KR101741580B1 - simulation method and device for diagnosing cardiac arrhythmia based on genetic mutation - Google Patents

Abstract

The cardiac simulation method includes a step of calculating the voltage change of single cardiac muscle cells due to the inflow and outflow of bio-ions using Equation (1), and a step of calculating a voltage of the heart, which is defined as a set of two successive regions within the cell and interstitial The ion currents in each region flow from one region to another region through the cell membrane and calculate (Equation 2) based on the current conservation law in which the current flowing out of the cell interior space flows into the interstitial region, Calculating a spatial current per volume through Equation (3), calculating a cell membrane current through Equation (4), and using a reaction-diffusion equation for cell membrane potential (Equation 5) Calculating a heart electrical conduction, applying a Galerkin method to Equation (5), using Euler forward difference method for a time term, calculating a grid point by using a finite element method, Deriving for the <Equation 6> simultaneous algebraic equations for the state value to a variable in the <Equation 1> of I _Na, I _CaL, I _to, I _Kr, I _K, I _K1, I _NaCa, I _{NaK ,} I _pCa I _{pK ,} I _{bCa ,} I _bK And replacing the selected one or plurality of currents with a mathematical model of each mutant ion channel calculated in advance by mutation of myocardial cells.

Description

Technical Field [0001] The present invention relates to a method and a device for cardiac simulation based on genetic mutation and a device for diagnosing cardiac arrhythmia based on genetic mutation.

The present invention relates to a cardiac simulation method and apparatus, and more particularly, to a cardiac simulation method and apparatus that mathematically models ion channel changes caused by abnormal activity of a protein due to a gene mutation.

The cell membrane of myocardial cells surrounds the intracellular organelles and has a structure in which a sparse protein is embedded in the phospholipid. Through this cell membrane, various substances come into the cell, and some of them have charged ions. Ions do not go directly into and out of the cell membrane, but they come in and out through the membrane proteins. The protein is called a channel protein, and the ion channel through the channel protein is called an ion channel. The ion channel is divided into Na ⁺ channel, Ca ²⁺ channel, K ⁺ channel and Cl ^- channel depending on the type of ions passing through. Because of the simultaneous action of these ion channels on the cell walls, the concentration difference (electrochemical potential difference) of ions is formed through the cell membrane, the cell action potential due to ion migration is generated and transmitted, and the contraction / relaxation mechanism It causes.

The contraction of myocardial cells is closely related to the intracellular calcium concentration of action potential (AP). In other words, depolarization of cell membrane potential due to the action of action potential occurs, resulting in the opening of the calcium ion channel in the T-tubule (one of the myocardial organelles). In this way, when a small amount of calcium ions are introduced into the cytoplasm, the sarcoplasmic recti (SR), which is a reservoir of intracellular calcium, induces a release of calcium (CICR, calcium induce calcium release) necessary for actual shrinkage. As the intracellular calcium concentration increases, calcium binds to troponin C, allowing the cross-bridge of myosin (thick filament) to attach to actin (thinfilament). This is followed by the contraction of the cross-bridge in the presence of ATP (adenosine triphosphate), which is the driving force of the force generation. When the action potential is terminated, the intracellular calcium is returned to the inside of the SR mainly by the SR calcium pump, and some of it is released to the outside of the cell by the Na / Ca exchange mechanism of the cell membrane.

On the other hand, the proteins constituting the ion channel may cause abnormal functions such as gain-of-function and loss-of-function due to gene mutation, It is one of the causes of heart disease. However, the mechanism by which these arrhythmias are expressed due to these mutations is not clearly understood, and thus there are limitations in the methods of treating cardiac arrhythmias until now.

1 is a diagram showing a conventional cardiac simulation method.

Referring to FIG. 1, a conventional cardiac simulation method performs a simulation for a single cell, a two-dimensional and a three-dimensional model, respectively.

In addition, the conventional cardiac simulation method is inconvenient to perform individual analysis and analysis because it is a method of individually inputting mutation conditions in a single cell, a two-dimensional and a three-dimensional model even when a simulation for a mutation is performed do.

Disclosure of the Invention The present invention has been proposed in order to solve the above-mentioned technical problems, and it is an object of the present invention to provide a method and an apparatus for correcting an abnormal activity of a protein due to mutation of each gene, A heart simulation method and apparatus capable of detecting an arrhythmia generated by a heart.

The present invention also provides a cardiac simulation method and apparatus capable of integrally simulating a single cell, a two-dimensional, and a three-dimensional model all at once, and performing an integrated analysis and analysis by only changing a single parameter input.

