JP2015165367A - Biological tissue simulation method and apparatus thereof - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a biological tissue simulation technology of precisely simulating behavior of a mother cell.SOLUTION: A biological tissue simulation method includes: arranging a mother cell model, a daughter cell model, and a non-dividing cell model, as particle models, in a simulation space; generating a first virtual particle model and a second virtual particle model which do not exert force to the daughter cell model and the non-dividing model, in a thickness direction of a mother cell layer, in a position holding the mother cell model; calculating first interparticle force which is exerted between cell models; calculating second interparticle force which is exerted between the mother cell model, the first virtual particle model, and the second virtual particle model; updating the positions of the daughter cell model and the non-dividing cell model with displacement calculated by use of the first interparticle force; updating the position of the mother cell model with displacement calculated by means of the first interparticle force and the second interparticle force; and updating the positions of the first and second virtual particle models with displacement calculated by use of the second interparticle force.

Description

  The present invention relates to a living tissue simulation technique.

  Patent Document 1 below proposes a simulation method that can more accurately simulate state changes such as growth and differentiation of actual living tissue accompanied by cell division of progenitor cells. This simulation method places the secondary cell model in the vicinity of the progenitor cell model, and responds to an increase in the position of the secondary cell model or the number of steps that have elapsed since the secondary cell model was generated. Increase the interparticle coefficient for the cell model and position the one secondary cell model based on the distance between the secondary cell model and the progenitor cell model or other secondary cell model and the interparticle coefficient. Including updating.

JP 2012-145988 A

  In this specification, a cell that forms a living tissue, a cell having a division ability is referred to as a mother cell, a cell that is divided from the mother cell is referred to as a daughter cell, and other cells that do not have a division ability. Cells are referred to as non-dividing cells. The cell in the present specification may be a so-called cell or a virtual unit provided for simulating a fluid tissue that maintains its volume.

  The epidermis that forms human skin tissue consists of a stratum corneum layer, a granule layer composed of 2 to 3 layers in order from the surface, a spiny layer composed of 5 to 10 layers, and a mother cell of the bottom. There is a basal layer (one layer) consisting of a kind of basal cells. In the basal layer, a plurality of basal cells are arranged in one layer, and irregularities are formed depending on the part of the body. About the unevenness | corrugation of a basal layer, it is known that it will decrease by aging, and it will be more severe in a spot part than other parts. By simulating the formation of such irregularities in the base layer, it can be used for skin care, aging care, and the like.

  However, there is no existing simulation method for simulating living tissue that accurately simulates the behavior of a mother cell such as a basal cell. Even in the above-described proposed method, there is not much mention about the behavior of mother cells (progenitor cells).

  The present invention has been made in view of such problems, and provides a living tissue simulation technique that accurately simulates the behavior of a mother cell.

  Each aspect of the present invention employs the following configurations in order to solve the above-described problems.

  The first aspect is the behavior of biological tissue formed by mother cells having division ability, daughter cells generated by division of the mother cells, and non-dividing cells existing on the opposite side of the daughter cells through the mother cell layer. The present invention relates to a biological tissue simulation method for simulating the above with at least one computer. The biological tissue simulation method according to the first aspect represents a mother cell model representing a mother cell, a daughter cell model representing a daughter cell, and a non-dividing cell according to the positional characteristics of the mother cell, the daughter cell, and the non-dividing cell. A non-dividing cell model is arranged in the simulation space as a particle model, and a first virtual particle model that does not exert any force on the daughter cell model and the non-dividing cell model at a position sandwiching the mother cell model in the thickness direction of the mother cell layer; A second virtual particle model is generated, a first interparticle force acting between cell models including a mother cell model, a daughter cell model, and a non-dividing cell model is calculated, and the mother cell model, the first virtual particle model, and the second virtual model are calculated. A second interparticle force acting between the particle model and the displacement calculated using the first interparticle force to update the positions of the daughter cell model and the non-dividing cell model; The position of the mother cell model is updated by the displacement calculated using the force between the two particles, and the positions of the first virtual particle model and the second virtual particle model are updated by the displacement calculated using the force between the second particles. Including updating.

