CN112365985A - Skeletal muscle multi-scale model modeling method based on sarcoplasmic reticulum environment - Google Patents
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- 238000000034 method Methods 0.000 title claims abstract description 37
- 210000001908 sarcoplasmic reticulum Anatomy 0.000 title claims abstract description 37
- 210000002027 skeletal muscle Anatomy 0.000 title claims abstract description 26
- 210000003205 muscle Anatomy 0.000 claims abstract description 45
- BHPQYMZQTOCNFJ-UHFFFAOYSA-N Calcium cation Chemical compound [Ca+2] BHPQYMZQTOCNFJ-UHFFFAOYSA-N 0.000 claims abstract description 39
- 229910001424 calcium ion Inorganic materials 0.000 claims abstract description 39
- 230000008569 process Effects 0.000 claims abstract description 22
- 230000007246 mechanism Effects 0.000 claims abstract description 14
- 230000008602 contraction Effects 0.000 claims abstract description 10
- 210000000663 muscle cell Anatomy 0.000 claims abstract description 10
- 210000002363 skeletal muscle cell Anatomy 0.000 claims abstract description 7
- 238000004134 energy conservation Methods 0.000 claims abstract description 5
- 229910019142 PO4 Inorganic materials 0.000 claims description 48
- 239000010452 phosphate Substances 0.000 claims description 48
- NBIIXXVUZAFLBC-UHFFFAOYSA-K phosphate Chemical compound [O-]P([O-])([O-])=O NBIIXXVUZAFLBC-UHFFFAOYSA-K 0.000 claims description 39
- 210000001087 myotubule Anatomy 0.000 claims description 25
- 230000005489 elastic deformation Effects 0.000 claims description 20
- NBIIXXVUZAFLBC-UHFFFAOYSA-N Phosphoric acid Chemical compound OP(O)(O)=O NBIIXXVUZAFLBC-UHFFFAOYSA-N 0.000 claims description 17
- 238000000926 separation method Methods 0.000 claims description 16
- 239000000463 material Substances 0.000 claims description 13
- 238000001556 precipitation Methods 0.000 claims description 11
- 102000003505 Myosin Human genes 0.000 claims description 9
- 108060008487 Myosin Proteins 0.000 claims description 9
- 102000007469 Actins Human genes 0.000 claims description 8
- 108010085238 Actins Proteins 0.000 claims description 8
- 230000008859 change Effects 0.000 claims description 7
- 230000003834 intracellular effect Effects 0.000 claims description 7
- 238000006243 chemical reaction Methods 0.000 claims description 6
- 230000000694 effects Effects 0.000 claims description 6
- 230000002503 metabolic effect Effects 0.000 claims description 6
- 229940085991 phosphate ion Drugs 0.000 claims description 6
- 108091005975 Myofilaments Proteins 0.000 claims description 5
- 239000006227 byproduct Substances 0.000 claims description 5
- 210000003632 microfilament Anatomy 0.000 claims description 5
- 230000000638 stimulation Effects 0.000 claims description 5
- 229910000147 aluminium phosphate Inorganic materials 0.000 claims description 4
- 238000004090 dissolution Methods 0.000 claims description 4
- 239000000047 product Substances 0.000 claims description 4
- OYPRJOBELJOOCE-UHFFFAOYSA-N Calcium Chemical compound [Ca] OYPRJOBELJOOCE-UHFFFAOYSA-N 0.000 claims description 3
- 239000002253 acid Substances 0.000 claims description 3
- 239000011575 calcium Substances 0.000 claims description 3
- 229910052791 calcium Inorganic materials 0.000 claims description 3
- 230000015556 catabolic process Effects 0.000 claims description 2
- 238000006731 degradation reaction Methods 0.000 claims description 2
- 239000000835 fiber Substances 0.000 claims description 2
- 230000002427 irreversible effect Effects 0.000 claims description 2
- 239000002002 slurry Substances 0.000 claims description 2
- 239000000126 substance Substances 0.000 claims description 2
- 230000002195 synergetic effect Effects 0.000 claims description 2
- 230000004118 muscle contraction Effects 0.000 abstract description 7
- 208000029578 Muscle disease Diseases 0.000 abstract description 2
- 230000012232 skeletal muscle contraction Effects 0.000 description 6
- 230000037149 energy metabolism Effects 0.000 description 2
- 230000001537 neural effect Effects 0.000 description 2
- 230000009471 action Effects 0.000 description 1
- 230000004913 activation Effects 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 238000007918 intramuscular administration Methods 0.000 description 1
- 238000013178 mathematical model Methods 0.000 description 1
- 239000012528 membrane Substances 0.000 description 1
- 230000003387 muscular Effects 0.000 description 1
- 108090000623 proteins and genes Proteins 0.000 description 1
- 102000004169 proteins and genes Human genes 0.000 description 1
- 210000003660 reticulum Anatomy 0.000 description 1
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Abstract
The invention provides a skeletal muscle multi-scale model based on a sarcoplasmic reticulum environment. The method comprises the following steps: the method comprises the following steps: establishing a human skeletal muscle cell transverse bridge kinetic model based on an actual microscopic mechanism and an operation mechanism of human muscle cells; step two: and establishing a muscle thermodynamic model based on the energy conservation rule of muscle cells and whole muscles in the contraction process. The invention provides a reasonable explanation based on the generation process from calcium ion release to muscle contraction force in the human muscle sarcoplasmic reticulum environment, and has theoretical guidance for researching the operation mechanism of the internal muscle of the skeleton and treating muscle diseases.