According to an embodiment of the present invention, there is provided a method for controlling a blood vessel, comprising: calculating a voltage change of single myocardial cells due to inflow and outflow of bio-ions using Equation (1); Ionic currents in each region of the heart, defined as a set of interstitial and interstitial regions, flow from one region to another through the cell membrane, and the current flowing out of the cell's interior space is the interstitial region Computing Equation (2) based on the current conservation law, computing a spatial current per volume through Equation (3), and calculating a cell current through Equation (4); Calculating heart conduction using Equation (5), which is a reaction-diffusion equation for cell membrane potential; The Galerkin method is applied to Equation (5) using the finite element method, and the Euler forward difference method for the time term is used to calculate the algebraic algebraic equation of the state value at the mesh points as a variable, Deriving Equation (6); And I _{Na ,} I _CaL, I _to, I _{Kr ,} I _{K ,} I _{K1 ,} I _{NaCa ,} I _{NaK ,} I _pCa I _{pK ,} I _{b C a ,} I b _K And replacing the selected one or plurality of currents with a mathematical model of each mutant ion channel previously calculated by mutation of myocardial cells.

&Quot; (1) &quot;

C _m is the electrical capacitance of the cell membrane per unit cell, V _m is the voltage of the cell, I _ion is the total bio-ion current flowing into the cell, and I _stim is the flow of perturbation current to induce excitation of the cell. (I _ion changes depending on cell model and channel type.)

I _Na is the fast inward Na + current, I _Kl is inward rectifier K ⁺ current, I _to the transient outward K ⁺ current, I _Kur is ultrarapid delayed rectifier K ⁺ current, I _Kr is rapid delayed rectifier K ⁺ current, I _Ks is ^{slow delayed rectifier K + current, I} Ca, L is ^{L-type inward Ca 2+ current,} I NaCa is ^{Na + / Ca 2+ exchanger current,} I NaK is ^{Na + / K + pump current,} I p, Ca is plateau current, and I _{b, Na} and I _{b, Ca} represent background Na ⁺ and Ca ²⁺ currents, respectively.

&Quot; (2) &quot;

where x is the spatial coordinate vector, J is the current density per unit area, and subscripts i and e denote intracellular space and interstitial space, respectively.

&Quot; (3) &quot;

I _v ( x , t) is the spatial current per unit volume, φ is the electric potential, and M ( x ) for the volume conductor is the 3 × 3 electric conduction tensor.

&Quot; (4) &quot;

I _m (x, t) is the plasma membrane currents, and is C _m is the capacitance per unit surface area membranes, I _app (x, t) is given stimulation current applied per unit area, V (x, t) is φ _i - φ _e , and I _ion ( x , t) is the sum of ion currents per unit area, which depends on the channel type. Information on ion currents and related constants is based on the above-described single myocardial cell model .

Equation (5)

And I _app (x, t) is given stimulation current applied per unit area, V (x, t) is φ _i - a cell membrane potential which is defined as _{φ e, I ion (x,} t) is a sum of the per unit area of the ion current The information about ion currents and related constants is based on the single cardiomyocyte model described above, β is the area ratio to volume, and k is anisotropic, which expresses the difference in physical properties with respect to the direction of the muscle fiber .

&Quot; (6) &quot;

K is a stiffness matrix, X is a variable value vector at each lattice point, R is an external force term, and a solution according to each time is obtained using the Newton-Raphson method.

Also, the step of simulating replacing the previously calculated mutant ion channel with a mathematical model can be used for the mutation of L532P and N588K, which cause mutation of KCNH2 gene (7), which is a mathematical expression model of an ion channel of I _Kr , to simulate the action potential of the mutant myocardial cells and the current per ion channel.

&Quot; (7) &quot;

I _{K, r} is the rapid delayed outward rectifier K + current is, x _r1 and x _r2 are each activation, inactivation gating variable, α _{x_ r1} and β _{x_ r1} is a forward, backward rate constant for gating varialbe respectively, τ _{x_ r2} is time constant for gating variable, P ₁ ~ P ₁₁ is an experimental value for WT and MT (N588K, L532P).

According to another embodiment of the present invention, there is provided a cardiac simulation apparatus for displaying an action potential calculated using a cardiac simulation method and a conductive pattern thereof in a two-dimensional or three-dimensional image based on a change in time and space.

A cardiac simulation method and apparatus according to an embodiment of the present invention proposes a single cell model capable of simulating the action potential of myocardial cells including the function of an ion channel, and based thereon, a two-dimensional cell tissue We propose a model. In addition, we propose a 3 - D cardiac simulator based on a medical image - based 3D cardiac model.

In addition, a simulation method and apparatus for predicting the occurrence of cardiac arrhythmia caused by abnormal function of the ion channel of myocardial cell due to gene mutation is proposed, and the correlation between the cardiac arrhythmia and myocardial cell gene mutation is analyzed, It can help to find a way to treat.