  The second aspect is the behavior of biological tissue formed by mother cells having division ability, daughter cells generated by division of the mother cells, and non-dividing cells existing on the opposite side of the daughter cells through the mother cell layer. The present invention relates to a biological tissue simulation apparatus that simulates the above. The biological tissue simulation apparatus according to the second aspect represents a mother cell model representing a mother cell, a daughter cell model representing a daughter cell, and a non-dividing cell according to the positional characteristics of the mother cell, the daughter cell, and the non-dividing cell. Arrangement means for arranging the non-dividing cell model as a particle model in the simulation space, and a first virtual that does not exert any force on the daughter cell model and the non-dividing cell model at a position sandwiching the mother cell model in the thickness direction of the mother cell layer Particle control means for generating a particle model and a second virtual particle model, each cell model including a mother cell model, a daughter cell model and a non-dividing cell model, and each including a first virtual particle model and a second virtual particle model For the virtual particle model, model information holding means for holding model information including the position and model type in the simulation space, a mother cell model, A first interparticle force acting between cell models including a cell model and a non-dividing cell model, and a second interparticle force acting between the mother cell model and the first virtual particle model and the second virtual particle model are calculated. The positions of the daughter cell model and the non-dividing cell model are updated by the force calculation means and the displacement calculated using the force between the first particles, and calculated using the force between the first particles and the force between the second particles. Position updating means for updating the position of the mother cell model by the displacement and updating the positions of the first virtual particle model and the second virtual particle model by the displacement calculated using the second interparticle force.

  Another aspect of the present invention may be a program that causes at least one computer to execute the method according to the first aspect, or may be a computer-readable storage medium that records such a program. . This recording medium includes a non-transitory tangible medium.

  According to each aspect described above, it is possible to provide a living tissue simulation technique that accurately simulates the behavior of a mother cell.

It is a figure which shows the biological tissue simulation method in 1st Embodiment. It is a figure which shows the example of the simulation space of the biological tissue of the epidermis and dermis in a person. It is a figure which shows notionally the hardware structural example of the biological tissue simulation apparatus in 1st Embodiment. It is a figure which shows notionally the process structural example of the biological tissue simulation apparatus in 1st Embodiment. The process in connection with the mother cell division of the simulation method in 2nd Embodiment is shown. The process in connection with the position update of the simulation method in 2nd Embodiment is shown. It is a figure which shows notionally the process structural example of the biological tissue simulation apparatus in 2nd Embodiment. It is the figure which showed notionally the effect of the 3rd virtual particle model. The process in connection with size control of the simulation method in 3rd Embodiment is shown. It is a figure which shows notionally the process structural example of the biological tissue simulation apparatus in 3rd Embodiment. It is a figure which shows the simulation result in a present Example. It is a figure which shows the simulation result in a present Example.

  Embodiments of the present invention will be described below. In addition, each embodiment given below is an illustration, respectively, and this invention is not limited to the structure of each following embodiment.

[First Embodiment]
[Biological tissue simulation method]
FIG. 1 is a diagram illustrating a biological tissue simulation method according to the first embodiment. Hereinafter, the biological tissue simulation method may be abbreviated as a simulation method for short. The simulation method in the first embodiment simulates the behavior of a living tissue formed by mother cells, daughter cells, and non-dividing cells existing on the opposite side of the daughter cells via the mother cell layer by at least one computer. To do. As shown in FIG. 1, the simulation method according to the first embodiment includes (S11) to (S17).

  (S11) includes particles of a mother cell model representing a mother cell, a daughter cell model representing a daughter cell, and a non-dividing cell model representing a non-dividing cell according to the positional characteristics of the mother cell, the daughter cell, and the non-dividing cell. This is a step of placing the model in the simulation space. Each cell model such as a mother cell model, daughter cell model, and non-dividing cell model is specifically a software object representing each cell. The software object may be generated as an instance in object-oriented software or may be generated by a structure. This embodiment does not limit a specific method for creating a software object of such a cell model.