Description
Technical Field
The invention relates to a multiscale modeling method for a contraction process based on a sarcoplasmic reticulum environment.
Background
At present, many skeletal muscle contraction models are studied, but most of the skeletal muscle contraction models are studied from neural activation to muscle contraction, and muscle contraction models are obtained according to an electrical stimulation model of neural signals, a membrane potential change model, an energy metabolism model and the like. However, in the actual muscle contraction process, it is observed that the sarcoplasmic reticulum environment plays an important role in the generation of muscle contraction and the generation of muscle force, and the existing model lacks research on the influence of the sarcoplasmic reticulum on the muscle contraction process, and based on the above problem, it is necessary to add the action mechanism of the sarcoplasmic reticulum environment to the skeletal muscle contraction model.
Disclosure of Invention
The invention provides a skeletal muscle model modeling method based on a sarcoplasmic reticulum environment, aiming at solving the problems that the existing skeletal muscle contraction model can not reflect the influence of the human muscle sarcoplasmic reticulum environment and a single-scale model can not completely express the muscle contraction process.
A skeletal muscle multi-scale model modeling method based on sarcoplasmic reticulum environment is realized according to the following steps:
the method comprises the following steps: establishing a human skeletal muscle cell transverse bridge kinetic model based on an actual microscopic mechanism and an operation mechanism of human muscle cells;
step two: establishing a human skeletal muscle intracellular phosphate reaction model based on the dynamic analysis of a human muscle intracellular metabolic byproduct phosphate;
step three: establishing a muscle thermodynamic model based on the energy conservation rule of muscle cells and whole muscles in the contraction process;
the invention has the following effects:
the traditional skeletal muscle model rarely relates to the metabolic mechanism of the intramuscular plasma reticulum environment, and the influence of different scales on the skeletal muscle contraction model is not distinguished. The invention introduces a skeletal muscle contraction model which can embody different contraction scales and sarcoplasmic reticulum environments based on the energy metabolism process in a human body. Has theoretical guidance effect on muscle disease treatment, exercise rehabilitation, internal operation mechanism of muscle and the like.
Drawings
FIG. 1 is a schematic diagram of a cross-bridge four-state cycle process;
FIG. 2 is a flow chart of a skeletal muscle multi-scale contraction model based on a sarcoplasmic reticulum environment.
Detailed Description
The first embodiment is as follows: the skeletal muscle multi-scale model modeling method based on the sarcoplasmic reticulum environment comprises the following steps
The method comprises the following steps: establishing a human skeletal muscle cell transverse bridge kinetic model based on an actual microscopic mechanism and an operation mechanism of human muscle cells;
step two: establishing a human skeletal muscle intracellular phosphate reaction model based on the dynamic analysis of a human muscle intracellular metabolic byproduct phosphate;
step three: and establishing a muscle thermodynamic model based on the energy conservation rule of muscle cells and whole muscles in the contraction process.