In addition, the cardiac simulation method and apparatus are proposed to easily change the characteristics of the cell into the parameter input method, and it is possible to reproduce the characteristic conditions of the existing myocardial cells according to various heart diseases. In particular, In order to simulate the function, it is proposed to substitute the functionalized ion channel condition and to simulate and analyze the action potential generation of each single myocardial cell and the current of each ion channel. Simulation results show that cardiac activity potential and contraction phenomenon can be visualized through data post-processing. That is, in the cardiac simulation method and apparatus according to the embodiment of the present invention, a single cell, a two-dimensional and a three-dimensional model can be integrally simulated at one time and integrated analysis and analysis can be performed by only changing one parameter input.

That is, the cardiac simulation method and apparatus proposed in the embodiment of the present invention can be helpful in studying the mechanism of the cardiac arrhythmogenesis. In addition, clinical trials for therapeutic drug development and toxicity identification can be substituted. In addition, patient-assisted arrhythmia diagnosis assistance can be performed.

1 shows a conventional cardiac simulation method;
Figure 2 illustrates a cardiac simulation method in accordance with an embodiment of the present invention.
3 is a graph showing the effect of a cell model.
Figure 4 shows the spiral wave activity and action potential shape in a two-dimensional tissue model.
FIG. 5 shows the spiral wave activity and action potential shape in a three-dimensional left atrial model.
Figure 6 is a graph depicting a vulnerability.
FIG. 7 is a graph showing the effect of the L532P and N588K gene mutations A graph showing the results of applying the ion channel model of I _Kr to a single myocardial cell model.
8 is a diagram showing the action potentials of epicardium, Mid myocardium, and endocardium of ventricular cells.
9 is a graph showing the action potential of atrial cells.
FIG. 10 is a diagram showing the form of ion currents for each ion channel with respect to the action potential in a steady state, and the form of a specific ion current according to an abnormal action potential. FIG.
Figure 11 is a cardiac two-dimensional tissue model simulation plot for KCNQ1 G229D mutation.
FIG. 12 is a three-dimensional simulation drawing of an atrium (left) and a ventricle (right) of a ventricular fibrillation (VF) pathology model.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings, in order to facilitate a person skilled in the art to easily carry out the technical idea of the present invention.

2 is a diagram illustrating a cardiac simulation method according to an embodiment of the present invention.

Referring to FIG. 2, a cardiac simulation method and apparatus according to an embodiment of the present invention can integrally simulate a single cell, a two-dimensional and a three-dimensional model at a time, and perform an integrated analysis and analysis.

The heart simulation method and apparatus according to the embodiment of the present invention will be described in detail as follows. The present embodiment mainly describes a heart simulation method and apparatus capable of integrally simulating a single cell, a two-dimensional and a three-dimensional model at a time by changing the parameter inputs of the L532P and N588K mutations causing the mutation of the KCNH2 gene do. Of course, it is possible to simulate single cells, two-dimensional and three-dimensional models of different gene mutations at once by changing parameter inputs.

The function of myocardial cells is electrical excitation and mechanical contraction, which are closely related to each other. In order to simulate the electrical excitation of cells, we need a model for the influx of biological ions (Na ⁺ , K ⁺ , Ca ^{2 +} , Cl ^-, etc.) and cell voltage change.

When the biomolecules having electricity are introduced into the cell or out of the cell, the voltage in the cell changes, and an equation for describing the same is described in Equation (1). That is, a step of calculating the voltage change of single myocardial cell due to the inflow and outflow of bio-ions using Equation (1) can be performed.

&Quot; (1) &quot;

C _m is the electrical capacitance of the cell membrane per unit cell, V _m is the cell voltage, I _ion is the total bio-ion current flowing into the cell, and Istim is the inflow of perturbation current to induce cell excitation. I _ion varies slightly depending on the cell model and channel type.

In the present embodiment, the human atrium cell model was the Courtemanche-Ramirez-Nattel model, and the atrial _ion of the atrial cell Is derived as shown in Equation (1).

I _Na in formula (1) is the fast inward Na + current, I _Kl is inward rectifier K ⁺ current, I _to the transient outward K ⁺ current, I _Kur is ultrarapid delayed rectifier K ⁺ current, I _Kr is rapid delayed rectifier K ⁺ current , I _Ks is ^{slow delayed rectifier K + current, I} Ca, L is ^{L-type inward Ca 2+ current,} I NaCa is ^{Na + / Ca 2+ exchanger current,} I NaK is ^{Na + / K + pump current,} I p _{, Ca} is plateau current, and I _{b, Na} and I _{b, Ca} represent background Na ⁺ and Ca ²⁺ currents, respectively.