  Each cell model has cell type information that can distinguish at least a mother cell, a daughter cell, and a non-dividing cell. Moreover, in (S11), since each cell model is arrange | positioned in the simulation space as a particle model, each cell model further has the information which shows the position in simulation space. The position of the cell model is represented by the position of the center of gravity of the cell model, for example. In this embodiment, since each cell model is handled as a so-called particle method particle model, each cell model preferably further has information indicating the size of the cell. The information indicating the size of the cell is represented by a diameter, a radius, a size in each three-dimensional axis direction, or the like. Each cell model may be expressed as a particle model.

  The simulation space is a three-dimensional calculation space that simulates the behavior of each cell model, and represents a part of a living tissue formed by each cell model.

  FIG. 2 is a diagram illustrating an example of a simulation space of a living tissue of the epidermis and dermis in a human. In the example of FIG. 2, the simulation space is a range surrounded by calculation boundaries A1, A2, A3, and A4, and the simulation method does not target cell models located outside this simulation space. In the example of FIG. 2, a part of the dermal tissue, basal layer, spiny layer, granule layer, and horny layer is set in the simulation space, and the shape of the skin surface is represented by the calculation boundary A1. The basal layer is formed from basal cells and pigment cells (melanocytes). In the following description, only the mother cells are exemplified as the cells forming the mother cell layer corresponding to the basal layer, but the mother cell layer contains other types of cells that are allowed, such as pigment cells. May be. However, there are other types of cells that are not allowed, such as daughter cells and non-dividing cells, in which the original mother cell layer of living tissue collapses due to entry into the mother cell layer. The simulation space setting method is not limited to the example of FIG. For example, when the hair tissue is a simulation target, the hair tissue or a part thereof is set to calculation boundaries A1 to A4 from the dermal papilla tissue, hair matrix cells, and daughter cells generated by dividing the hair matrix cells. .

  Further, the positional characteristics of the mother cell, the daughter cell, and the non-dividing cell mean the nature of the positional relationship of each cell in the living tissue. For example, in human epidermal tissue, there is a basal layer (corresponding to the mother cell layer) formed so that basal cells corresponding to mother cells and pigment cells (melanocytes) do not overlap in the thickness direction. There are spiny cells corresponding to daughter cells, and dermal tissue corresponding to non-dividing cells is present on the subcutaneous tissue side from the basal layer. In this example, depending on the characteristics of such a basal layer and the positional relationship between the spinous layer, the basal layer and the dermal tissue, a daughter cell (spinous cell) model, a mother cell (basal cell) model, and a non-dividing cell The model is placed. In hair tissue, hair matrix cells corresponding to mother cells are present on the surface of the hair papillary tissue consisting of hair papillary cells corresponding to non-dividing cells, and non-dividing cells divided from the hair matrix cells on the opposite side. Exists. In this example, depending on the positional relationship between the hair matrix cells, the hair papilla cells and the non-dividing cells, a mother cell (hair matrix cell) model, a non-dividing cell (hair papilla cell) model, and a secondary cell model are used. Be placed.

  (S12) is a step of generating the first virtual particle model and the second virtual particle model at positions where the mother cell model is sandwiched in the thickness direction of the mother cell layer. Thereby, a set of the first virtual particle model and the second virtual particle model is generated for one mother cell model of the object, and the generated first virtual particle model and second virtual particle model are generated in the simulation space. They are arranged at positions facing each other across the target mother cell model. The first virtual particle model and the second virtual particle model do not represent cells that form a living tissue, but are software objects that are virtually provided for calculation in order to control the behavior of each cell model. Each virtual particle model is defined as a model that has no power on the daughter cell model and the non-dividing cell model. Each virtual particle model may also be described as a particle model.

  Since the virtual particle model is arranged in the software space, it has information indicating the position in the software space. The virtual particle model may have information indicating the size or may not have the size (for example, the volume may be zero). Since each virtual particle model needs to be distinguished from a cell model, the virtual particle model further includes information indicating that it is a virtual particle model or not a cell model.

