our understanding of the EHG as well as its relationship with the physiologic phenomena involved in uterine contractility, we plan to model these phenomena in terms of generation and propagation of uterine electrical activity. This activity can be realistically modeled by representing the principal ionic dynamics at the cell level, the propagation of electrical activity at the tissue level and then the way it is reflected on the skin surface through the intervening tissue. We present in this paper the different steps leading to the development and validation of a biophysics based multiscale model of the EHG, going from the cell to the electrical signal measured on the abdomen.

Toward a multiscale model of the uterine electrical activity.

A comprehensive multiscale model of the uterine muscle electrical activity would permit understanding the important link between the genesis and evolution of the action potential at the cell level and the process leading to labor. Understanding this link can open the way to more effective tools for the prediction of labor and prevention of preterm delivery. A first step toward the realization of such a model is presented here. By using as starting point a previously published model of the generation of the uterine muscle action potential at the cell level, a significant reduction of the model complexity is here achieved in order to simulate 2-D propagation of the cellular activity at the uterine tissue level, for tissue strips of arbitrary dimension. From the obtained dynamic behavior of the electrical activity simulated at the tissue level, the use of a previously validated volume conductor model at the organ level permits us to simulate the electrohysterogram as recorded on the abdominal surface by an electrode array. Qualitative evaluation of the model at the cell level and at the organ level confirms the potential of the proposed multiscale approach for further refinement and extension aiming at clinical application.

Smooth muscle modeling and experimental identification: application to bladder isometric contraction.

This paper presents an original smooth muscle model based on the Huxley microscopic approach. This model is the main part of a comprehensive lower urinary track model. The latter is used for simulation studies and is assessed through experiments on rabbits, for which a subset of parameters is estimated, using intravesical pressure measurements in isometric conditions. Bladder contraction is induced by electrical stimulation that determines the onset and thus synchronizes simulation and experimental data. Model sensitivity versus parameter accuracy is discussed and allows the definition of a subset of four parameters that must be accurately identified in order to obtain good fitting between experimental and acquired data. Preliminary experimental data are presented as well as model identification results. They show that the model is able to follow the pressure changes induced by an artificial stimulus in isometric contractions. Moreover, the model gives an insight into the internal changes in calcium concentration and the ratio of the different chemical species present in the muscle cells, in particular the bounded and unbounded actin and myosin and the normalized concentration of intracellular calcium.

A toolchain to simulate and investigate selective stimulation strategies for FES.

When contracting a muscle using NFES (Neural Functional Electrical Stimulation), the stimulus always activates the axons of greater diameter first. Also selective activation of given fascicle inside a nerve is not possible with classical cuff electrode as the recruitment is performed uniformly around the nerve. These limits lead to poorly selective muscle recruitment, inducing fatigue and possible pain. To overcome this, selective stimulation strategies can be used. We propose a toolchain to investigate, simulate and tune selective stimulation strategies. It consists of a conduction volume model to compute the electric field generated in the nerve by a cuff electrode surrounding it; an axon model to predict the effect of the field on the nerve fibre - the generation, propagation and possible block of action potentials; and an interface script that links the two models and generates the code of the input function for the nerve fibre model. We present some simulation results to illustrate the possibilities of the toolchain to simulate such strategies. Ongoing experimental validations are also discussed. They will enable us to tune the model and may lead to further improvements.

Smooth muscle model for functional electrical stimulation applications: simulation of realistic bladder behavior under FES.

In this paper, we present a smooth muscle model which enables simulation of functional electrical stimulation (FES) induced contraction. The major novelty of this new version of our model is that it includes muscle cell calcium dynamics. We establish the relationship between calcium concentration and electrical potential of the membrane cell. Calcium concentration drives the microscopic mechanics of the muscle inducing contraction. We also refined the mechanical model: smooth muscles have slower dynamics than striated ones, it is therefore possible to neglect the second order terms in the differential equations. Validation of the model is achieved through the simulation of a well known example: the bladder electrical stimulation with a Finetech / Brindley implant. The obtained results are compared qualitatively with the experimental data available in the literature and show good consistency both in shape and time course. In order to obtain quantitative simulations, we need to perform the identification of the model through in-vivo testing on animals. Once this validation step is done, it will be possible to apply our methodology to human bladder neural stimulation.

Smooth muscle model for functional electrical stimulation applications.

We present a new model of smooth muscle that can be used to simulate the effect of Functional Electrical Stimulation (FES). It is composed of a set of differential equations based on the physiological reality so that parameter's values are meaningful and can be used for quantitative and objective evaluation of the muscle state. Moreover, the model has an input controlled by an FES signal so that it can simulate the behavior of the muscle under artificial stimulation. We apply this model to the simulation of the bladder contraction through the detrusor stimulation. It shows that the model is able to predict the time response, the intravesical pressure and the necessary time to empty the bladder. Simulations show consistent data with the literature. These preliminary results, after in vivo validations, will be used to caracterise bladders that need to be stimulated, for instance for paraplegics, and then to optimize the needed stimulation when neuroprosthesis are used to restore the emptying function.