Given an input condition of stimulation current (I _stim ) for a cell in Equation (1), a temporal change in voltage and calcium concentration can be obtained as an output.

For reference, when a gene mutation of an ion channel protein is caused, the formula of one of the ion channels of Equation (1) is changed to cause a change in the whole cell activity potential. The ion currents of the respective channels are changed, and the depolarization amplitude of the cell action potential is shortened or the duration of the plateau is shortened, thereby changing the action potential and electrical characteristics of the whole cell model.

Next, electrical conduction of the atria and ventricles is generally interpreted as a bidomain method model. Cardiac tissue is spatially divided into two continuous areas, intracellular and interstitial. Each region behaves as if it is a volumetric conductor with a specific volume average galvanic field, current and electric conduction tensor. Ionic currents can flow from one region to another through the cell membrane and induce an expression for the dual region from the current retention that all currents leaving the intracellular space must enter the interstitial region. In other words, ionic currents in each region of the heart, defined as a set of interstitial and interstitial regions, flow from one region to another through the cell membrane, The equation (2) can be calculated based on the current conservation law that flows into the region.

&Quot; (2) &quot;

where x is the spatial coordinate vector, J is the current density per unit area, and subscripts i and e represent intracellular space and interstitial space, respectively. Also, the step of computing the cell current through Equation (3) can be performed by calculating the spatial current per volume through Equation (3).

&Quot; (3) &quot;

I _v (x, t) is the spatial current per unit volume, φ is the electric potential, and M (x) for the volume conductor is the electric conduction tensor of 3 × 3.

&Quot; (4) &quot;

I _m (x, t) is the plasma membrane currents, and is C _m is the capacitance per unit surface area membranes, I _app (x, t) is given stimulation current applied per unit area, V (x, t) is φ _i - φ _e , and I _ion (x, t) is the sum of ion currents per unit area, which depends on the channel type, and information on ion currents and related constants is based on the above-described single myocardial cell model .

Next, the electrical conduction in the heart is finally induced into a reaction-diffusion equation for the cell membrane potential as shown in Equation (5). That is, a step of calculating the cardiac conduction can be performed using Equation (5), which is a reaction-diffusion equation for the cell membrane potential.

Equation (5)

And I _app (x, t) is given stimulation current applied per unit area, V (x, t) is φ _i - a cell membrane potential which is defined as _{φ e, I ion (x,} t) is a sum of the per unit area of the ion current Depending on the channel type, information on ion currents and related constants is based on the single-myocardial cell model described above. β is the area ratio with respect to the volume, and k is anisotropy expressing the difference of the physical properties according to the direction of the muscle fiber.

Next, using the finite element method to solve Equation (5), applying the Galerkin method to Equation (5), and using Euler forward difference method for the time term, Algebraic algebraic equations with state values at mesh points as variables are derived. That is, the Galerkin method is applied to Equation (5) using the finite element method, and the Euler forward difference method for the time term is used to calculate the Algebraic Algebraic Equation using state values at the mesh points as variables The step of deriving Equation (6) can be performed.

&Quot; (6) &quot;

K is a stiffness matrix, X is a vector of variable values at each grid point, and R is an external force term. The solution is obtained by using the Newton-Raphson method.

Finally, the functions of each of the mutant ion channels of the myocardial cells derived from the patch-clamp experiments and the experimental literature of myocardial cells are implemented as a mathematical model. After replacing or further implanting the implemented mathematical model into the normal ion channel model of the normal single myocardial cell model, the cell conditions required for the simulation are entered into the parameter configuration file. That is, one or a plurality of currents selected from among I _Na, I _CaL, I _to, I _Kr, I _K, I _K1, I _NaCa, I _NaK, I _pCa I _pK, I _{bCa and} I _bK of _Equation A step of simulating the substitution of a mathematical model of a previously calculated mutant ion channel by the mutation of myocardial cells can be performed.

That is, the step of replacing the previously calculated mutant ion channel with the mathematical model of the mutant ion channel,

For example, for L532P and N588K mutations causing mutations in the KCNH2 gene The substitution of Equation (7) for the ion channel of I _Kr can simulate the action potential of the mutant myocardial cells and the current for each ion channel, and simulate single myocardial cells for the modified conditions to obtain mutant myocardial cells The action potential and the current for each ion channel can be observed and analyzed.

&Quot; (7) &quot;

In Equation 7, I _Kr is a rapid delayed outward rectifier K + current, and x _r1 and x _r2 are activation and inactivation gating variables, respectively. α and β _{x_ x_} is _{r1 r1} is forward, backward rate constant for gating varialbe respectively, τ is the time constant for gating _{x_ r2} variable. P ₁ ~ P ₁₁ is an experimental value for WT and MT (N588K, L532P).

