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A Continuum Framework for Modeling the Excitation–Contraction Coupling of Smooth Muscle
Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, Faculty of Science & Engineering.
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Excitation-contraction coupling of smooth muscle refers to a chain of coupled physiological processes which convert a stimulus to a mechanical response. These processes can be disassociated into ionic transport during cell membrane excitation, activation of myosin light chains, and muscle contraction caused by actin-myosin interaction (filament sliding). This thesis concerns the development of a framework which allows to model the smooth muscle excitation-contraction coupling constitutively by applying the principle of virtual power and dissipation inequality. In doing so, the transport of ions through membrane channels is characterized by an ionic flux and an ionic supply, both governed by an electrochemical potential energy. By letting the Helmholtz free energy to be dependent on the myosin light chain configurations during contraction, the myosin light chain activation process, i.e., myosin phosphorylation, is included. The activation process links the membrane excitation to the filament sliding. A contractile element is presented to replicate the active deformation caused by the filament sliding within the smooth muscle cell. This deformation is coupled to the overall deformation of the muscle tissue by assuming a distinct principal alignment for the contractile elements.

By employing this framework, an electro-chemo-mechanical model is derived by which the mechanical response of smooth muscle to an electrical stimulus is determined. This model is evaluated by comparing the model response to the experimental isometric stress data obtained from rat uterine smooth muscle tissue. By implementing this model in a finite element program, human uterine contractions during labor are simulated. This simulation determines important clinical factors, e.g., intrauterine pressure and provides the opportunity to investigate the effect of physiological and structural parameters on the uterine contractility.

Finally, a methodology to accommodate individualized parameters from intrauterine pressure measurements is established. This methodology allows to develop models with potentials of being used clinically to diagnose difficulties during labor and delivery.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2015. , 39 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1687
National Category
Mechanical Engineering Applied Mechanics Materials Engineering
Identifiers
URN: urn:nbn:se:liu:diva-121015ISBN: 978-91-7519-020-4 (print)OAI: oai:DiVA.org:liu-121015DiVA: diva2:850827
Public defence
2015-09-08, C3, Hus C, Campus Valla, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2015-09-02 Created: 2015-09-02 Last updated: 2015-09-02Bibliographically approved
List of papers
1. A continuum model for skeletal muscle contraction at homogeneous finite deformations
Open this publication in new window or tab >>A continuum model for skeletal muscle contraction at homogeneous finite deformations
2013 (English)In: Biomechanics and Modeling in Mechanobiology, ISSN 1617-7959, E-ISSN 1617-7940, Vol. 12, no 5, 965-973 p.Article in journal (Refereed) Published
Abstract [en]

The contractile force in skeletal muscle models is commonly postulated to be the isometric force multiplied by a set of experimentally motivated functions which account for the muscle’s active properties. Although both flexible and simple, this approach does not automatically guarantee a thermodynamically consistent behavior. In contrast, the continuum mechanical model proposed herein is derived from fundamental principles in mechanics and guarantees a dissipative behavior. Further, the contractile force is associated with a friction clutch which provides a simple and well-defined macroscopic model for cycling cross-bridges. To show the performance of the model, it is specialized to standard experiments for rabbit tibialis anterior muscle. The results show that the model is able to capture important characteristics of skeletal muscle.

Place, publisher, year, edition, pages
Springer, 2013
Keyword
Skeletal muscle, Contractile element, Dissipation inequality, Strain-energy function, Continuum model
National Category
Other Mechanical Engineering
Identifiers
urn:nbn:se:liu:diva-85805 (URN)10.1007/s10237-012-0456-x (DOI)000324378900008 ()
Funder
Swedish Research Council
Available from: 2012-11-28 Created: 2012-11-28 Last updated: 2015-09-02Bibliographically approved
2. A continuum model for excitation–contraction of smooth muscle under finite deformations
Open this publication in new window or tab >>A continuum model for excitation–contraction of smooth muscle under finite deformations
2014 (English)In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 355, 1-9 p.Article in journal (Refereed) Published
Abstract [en]

The main focus in most of continuum based muscle models is the muscle contraction dynamics while other physiological processes governing muscle contraction, e.g., the cell membrane excitation and the activation, are ignored. These latter processes are essential to initiate contraction and to determine the amount of generated force, and by excluding them, the developed model cannot replicate the true behavior of the muscle in question. The aim of this study is to establish a thermodynamically and physiologically consistent framework which allows to model smooth muscle contraction by including cell membrane excitability and kinetics of myosin phosphorylation, along with dynamics of smooth muscle contraction. The model accounts for these processes through a set of coupled dissipative constitutive equations derived by applying the first principles. To show the performance of the derived model, it is evaluated for two different cases: a mechanochemical study of pig taenia coli cells where the excitation process is excluded, and a complete excitation–contraction process of rat myometrium. The results show that the model is able to replicate important aspects of the smooth muscle EC process acceptably.