The second embodiment is as follows: the first difference between the present embodiment and the specific embodiment is: the specific process for establishing the human skeletal muscle cell transverse bridge kinetic model in the step one is as follows:
after the sarcoplasmic reticulum in the muscle receives an electric signal, calcium ions are released from the sarcoplasmic reticulum, the calcium ions are combined with the calcium collecting protein of myosin to expose binding sites connected with a transverse bridge, so that the whole skeletal muscle fiber is promoted to perform gliding movement, ATP is hydrolyzed in the process to produce ADP, phosphate and energy, the generated energy provides power support for the movement of the transverse bridge, and the phosphate is taken as a metabolic byproduct to cause the reaction rate of the muscle fiber to be slow, so that the final muscle force is reduced.
The process of state transition from the sarcoplasmic reticulum of the muscular system releasing calcium ions to the circulatory movement of the transverse bridge is shown in figure 1;
the equilibrium equation of the four-state cycle process of the transverse bridge model is
Roff(t)+D(t)+A1(t)+A2(t)＝1 (1)
Wherein R isoff、D、A1、A2T is respectively a transverse bridge circulation separation state, a transverse bridge circulation pre-connection state, a transverse bridge circulation front stroke, a transverse bridge circulation rear stroke and time;
the balance equation of the horizontal bridge in the circulating pre-connection state is
Wherein D, f', f, kon、koff、A1、A2G is a transverse bridge circulating pre-connection state, a speed coefficient from a pre-connection state to a front stroke, a speed coefficient from a front stroke to a pre-connection state, a speed coefficient from a separation state to a pre-connection state, a speed coefficient from a pre-connection state to a separation state, a transverse bridge circulating front stroke, a transverse bridge circulating back stroke and a speed coefficient from a back stroke to a pre-connection state respectively;
the balance equation of the front stroke of the transverse bridge circulation is
D, A therein1、A2F, f ', h and h' are respectively a transverse bridge circulation pre-connection state, a transverse bridge circulation front stroke, a transverse bridge circulation rear stroke, a speed coefficient from a pre-connection state to a front stroke, a speed coefficient from a front stroke to a pre-connection state, a speed coefficient from a front stroke to a rear stroke and a speed coefficient from a rear stroke to a front stroke;
the balance equation of the transverse bridge cycle back stroke is
Wherein A is1、A2H, h' and g are respectively a transverse bridge cycle front stroke, a transverse bridge cycle rear stroke, a front stroke to rear stroke rate coefficient, a rear stroke to front stroke rate coefficient and a rear stroke to pre-connection state rate coefficient;
the open-close coefficient equation of the transverse bridge connection is
Wherein k ison、
koff、
p、pm、pn、pc、pS、pSR、pSR CT is the transverse bridge opening coefficient, the opening coefficient under no calcium ion stimulation, the opening coefficient under calcium ion stimulation, the transverse bridge separation coefficient, the current calcium ion concentration, the calcium ion concentration when the maximum force is generated by 50 percent, the balance coefficient of phosphate in sarcoplasmic reticulum, the phosphate in sarcoplasmic reticulum andthe equilibrium coefficient of calcium ion precipitation, the concentration of phosphate in the sarcoplasmic acid net, the concentration of phosphate and calcium ion precipitation in the sarcoplasmic acid net and the time;
the rate equation of the pre-connection state from the front stroke to the transverse bridge based on the muscle wire separation and synergistic effect is
Wherein f, f0、x0、x1、x2V is a velocity coefficient from a pre-connection state to a front stroke, a constant coefficient related to the front stroke, an average deformation amount caused by a power stroke, an average elastic deformation amount caused by the front stroke, an average elastic deformation amount caused by a rear stroke and an adjacent transverse bridge influence coefficient respectively;
the separation ratio equation caused by myofilament deformation is
Wherein g is0、g、x0、x2Rho is a separation rate constant coefficient, an irreversible separation rate coefficient, an average deformation caused by a power stroke, an average elastic deformation caused by a rear stroke and a deformation influence level respectively;
the elastic deformation equation of muscle fiber caused by the front stroke and the back stroke during unequal length contraction is
D, A therein1、A2、h′、x0、x1、x2、