The simulation of the mutations of L532P and N588K that cause KCNH2 gene mutation will be described in more detail as follows.

Atrial arrhythmia is a typical cardiac disorder caused by abnormal electrical signaling and transmission, which can lead to atrial fibrillation leading to death. Among these causes, it is known that the myocardial repolarization disorder occurs due to the genetic defect of the ion channel. Gene mutations associated with arrhythmia have been identified by several studies, including mutations in the KCNH2 gene, one of the most common genetic disorders. This mutation is an arrhythmia-related genetic disorder that causes an abnormal QT interval by inhibiting the rapid delayed rectifier potassium channel (I _Kr ).

The cardiac simulation method and apparatus according to the embodiment of the present invention can verify the correlation that the KCNH2 gene mutation causes atrial arrhythmia. To this end, two-dimensional and three-dimensional simulations are performed after N588K and L532P mutations are applied to the CRN cell model, and the electrical conduction patterns of wild-type (WT) and mutant-type (MT) are compared. As a result of the pattern comparison, the conduction waveform of MT is self-terminated by early self-termination of WT, and the irregular wave is generated (L532P) because the conduction waveform maintains reentrant wave (N588K) or spiral break-up occurs. Thus, through the cardiac simulation method and apparatus according to the embodiment of the present invention, it was confirmed that KCNH2 gene mutation increases the vulnerability of atrial tissue and becomes a factor of arrhythmia.

Arrhythmia, on the other hand, refers to abnormal rhythm of heart rhythm when the synchrony between myocardial cells is broken. When arrhythmia persists, excitation and contraction occur at each tissue site, leading to death because the blood can not be ejected effectively. Arrhythmia is largely due to a variety of causes and types, including disturbances in electrical signal conduction systems, arrhythmias due to heart failure, secondary arrhythmias caused by systemic diseases, and arrhythmias due to gene abnormalities.

The KCNH2 gene mutation is the first gene to be mutated from SQTS patients and functions to encode the alpha-subunit of I _Kr responsible for the entry and exit of potassium ions in myocardial cells. This gene plays a role in regulating the change in activity voltage in heart and nervous tissue, and is known to affect heart rate as an important factor in cardiac repolarization. The mechanism of KCNH2 mutation is N588K and N532P mutations. N588K is a focal-associated gain-of-function mutation in which the negatively charged asparagine (N) of Residue N588 at the outer entrance of the KCNH2 channel subunit (S5) is replaced by positively charged lysine (K). And L532P is a mutation in which the leucine (L) of Residue L532 located in the voltage sensor (S4) of the KCNH2 channel is replaced with proline (P). Changes in the KCNH2 ion channel caused by these mutations cause cardiac-acute acute sudden death resulting in abnormal QT intervals on the electrocardiogram. Therefore, it is very important to clarify the connection with cardiac arrhythmia through many experiments related to KCNH2 ion channel. Experimental measurement of KCNH2 ion channel has a disadvantage that it takes a lot of time and cost.

Therefore, in this embodiment, the change of atrial conduction pattern due to KCNH2 ion channel mutation was applied to a three-dimensional atrium model as well as a cell model and a two-dimensional tissue model, and the results were analyzed. The three-dimensional atrium geometry was modeled with only the left atrium (LA). The reason for this is that AF has a clinical viewpoint as LA disease because the efective refractory period (ERP) of general LA is shorter than the ERP of right atrium (RA) and AF driver is mostly present in LA. Thus, in this example, the I _Kr mutation experiment values measured in the previous study were applied to the CRN cell model, and the N588K and L532P mutation models were constructed and applied to the three-dimensional finite element LA model. The effect of KCNH2 ion channel variation on proarrhythmic was analyzed by comparing the difference between WT and MT of action potential duration (APD), restitution curve and vulnerable window.

_To I, I _CaL, I _Kur sikimyeo current decreases, respectively 80%, 30%, 90% and increasing the I _Kr 50% through which AF action potential is earned a result similar to the clinical. Therefore, in this embodiment, the CRN cell model is modified to simulate the actual AF action potential to be implemented in the 3D left atrial model.

I _Kr was modified to the CRN model in order to implement the changes I _Kr caused by a gene mutation. For this, the maximal I _Kr conductance, activation and inactivation gate value, and α-subunit and β-subunit value of the CRN model were substituted for the measured gene mutation experiments. The L532P mutation was applied to the Xenopus laevis oocyte by double-electrode voltage-clamp and the N588K mutation was applied to the Chinese hamster ovary cell measured at 37 ° C at room temperature. The CRN model using the N588K and L532P gene mutations in I _Kr is as follows.

