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A General Mathematical Algorithm for Predicting the Course of Unfused Tetanic Contractions of Motor Units in Rat Muscle
- Source :
- PLoS ONE, Vol 11, Iss 9, p e0162385 (2016), PLoS ONE
- Publication Year :
- 2016
- Publisher :
- Public Library of Science (PLoS), 2016.
-
Abstract
- An unfused tetanus of a motor unit (MU) evoked by a train of pulses at variable interpulse intervals is the sum of non-equal twitch-like responses to these stimuli. A tool for a precise prediction of these successive contractions for MUs of different physiological types with different contractile properties is crucial for modeling the whole muscle behavior during various types of activity. The aim of this paper is to develop such a general mathematical algorithm for the MUs of the medial gastrocnemius muscle of rats. For this purpose, tetanic curves recorded for 30 MUs (10 slow, 10 fast fatigue-resistant and 10 fast fatigable) were mathematically decomposed into twitch-like contractions. Each contraction was modeled by the previously proposed 6-parameter analytical function, and the analysis of these six parameters allowed us to develop a prediction algorithm based on the following input data: parameters of the initial twitch, the maximum force of a MU and the series of pulses. Linear relationship was found between the normalized amplitudes of the successive contractions and the remainder between the actual force levels at which the contraction started and the maximum tetanic force. The normalization was made according to the amplitude of the first decomposed twitch. However, the respective approximation lines had different specific angles with respect to the ordinate. These angles had different and non-overlapping ranges for slow and fast MUs. A sensitivity analysis concerning this slope was performed and the dependence between the angles and the maximal fused tetanic force normalized to the amplitude of the first contraction was approximated by a power function. The normalized MU contraction and half-relaxation times were approximated by linear functions depending on the normalized actual force levels at which each contraction starts. The normalization was made according to the contraction time of the first contraction. The actual force levels were calculated initially from the recorded tetanic curves and subsequently from the modeled curves obtained from the summation of all models of the preceding contractions (the so called “full prediction”). The preciseness of the prediction was verified by two coefficients estimating the error between the modeled and the experimentally recorded curves. The proposed approach was tested for 30 MUs from the database and for three additional MUs, not included in the initial set. It was concluded that this general algorithm can be successfully used for modeling of a unfused tetanus course of a single MU of fast and slow type.
- Subjects :
- Bacterial Diseases
0301 basic medicine
Muscle Physiology
Contraction (grammar)
Physiology
lcsh:Medicine
Pathology and Laboratory Medicine
Mathematical and Statistical Techniques
0302 clinical medicine
Medicine and Health Sciences
lcsh:Science
Fatigue
Mathematics
Motor Neurons
Multidisciplinary
Approximation Methods
Mathematical Models
Applied Mathematics
Simulation and Modeling
Curve Fitting
Infectious Diseases
Amplitude
Muscle Fatigue
Physical Sciences
Curve fitting
medicine.symptom
Algorithm
Algorithms
Muscle Contraction
Research Article
Muscle contraction
Normalization (statistics)
Research and Analysis Methods
Models, Biological
03 medical and health sciences
Signs and Symptoms
Diagnostic Medicine
medicine
Animals
Muscle, Skeletal
Power function
Tetanus
lcsh:R
Biology and Life Sciences
Electric Stimulation
Rats
Motor unit
Algebra
030104 developmental biology
lcsh:Q
Mathematical Functions
Algebraic Geometry
030217 neurology & neurosurgery
Analytic function
Subjects
Details
- Language :
- English
- ISSN :
- 19326203
- Volume :
- 11
- Issue :
- 9
- Database :
- OpenAIRE
- Journal :
- PLoS ONE
- Accession number :
- edsair.doi.dedup.....cb4938de0ba7c2482a750535b1dca012