The system is respectively in a transverse bridge circulating pre-connection state, a transverse bridge circulating front stroke, a transverse bridge circulating back stroke, a speed coefficient from a back stroke to a front stroke, an average deformation caused by a power stroke, an average elastic deformation caused by a front stroke, an average elastic deformation caused by a back stroke and a relative sliding speed between thick and thin muscle wires;
the third concrete implementation mode: the present embodiment differs from the first or second embodiment in that: the second step is based on the dynamic analysis of the metabolic byproduct phosphate in the human muscle cells, and the specific process of establishing a human skeletal muscle cell phosphate reaction model is as follows:
the equation for the concentration of phosphate in muscle slurry is
Wherein b isp、h0、hp、kp、A1、A2、PS、PSR、V2Respectively the degradation rate of phosphate in the sarcoplasm, the forward speed of a power stroke, the reverse power stroke speed, the transportation speed of the sarcoplasm phosphate into the SR, the front stroke of a transverse bridge cycle, the rear stroke of the transverse bridge cycle, the concentration of the phosphate in the sarcoplasm, the concentration of the phosphate in a sarcoplasm net and the volume of the sarcoplasm in a final removal pool;
the equation for phosphate concentration in sarcoplasmic reticulum is
Wherein k isP、P、PSR、
Bp、
PP、
The transport rate of the sarcoplasmic phosphate entering the SR, the concentration of the phosphate in the sarcoplasmic net, the volume of the sarcoplasmic net for removing the final pond, the phosphate precipitation dissolution rate, the concentration of the phosphate and calcium ions in the sarcoplasmic net, the phosphoric acid solubility product and the concentration of the calcium ions in the sarcoplasmic net are respectively;
the equation for the concentration of phosphate and calcium ion deposits in the sarcoplasmic reticulum is
Wherein A isP、PSR、
PP、BP、
Respectively the phosphate precipitation rate, the concentration of phosphate in the sarcoplasmic reticulum, the concentration of calcium ions in the sarcoplasmic reticulum, the phosphoric acid solubility product, the phosphate precipitation dissolution rate, and the concentration of phosphate and calcium ions in the sarcoplasmic reticulum;
based on the microstructure and the operation mechanism of human muscle fibers, the microscopic state equation of the cross-bridge connection is solved through the expression of the connection state of the cross-bridge and the state relation of each state.
The fourth concrete implementation mode: this embodiment differs from the first, second or third embodiment in that: in the third step, based on the energy conservation rule of muscle cells and whole muscles in the contraction process, the specific process of establishing the muscle thermodynamic mathematical model is as follows:
according to the principle of virtual work, the skeletal muscle energy equation is derived as
Wherein p is,
F、Fa、FCa、
The power of the macroscopic work done by the muscle, the integral deformation rate coefficient of the transverse bridge, the deformation rate coefficient caused by the slippage of the muscle wire, the stress related to the integral deformation of the transverse bridge, the stress related to the deformation caused by the slippage of the muscle wire, the stress related to the concentration of calcium ions and the change rate coefficient of the concentration of calcium ions are respectively;
the micro energy expression equation of muscle fiber is
Ψ＝Ψ(λ,λa,s,β) (15)
Where Ψ, λaS and beta are respectively the microcosmically related internal energy of muscle fiber, the integral deformation of a transverse bridge, the deformation caused by muscle fiber slippage, an internal state function and the calcium ion concentration;
the Clausius-Planck inequality equation neglecting the effect of thermal effects is
Wherein
p is the muscle fiber microscopic acting power and the muscle macroscopic acting power respectively;
the inequality equation of the change of the internal state of the muscle fiber is obtained by substituting the formula (16) with the formula (14) and the formula (15):
wherein F, Ψ, λ, Fa、λa、si、FCaBeta is the stress related to the whole deformation of the transverse bridge, the internal energy related to the microcosmic muscle fiber, the whole deformation of the transverse bridge, the stress related to the deformation caused by the slippage of the muscle wire, the state variable of the ith transverse bridge, the stress related to the calcium ion concentration and the calcium ion concentration；
The skeletal muscle total strain energy equation is:
Ψ＝Ψe(λ)N(λa)Ψa(λe,si)+ΨXB(si)+Ψc(β) (18)