In this example, a KCNH2 mutation simulation was performed using an electrophysiologic three-dimensional atrial model. To this end, the CRN cell model was modified into two aspects. The first modified ion currents were applied to the cell model, and second, the N588K and L532P mutation clinical data were assigned to the cell model. This modified cell model was reproduced and validated for cell model and tissue model studies, and then applied to anatomic left atrial model to observe KCNH2 mutation.

FIG. 3 is a graph showing the influence of a cell model, FIG. 4 is a spiral wave activity and action potential shape in a two-dimensional tissue model, FIG. 5 is a spiral wave activity and action potential shape in a 3D- Is a graph showing a vulnerability.

Referring to FIGS. 3 to 6, the effect of the modified CRN cell model can be confirmed through AP (FIG. 3 a) and I _Kr current (FIG. 3 b). First, the maximum amplitude of I _Kr current was higher than that of the original CRN model in the modified CRN model of the present embodiment, and occurred earlier than that of the original CRN model. These changes in I _Kr caused shortening of the APD and APD 50 and APD 90 were shorter than those of the modified CRN model. It was confirmed that the modified ion current shortened the APD of the CRN model. The fact that the APD is shortened is an important factor that induces the fibrillation phenomenon by increasing the vulnerability of the 2D and 3D models, which means that the modified CRN cell model is a model that causes the fibrillation more well than the existing cell model.

Results of applying the KCNH2 mutation in the cell model and N588K L532P mutation has been identified that is, speed when I _Kr current that reaches the highest increases the maximum amplitude. This change in I _Kr causes the repolarization to occur earlier, making the pleat of the AP shorter than normal and ultimately shortening the APD as a whole. This suggests that there is a relationship between KCNH2 mutation and SQTS, and it also provides a comprehensive description of the increase in tissue susceptibility that reentry occurs and sustains.

Analysis of the 2D tissue model and 3D left atrial model by applying the N588K and L532P mutations to the cell model revealed that the vulnerability was increased by the mutation effect. In the case of WT, the spiral wave is self-terminated due to a lack of sufficient space to activate within the tissue due to the thick wavelength. However, due to the influence of the N588K and L532P mutations, the MT is significantly shortened in wavelength, which allows the spiral wave to remain constant. In 2D and 3D tissue, the N588K-hERG SQT1 mutation has the effect of reducing the minimum substrate size at which reentry occurs and can be maintained. These results were confirmed by the N588K mutation effect in the present example, and in particular, the L532P mutation was found to have a wave break-up phenomenon after a lapse of time, resulting in a fading phenomenon in which irregular conduction is maintained. The impact of the KCNH2 mutation on the vulnerability of the LA model is also confirmed by the vulnerable graph of FIG. In the case of WT, reentrant waves were generated within the range of 40 ms, but in the case of MT, reentrant waves were generated within the range of 80 and 100 ms in the N588K and L532P mutations, respectively. This suggests that the effect of MT increases the vulnerability of the LA model and that the KCNH2 mutation is the cause of atrial fibrillation.

As a result, the 3D atrial model demonstrated that the KCNH2 gene mutation increased the vulnerability of the atria and that the reentrant wave was maintained constantly. In particular, the CRN modified cell model shows that the L532P gene mutation is a factor causing atrial fibrillation.

FIG. 7 is a graph showing the effect of the L532P and N588K gene mutations I _{Kr &} lt _{; /} RTI & gt _; is applied to a single myocardial cell model.

The first graph 11 shows the action potential change and the second graph 12 shows the current change of the ion channel of I _Kr . In the simulation results, the effectiveness of the simulation results is verified by comparing the action potential duration (APD) of the action potential and the current of the ion channel with the experimental results. Based on the validated simulation conditions, we performed two - dimensional myocardial tissue simulation to analyze the conduction patterns of the action potentials of the myocardial cells on the myocardial tissue model and to investigate the pattern of reentry wave generation and regeneration wave differentiation or extinction Analyze.

The regressive wave is an important factor for judging the arrhythmia in conduction of the action potential of the heart. The conduction pattern of the action potential is abnormal, and the action potential measured in the tissue in which the regenerative wave is observed is tachycardia This regressive wave breaks up under certain conditions into several small regressive waves, which are observed in the form of fibrillation.

Three-dimensional cardiac simulation was performed by implanting a single myocardial cell model into a three-dimensional node grid as in the case of a two-dimensional cell tissue model, and analyzing the action potential and its conduction pattern over time of the entire model To predict cardiac arrhythmias. That is, the cardiac simulation apparatus displays the action potential and its conduction pattern calculated using the cardiac simulation method described above as a two-dimensional or three-dimensional color image based on the change in time and space.

8 is a graph showing the action potentials of epicardium, Mid myocardium, and endocardium of ventricular cells. That is, the patch clamp experimental data and the action potential simulation results of the ventricular cell model are shown in comparison. 9 is a graph showing the action potential of atrial cells. That is, the patch clamp experimental data and the action potential simulation results of the atrial cell model are shown in comparison.