Place, publisher, year, edition, pages
Elsevier, 2014
Keyword
Smooth muscle excitation–contraction, Smooth muscle continuum model, The membrane model, Hodgkin-Huxley model, Hai-Murphy model
National Category
Other Mechanical Engineering
Identifiers
urn:nbn:se:liu:diva-100778 (URN)10.1016/j.jtbi.2014.03.016 (DOI)000337865100001 ()
Available from: 2013-11-12 Created: 2013-11-12 Last updated: 2015-09-02Bibliographically approved
3. Simulating uterine contraction by using an electro-chemo-mechanical model
Open this publication in new window or tab >>Simulating uterine contraction by using an electro-chemo-mechanical model
2016 (English)In: Biomechanics and Modeling in Mechanobiology, ISSN 1617-7959, E-ISSN 1617-7940, Vol. 15, no 3, 497-510 p.Article in journal (Refereed) Published
Abstract [en]

Contractions of uterine smooth muscle cells consist of a chain of physiological processes. These contractions provide the required force to expel the fetus from the uterus. The inclusion of these physiological processes is, therefore, imperative when studying uterine contractions. In this study, an electro-chemo-mechanical model to replicate the excitation, activation, and contraction of uterine smooth muscle cells is developed. The presented modeling strategy enables efficient integration of knowledge about physiological processes at the cellular level to the organ level. The model is implemented in a three-dimensional finite element setting to simulate uterus contraction during labor in response to electrical discharges generated by pacemaker cells and propagated within the myometrium via gap junctions. Important clinical factors, such as uterine electrical activity and intrauterine pressure, are predicted using this simulation. The predictions are in agreement with clinically measured data reported in the literature. A parameter study is also carried out to investigate the impact of physiologically related parameters on the uterine contractility.

Place, publisher, year, edition, pages
Springer, 2016
Keyword
Excitation-contraction model of uterine smooth muscle; Uterus contraction; Intrauterine pressure; Uterine electrical activity
National Category
Applied Mechanics
Identifiers
urn:nbn:se:liu:diva-121013 (URN)10.1007/s10237-015-0703-z (DOI)000376014800002 ()26162461 (PubMedID)
Available from: 2015-09-02 Created: 2015-09-02 Last updated: 2016-06-13Bibliographically approved
4. Identification of the mechanical parameters for the human uterus in vivo using intrauterine pressure measurements
Open this publication in new window or tab >>Identification of the mechanical parameters for the human uterus in vivo using intrauterine pressure measurements
2016 (English)In: International Journal for Numerical Methods in Biomedical Engineering, ISSN 2040-7939, E-ISSN 2040-7947Article in journal (Refereed) Epub ahead of print
Abstract [en]

There are limited experimental data to characterize the mechanical response of human myometrium. A method is presented in this work to identify mechanical parameters describing the active response of human myometrium from the in vivo intrauterine pressure measurements. A finite element model is developed to compute the intrauterine pressure during labor in response to an increase in the intracellular calcium ion concentration within myometrial smooth muscle cells. The finite element model provides the opportunity to tune mechanical parameters in order to fit the computed intrauterine pressure to in vivo measurements. Since the model is computationally expensive, a cheaper meta-model is generated to approximate the model response. By fitting the meta-model response to the in vivo measurements, the parameters used to determine the active response of human myometrial smooth muscle are identified.

Place, publisher, year, edition, pages
John Wiley & Sons, 2016
Keyword
Intrauterine pressure, Response surface methodology, Parameter Identification, Meta-modeling
National Category
Applied Mechanics Mechanical Engineering
Identifiers
urn:nbn:se:liu:diva-121014 (URN)10.1002/cnm.2778 (DOI)
Note

At the time of the thesis presentation this publication was in status Manuscript.

Available from: 2015-09-02 Created: 2015-09-02 Last updated: 2016-04-13Bibliographically approved

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