wherein Ψ, Ψe、Ψa、λ、ΨXB、Ψc、N、λa、λe、siBeta is respectively internal energy microcosmically related to muscle fibers, energy related to passive behavior, elastic energy of connection of a transverse bridge, integral deformation of the transverse bridge, chemical energy related to movement of the transverse bridge, calcium concentration related energy, elastic energy related coefficient of the transverse bridge, deformation caused by muscle fiber slippage, elastic deformation of the transverse bridge, ith transverse bridge state variable and calcium ion concentration;
the muscle passive state one-dimensional energy expression equation is as follows:
therein Ψe、Ψ′e、c1And lambda is the passive behavior related energy, the passive energy change rate, the material coefficient and the whole deformation of the transverse bridge respectively;
the energy scaling function for the transverse bridge connection is:
wherein N is,
λaXi is respectively the transverse bridge connection overlapping coefficient, the optimum cross coefficient of actin and myosin, the deformation caused by the slippage of the myofilament and the function bandwidth;
the elastic energy equation of the transverse bridge is as follows:
therein Ψa、E1、E2、s3、s4、λeRespectively including transverse bridge connection elastic energy, actin material constant, myosin material constant, transverse bridge connection front stroke state rigidity coefficient, transverse bridge connection rear stroke state rigidity coefficient and transverse bridge elastic deformation;
the skeletal muscle fiber-to-fiber slip rate equation is:
wherein
f1、f2、s3、s4、μ、E1、E2、λe、λa、
Xi is the slip rate between muscle fibers, a material constant, a rigidity coefficient of a transverse bridge connection front stroke state, a rigidity coefficient of a transverse bridge connection rear stroke state, a material constant, an actin material constant, a myosin material constant, a transverse bridge elastic deformation, a deformation caused by the slippage of muscle filaments, an optimal cross coefficient of actin and myosin and a function bandwidth respectively;
the skeletal muscle total stress shows the equation:
wherein F, Ψe、Ψa、λ、λa、λeAnd N is skeletal muscle stress, passive behavior related energy, transverse bridge connection elastic energy, total deformation of transverse bridge connection, deformation caused by muscle wire slippage, transverse bridge elastic deformation and energy scaling coefficient of transverse bridge connection.
Claims (4)
1. A skeletal muscle multi-scale model modeling method based on a sarcoplasmic reticulum environment is characterized by comprising the following steps:
the method comprises the following steps: establishing a human skeletal muscle cell transverse bridge kinetic model based on an actual microscopic mechanism and an operation mechanism of human muscle cells;
step two: establishing a human skeletal muscle intracellular phosphate reaction model based on the dynamic analysis of a human muscle intracellular metabolic byproduct phosphate;
step three: and establishing a muscle thermodynamic model based on the energy conservation rule of muscle cells and whole muscles in the contraction process.
2. The method for modeling the skeletal muscle multi-scale model based on the sarcoplasmic reticulum environment as recited in claim 1, wherein the specific process of the human skeletal muscle cell cross bridge kinetic model is as follows:
the equilibrium equation of the four-state cycle process of the transverse bridge model is
Roff(t)+D(t)+A1(t)+A2(t)＝1 (1)
Wherein R isoff、D、A1、A2T is respectively a transverse bridge circulation separation state, a transverse bridge circulation pre-connection state, a transverse bridge circulation front stroke, a transverse bridge circulation rear stroke and time;
the balance equation of the horizontal bridge in the circulating pre-connection state is
Wherein D, f', f, kon、koff、A1、A2G is a transverse bridge circulating pre-connection state, a speed coefficient from a pre-connection state to a front stroke, a speed coefficient from a front stroke to a pre-connection state, a speed coefficient from a separation state to a pre-connection state, a speed coefficient from a pre-connection state to a separation state, a transverse bridge circulating front stroke, a transverse bridge circulating back stroke and a speed coefficient from a back stroke to a pre-connection state respectively;
the balance equation of the front stroke of the transverse bridge circulation is
D, A therein1、A2F, f ', h and h' are respectively a transverse bridge circulation pre-connection state, a transverse bridge circulation front stroke, a transverse bridge circulation rear stroke, a speed coefficient from a pre-connection state to a front stroke, a speed coefficient from a front stroke to a pre-connection state, a speed coefficient from a front stroke to a rear stroke and a speed coefficient from a rear stroke to a front stroke;