Referring to FIGS. 8 and 9, patch clamp experimental data of ventricular and atrial cells and results of cardiac simulation methods according to this embodiment are compared.

That is, in the patch clamp experiment, a fine pipette having an inside diameter of 0.5 to 3.0 μm is adhered to the cell membrane using a slight suction force, so that current flows only through the inside of the cell. At this time, the experimental conditions are set so that one or two or three ion channels are introduced into the micropipette through a lot of trial and error. After finishing this process, the flow of minute current through these ion channels can be recorded by using the amplifying device, so that the frequency of opening each ion channel and the amount of electricity passing through the ion channel can be measured. This patch clamp method can be used to track the activity of ion channels and to study various regulatory actions that affect their activity.

As shown in Figs. 8 and 9, the simulation data of the patch clamp method and the simulation result of the cardiac simulation method according to the embodiment of the present invention are almost the same, so that the simulation reliability is secured.

FIG. 10 is a diagram showing the form of ion current according to each ion channel with respect to the action potential in the steady state and the form of the specific ion current according to the abnormal action potential.

1 shows a normal form of the ion currents I _Na, I _CaL, I _to, I _cl, I _kur, I _Kr, I _Ks, I _K1, I _{f and} I _NCX , ) Represents an abnormal shape of the I _CaL ion current, and the third drawing (15) represents the Incx It is an abnormal form of ion current.

In other words, by studying the mathematical modeling of changes in ion channels caused by abnormal activity of proteins due to gene mutations, it is possible to study cardiac abnormalities such as arrhythmia.

FIG. 11 shows the results of a cardiac two-dimensional tissue model simulation for the KCNQ1 G229D mutation, and it is possible to observe the differentiation of the regressive wave and the regenerative wave caused by the change of the specific ion channel.

Figure 12 shows the results of three-dimensional simulations of atrial (left) and ventricular (right) ventricular fibrillation (VF) pathology models.

The cardiac simulation apparatus displays the action potentials and their conduction patterns calculated using the above-described cardiac simulation method as two-dimensional or three-dimensional images based on the change of time and space, and detects abnormalities of the heart caused by genetic mutation Can be studied.

In the above-described embodiment, a heart simulation method and apparatus capable of integrally simulating a single cell, a two-dimensional, and a three-dimensional model at a time by only changing the parameter inputs of the L532P and N588K mutations causing the KCNH2 gene mutation .

However, the method and apparatus for cardiac simulation according to the embodiment of the present invention are not limited to mutation of KCNH2 gene but various gene mutation models such as KCNQ1 V241F and KCNQ1 G229D can be implanted in the heart simulator, The mutation model can be selected and the arrhythmia result can be derived after setting the simulation condition through the parameter input. In other words, the ion channels of the ventricles or atrial cells have their respective formulas, and the sum of these ion channels shows electrical characteristics such as the action potential of the cells. Therefore, it is possible to integrally simulate a single cell, a two-dimensional and a three-dimensional model for a corresponding mutation at once by substituting the previously calculated mathematical model of each mutant ion channel.

A cardiac simulation method and apparatus according to an embodiment of the present invention proposes a single cell model capable of simulating the action potential of myocardial cells including the function of an ion channel, and based thereon, a two-dimensional cell tissue We propose a model. In addition, we propose a 3 - D cardiac simulator based on a medical image - based 3D cardiac model.

In addition, a simulation method and apparatus for predicting the occurrence of cardiac arrhythmia caused by abnormal function of the ion channel of myocardial cell due to gene mutation is proposed, and the correlation between the cardiac arrhythmia and myocardial cell gene mutation is analyzed, It can help to find a way to treat.

In addition, the cardiac simulation method and apparatus are proposed to easily change the characteristics of the cell into the parameter input method, and it is possible to reproduce the characteristic conditions of the existing myocardial cells according to various heart diseases. In particular, In order to simulate the function, it is proposed to substitute the functionalized ion channel condition and to simulate and analyze the action potential generation of each single myocardial cell and the current of each ion channel. Simulation results show that cardiac activity potential and contraction phenomenon can be visualized through data post-processing. That is, in the cardiac simulation method and apparatus according to the embodiment of the present invention, a single cell, a two-dimensional and a three-dimensional model can be integrally simulated at one time and integrated analysis and analysis can be performed by only changing one parameter input.

That is, the cardiac simulation method and apparatus proposed in the embodiment of the present invention can be helpful in studying the mechanism of the cardiac arrhythmogenesis. In addition, clinical trials for therapeutic drug development and toxicity identification can be substituted. In addition, patient-assisted arrhythmia diagnosis assistance can be performed.

