Laurent Sommacal

Fractional Multi-models of the Frog Gastrocnemius Muscle

In this article, frog gastrocnemius muscles are studied, and a multi-model identification presented. A transfer function is defined with few parameters to simulate striated muscle (Gastroctnemius) behaviour, for inclusion in a future real-time salamander computer model. A two-model structure permits description of both contraction and relaxation properties. Here, two physiological influences, fatigue and fibre types, are taken into account. A multi-model structure for each fibre type (fast (IIB), intermediate (IIA) and slow (I) fibres) is also used for inclusion in a future agonist-antagonist structure computer model.

Fractional multi-models of the gastrocnemius frog muscle

Abstract Frog gastrocnemius muscles are studied, and a multi-model identification presented. A transfer function is here defined with few parameters to simulate striated muscle (Gastroctnemius) behaviour, for inclusion in a future real-time salamander computer model. A two-model structure permits description of both contraction and relaxation properties. Here, two physiological influences, fatigue and fibre types, are taken into account. A multi-model structure for each fibre type (Fast (IIB), Intermediate (IIA) and Slow (I) fibres) is also used for inclusion in a future agonist-antagonist structure computer model.

A comparison between two fractional multimodels structures for rat muscles modelling

Abstract Peroneus digiti quarti and peroneus brevis muscles responses of the rat are studied for 10 Hz pulses stimulations. A comparison between two multimodels structures is presented. These multimodels include fractional sub-models. The multimodels allow distinguishing contraction and relaxation phases for identification. Fractional orders used in the sub-models lead to minimize the size of transfer functions. The present study develops the multimodels structure earlier established, by including variation functions of extra parameters for IIA and IIB fibres and to explain muscle response for Motor Units (MU) stimulations at 10 Hz. The multimodels explains rat striated muscle responses, and so, allow its inclusion in a future muscle computer model.

Fractional model of a gastrocnemius muscle for tetanus pattern

This study talks about gastrocnemius muscle identification. During biological activation, every contractile structure is unsynchronized. Likewise, contraction and relaxation phases depend on all contractile elements, the activation type and the state of health. Moreover, gastrocnemius muscle is composed of three fibre types: Fast Fatigable (FF), Fast Resistant (FR) and Slow (S) fibres. Some recent works highlight a fractal structure of the muscle, which consolidate the approach based on the use of a non integer (or fractal) model to characterize its dynamic behavior. A fractional structure model, due to its infinite dimension nature, is particularly adapted to model complex systems with few parameters and to obtain a real time exploitable model. According to its complexity, muscle structure and activation mechanisms, and to these previous considerations, an identification based on fractional model is presented. A model is proposed for the tetanus pattern response in a high tiredness state. It is based on a multi-model structure, which corresponds to the decomposition in contraction and relaxation phases. This multi-model structure is expected to be included subsequently in agonist-antagonist structure.

Synthesis of Havriliak-Negami functions for time-domain system identification

Abstract Fractional differentiation models have proven their usefulness in representing high dimensional systems with only few parameters. Generally, two elementary fractional functions are used in time-domain identification: Cole-Cole and Davidson-Cole functions. A third elementary function, called Havriliak-Negami, generalizes both previous ones and is particularly dedicated to dielectric systems. The use of this function is however not very popular in time-domain identification because it has no simple analytical impulse response. The only synthesis method of Havriliak-Negami elementary functions proposed in the literature is based on diffusive representation which sets restrictive conditions on fractional orders. A new synthesis method, with no such restrictions, is developed in this paper. For that purpose Havriliak-Negami function is first split into a Davidson-Cole function and a complementary one. Both functions are then synthesized in a limited frequency band using poles and zeros recursive distribution developed by Oustaloup (1995). As an example, this Havriliak-Negami function is used for a thermal system modeling.

Havriliak-Negami function for thermal system identification

Fractional differentiation models have proven their usefulness in representing high dimensional systems with only few parameters. Generally, two elementary fractional functions are used in time-domain identification: Cole-Cole and Davidson-Cole functions. A third elementary function, called Havriliak-Negami, generalizes both previous ones and is particularly dedicated to dielectric systems. The use of this function is however not very popular in time-domain identification because it has no simple analytical impulse response. The only synthesis method of Havriliak-Negami elementary functions proposed in the literature is based on diffusive representation which sets restrictive conditions on fractional orders. A new synthesis method, with no such restrictions, is based on the splitting the Havriliak-Negami function into a Davidson-Cole function and a complementary one. Both functions are then synthesized in a limited frequency band using a recursive distribution of poles and zeros developed by [Ous95].