the balance equation of the transverse bridge cycle back stroke is
Wherein A is1、A2H, h' and g are respectively a transverse bridge cycle front stroke, a transverse bridge cycle rear stroke, a front stroke to rear stroke rate coefficient, a rear stroke to front stroke rate coefficient and a rear stroke to pre-connection state rate coefficient;
the open-close coefficient equation of the transverse bridge connection is
Wherein k ison、
koff、
[Ca2+]、
p、pm、pn、pc、pS、pSR、pSR CT is a transverse bridge opening coefficient, an opening coefficient under no calcium ion stimulation, an opening coefficient under calcium ion stimulation, a transverse bridge separation coefficient, a current calcium ion concentration, a calcium ion concentration when the maximum force is generated by 50%, a balance coefficient of phosphate in sarcoplasmic reticulum, a balance coefficient of phosphate and calcium ion precipitation in sarcoplasmic reticulum, a concentration of phosphate and calcium ion precipitation in sarcoplasmic reticulum, and time;
the rate equation of the pre-connection state from the front stroke to the transverse bridge based on the muscle wire separation and synergistic effect is
Wherein f, f0、x0、x1、x2V is a velocity coefficient from a pre-connection state to a front stroke, a constant coefficient related to the front stroke, an average deformation amount caused by a power stroke, an average elastic deformation amount caused by the front stroke, an average elastic deformation amount caused by a rear stroke and an adjacent transverse bridge influence coefficient respectively;
the separation ratio equation caused by myofilament deformation is
Wherein g is0、g、x0、x2Rho is a separation rate constant coefficient, an irreversible separation rate coefficient, an average deformation caused by a power stroke, an average elastic deformation caused by a rear stroke and a deformation influence level respectively;
the elastic deformation equation of muscle fiber caused by the front stroke and the back stroke during unequal length contraction is
D, A therein1、A2、h′、x0、x1、x2、
The system is respectively in a transverse bridge circulating pre-connection state, a transverse bridge circulating front stroke, a transverse bridge circulating back stroke, a speed coefficient from a back stroke to a front stroke, an average deformation caused by a power stroke, an average elastic deformation caused by a front stroke, an average elastic deformation caused by a back stroke and a relative sliding speed between thick and thin muscle wires;
based on the microstructure and the operation mechanism of human muscle fibers, the microscopic state equation of the cross-bridge connection is solved through the expression of the connection state of the cross-bridge and the state relation of each state.
3. The method for modeling the skeletal muscle multi-scale model based on the sarcoplasmic reticulum environment as recited in claim 1, wherein the specific process of the human skeletal muscle intracellular phosphate reaction model is as follows:
the equation for the concentration of phosphate in muscle slurry is
Wherein b isp、h0、hp、kp、A1、A2、PS、PSR、V2Respectively the degradation rate of phosphate in the muscle pulp, the forward speed of the power stroke, the reverse power stroke speed, the transportation speed of phosphate in the muscle pulp into SR, the front stroke of the transverse bridge cycle, the back stroke of the transverse bridge cycle, and the phosphate in the muscle pulpConcentration, concentration of phosphate in the sarcoplasmic reticulum, volume of sarcoplasmic acid removed from the final pond;
the equation for phosphate concentration in sarcoplasmic reticulum is
Wherein k isP、P、PSR、
Bp、
PP、
The transport rate of the sarcoplasmic phosphate entering the SR, the concentration of the phosphate in the sarcoplasmic net, the volume of the sarcoplasmic net for removing the final pond, the phosphate precipitation dissolution rate, the concentration of the phosphate and calcium ions in the sarcoplasmic net, the phosphoric acid solubility product and the concentration of the calcium ions in the sarcoplasmic net are respectively;
the equation for the concentration of phosphate and calcium ion deposits in the sarcoplasmic reticulum is
Wherein A isP、PSR、
PP、BP、
The phosphate precipitation rate, the phosphate concentration in the sarcoplasmic reticulum, the calcium ion concentration in the sarcoplasmic reticulum, the phosphoric acid solubility product, the phosphate precipitation dissolution rate, and the phosphate and calcium ion precipitation concentration in the sarcoplasmic reticulum are respectively.