Thus, those skilled in the art will appreciate that the present invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. It is therefore to be understood that the embodiments described above are to be considered in all respects only as illustrative and not restrictive. The scope of the present invention is defined by the appended claims rather than the detailed description and all changes or modifications derived from the meaning and scope of the claims and their equivalents are to be construed as being included within the scope of the present invention do.

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Claims (3)

Calculating a voltage change of single myocardial cells due to the inflow and outflow of bio-ions using Equation (1);
Ionic currents in each region of the heart, defined as a set of interstitial and interstitial regions, flow from one region to another through the cell membrane, and the current flowing out of the cell's interior space is the interstitial region Computing Equation (2) based on the current conservation law, computing a spatial current per volume through Equation (3), and calculating a cell current through Equation (4);
Calculating heart conduction using Equation (5), which is a reaction-diffusion equation for cell membrane potential;
The Galerkin method is applied to Equation (5) using the finite element method, and the Euler forward difference method for the time term is used to calculate the algebraic algebraic equation of the state value at the mesh points as a variable, Deriving Equation (6); And
A current of one or more selected from I _Na, I _CaL, I _to I _Kr, I _K, I _K1, I _NaCa, I _NaK, I _pCa I _pK, I _{b C a and} I _bK of _Equation And replacing the simulation model with a mathematical model of each mutant ion channel previously calculated by the mutation of the mutant ion channel,
The step of simulating replacing the previously calculated mutant ion channel with a mathematical model can be used for the mutation of the L532P and N588K mutants causing the KCNH2 gene And replaced by the <Equation 7> equation model for the ion channel of the I _Kr simulate the action potential, and each current of the ion channel mutations cardiomyocytes
comparing the pattern of the wild-type (WT) with that of the mutant-type (MT) to verify the association of the gene mutation to cause cardiac arrhythmia.

&Quot; (1) &quot;

C _m is the electrical capacitance of the cell membrane per unit cell, V _m is the voltage of the cell, I _ion is the total bio-ion current flowing into the cell, and I _stim is the flow of perturbation current to induce excitation of the cell. (I _ion changes depending on cell model and channel type.)
I _Na is the fast inward Na + current, I _Kl is inward rectifier K ⁺ current, I _to the transient outward K ⁺ current, I _Kur is ultrarapid delayed rectifier K ⁺ current, I _Kr is rapid delayed rectifier K ⁺ current, I _Ks is ^{slow delayed rectifier K + current, I} Ca, L is ^{L-type inward Ca 2+ current,} I NaCa is ^{Na + / Ca 2+ exchanger current,} I NaK is ^{Na + / K + pump current,} I p, Ca is plateau current, and I _{b, Na} and I _{b, Ca} represent background Na ⁺ and Ca ²⁺ currents, respectively.
&Quot; (2) &quot;

where x is the spatial coordinate vector, J is the current density per unit area, and subscripts i and e denote intracellular space and interstitial space, respectively.
&Quot; (3) &quot;

I _v ( x , t) is the spatial current per unit volume, φ is the electric potential, and M ( x ) for the volume conductor is the 3 × 3 electric conduction tensor.
&Quot; (4) &quot;

I _m (x, t) is the plasma membrane currents, and is C _m is the capacitance per unit surface area membranes, I _app (x, t) is given stimulation current applied per unit area, V (x, t) is φ _i - φ _e , and I _ion ( x , t) is the sum of ion currents per unit area, which depends on the channel type. Information on ion currents and related constants is based on the above-described single myocardial cell model .
Equation (5)

And I _app (x, t) is given stimulation current applied per unit area, V (x, t) is φ _i - a cell membrane potential which is defined as _{φ e, I ion (x,} t) is a sum of the per unit area of the ion current The information about ion currents and related constants is based on the single cardiomyocyte model described above, β is the area ratio to volume, and k is anisotropic, which expresses the difference in physical properties with respect to the direction of the muscle fiber .
&Quot; (6) &quot;

K is a stiffness matrix, X is a variable value vector at each lattice point, R is an external force term, and a solution according to each time is obtained using the Newton-Raphson method.
&Quot; (7) &quot;

I _Kr is rapid delayed outward rectifier K + current is, x _r1 and x _r2 are each activation, inactivation gating variable, α _{x_r1} and β _{x_r1} are respectively forward, backward rate constant for gating varialbe, τ _{x_r2} the time constant for gating variable, P ₁ ~ P ₁₁ are experimental values for WT and MT (N588K, L532P).
delete A cardiac simulation apparatus for displaying an action potential and a conduction pattern calculated using the heart simulation method according to claim 1 as a two-dimensional or three-dimensional image based on a time change and a space.

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