4. The method for modeling the skeletal muscle multi-scale model based on the sarcoplasmic reticulum environment as recited in claim 1, wherein the specific process from the microstructure of the muscle fiber to the thermodynamic model of the macroscopic muscle is as follows:
according to the principle of virtual work, the skeletal muscle energy equation is derived as
Wherein p is,
F、Fa、FCa、
The power of the macroscopic work done by the muscle, the integral deformation rate coefficient of the transverse bridge, the deformation rate coefficient caused by the slippage of the muscle wire, the stress related to the integral deformation of the transverse bridge, the stress related to the deformation caused by the slippage of the muscle wire, the stress related to the concentration of calcium ions and the change rate coefficient of the concentration of calcium ions are respectively;
the micro energy expression equation of muscle fiber is
Ψ＝Ψ(λ,λa,s,β) (15)
Where Ψ, λaS and beta are respectively the microcosmically related internal energy of muscle fiber, the integral deformation of a transverse bridge, the deformation caused by muscle fiber slippage, an internal state function and the calcium ion concentration;
the Clausius-Planck inequality equation neglecting the effect of thermal effects is
Wherein
p is divided intoThe micro acting power of muscle fiber and the macro acting power of muscle are distinguished;
the inequality equation of the change of the internal state of the muscle fiber is obtained by substituting the formula (16) with the formula (14) and the formula (15):
wherein F, Ψ, λ, Fa、λa、si、FCaBeta is stress related to the integral deformation of the transverse bridge, internal energy related to the microcosmic muscle fiber, integral deformation of the transverse bridge, stress related to the deformation caused by the slippage of the muscle wire, the ith transverse bridge state variable, stress related to the concentration of calcium ions and the concentration of the calcium ions respectively;
the skeletal muscle total strain energy equation is:
Ψ＝Ψe(λ)N(λa)Ψa(λe,si)+ΨXB(si)+Ψc(β) (18)
wherein Ψ, Ψe、Ψa、λ、ΨXB、Ψc、N、λa、λe、siBeta is respectively internal energy microcosmically related to muscle fibers, energy related to passive behavior, elastic energy of connection of a transverse bridge, integral deformation of the transverse bridge, chemical energy related to movement of the transverse bridge, calcium concentration related energy, elastic energy related coefficient of the transverse bridge, deformation caused by muscle fiber slippage, elastic deformation of the transverse bridge, ith transverse bridge state variable and calcium ion concentration;
the muscle passive state one-dimensional energy expression equation is as follows:
therein Ψe、Ψ′e、c1And lambda is the passive behavior related energy, the passive energy change rate, the material coefficient and the whole deformation of the transverse bridge respectively;
the energy scaling function for the transverse bridge connection is:
wherein N is,
λaXi is respectively the transverse bridge connection overlapping coefficient, the optimum cross coefficient of actin and myosin, the deformation caused by the slippage of the myofilament and the function bandwidth;
the elastic energy equation of the transverse bridge is as follows:
therein Ψa、E1、E2、s3、s4、λeRespectively including transverse bridge connection elastic energy, actin material constant, myosin material constant, transverse bridge connection front stroke state rigidity coefficient, transverse bridge connection rear stroke state rigidity coefficient and transverse bridge elastic deformation;
the skeletal muscle fiber-to-fiber slip rate equation is:
wherein
f1、f2、s3、s4、μ、E1、E2、λe、λa、
Xi is the slip rate between muscle fibers, material constant, rigidity coefficient of transverse bridge connected front stroke state, rigidity coefficient of transverse bridge connected back stroke state, materialConstant, actin material constant, myosin material constant, transverse bridge elastic deformation, deformation caused by myofilament sliding, optimal cross coefficient of actin and myosin and function bandwidth;
the skeletal muscle total stress shows the equation:
wherein F, Ψe、Ψa、λ、λa、λeAnd N is skeletal muscle stress, passive behavior related energy, transverse bridge connection elastic energy, total deformation of transverse bridge connection, deformation caused by muscle wire slippage, transverse bridge elastic deformation and energy scaling coefficient of transverse bridge connection.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20160055276A1 (en) * | 2014-08-19 | 2016-02-25 | Daegu Gyeongbuk Institute Of Science And Technology | Modeling System and Method for Muscle Cell Activation |
| CN106202739A (en) * | 2016-07-14 | 2016-12-07 | 哈尔滨理工大学 | A kind of skeletal muscle mechanical behavior multi-scale Modeling method |
| CN107330275A (en) * | 2017-06-30 | 2017-11-07 | 哈尔滨理工大学 | A kind of modeling method to skeletal muscle fast muscle fiber excitation-contraction process |
| CN107609338A (en) * | 2017-10-24 | 2018-01-19 | 哈尔滨理工大学 | A kind of Skeletal Muscle Contraction model based on metabolism physiology |
| CN108629074A (en) * | 2018-03-15 | 2018-10-09 | 哈尔滨理工大学 | A kind of finite element model of skeletal muscle muscle bundle |
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