  (S13) is a step of calculating a first interparticle force acting between cell models including a mother cell model, a daughter cell model, and a non-dividing cell model. The first interparticle force is calculated using a so-called particle method by regarding each cell model as a particle. The first interparticle force is between mother cell models, between mother cell models and daughter cell models, between mother cell models and non-dividing cell models, between daughter cell models, between non-dividing cell models, and daughter cell models. With respect to the non-dividing cell model, it is calculated using the interparticle distance between the cell models. The interparticle distance is calculated as the Euclidean distance between the particle models in the software space (three-dimensional calculation space). When the position of each particle model is indicated by the position of the center of gravity of the model, the interparticle distance is calculated as the distance between the center of gravity of the particle model. Hereinafter, the interparticle distance may be simply expressed as a distance.

  In order to reduce the amount of calculation, it is desirable that the combination of cell models for which the first interparticle force is obtained is a combination having an interparticle distance of a predetermined value or less. In addition, since the daughter cell model and the non-dividing cell model exist at positions sandwiching the mother cell model, it is desirable that the interparticle force between them is excluded from the calculation target. For the calculation of the first interparticle force, a method similar to that described in Patent Document 1 may be used.

  (S14) is a step of calculating a second interparticle force acting between the mother cell model and the first virtual particle model and the second virtual particle model. In other words, (S14) calculates the second interparticle force between the mother cell model and the first virtual particle model and the second interparticle force between the mother cell model and the second virtual particle model. . In order to reduce the amount of calculation, it is desirable that the combination of the mother cell model and the virtual particle model for which the second interparticle force is obtained is a combination in which the interparticle distance is a predetermined value or less. For the calculation of the second interparticle force, a method similar to that described in Patent Document 1 may be used.

  (S15) is a step of updating the positions of the daughter cell model and the non-dividing cell model based on the displacement calculated using the first interparticle force obtained in (S13). The calculated displacement is calculated using all interparticle forces and equations of motion that affect the target cell model or virtual particle model, and indicates the change in position for moving the target model to the position where the force is balanced. . Here, the displacement of the target daughter cell model or non-dividing cell model is calculated using the first interparticle force, the equation of motion, etc. obtained in (S13). (S15) updates the positions of the daughter cell model and the non-dividing cell model by applying the displacement to the current position.

  (S16) is a step of updating the position of the mother cell model by the displacement calculated using the first interparticle force obtained in (S13) and the second interparticle force obtained in (S14). .

  (S17) is a step of updating the positions of the first virtual particle model and the second virtual particle model by the displacement calculated using the second interparticle force obtained in (S14).

  However, the execution order of the steps in the simulation method is not limited to the order shown in FIG. The execution order of the steps can be changed within a range that does not hinder the contents. For example, the execution order of (S15), (S16), and (S17) is arbitrary, and may be executed in parallel. In addition, (S15) may be executed before (S14). Further, in FIG. 1, for the convenience of explanation, since it is simply illustrated by a flowchart, the simulation method in the first embodiment is not limited to the content illustrated in FIG. 1. For example, (S13) to (S17) can be executed for each software object (for each cell model and each virtual particle model). (S13) is not executed for the virtual particle model. (S14) is not executed for the daughter cell model and the non-dividing cell model.

  The simulation method in the first embodiment can be executed by at least one computer such as a biological tissue simulation apparatus described below. However, the above-described simulation method may include a process in which at least a part is performed by a person. For example, in (S11), the initial placement (placement at the start of simulation) of the mother cell model, daughter cell model, and non-dividing cell model may be realized based on information input by a person. Specifically, the required number of each cell model and the position of each cell model may be input by a person, and the input information may be set in the at least one computer. Even in this case, (S11) itself is a process executed by at least one computer, and the simulation method in the first embodiment can be said to be the creation of a technical idea utilizing the laws of nature as a whole.

[Biological tissue simulation device]
FIG. 3 is a diagram conceptually illustrating a hardware configuration example of the biological tissue simulation apparatus 1 in the first embodiment. Hereinafter, the biological tissue simulation apparatus may be abbreviated as a simulator. The simulator 1 is a so-called computer and includes, for example, a CPU (Central Processing Unit) 2, a memory 3, a communication unit 4, an input / output interface (I / F) 5, and the like that are connected to each other via a bus. The memory 3 is a RAM (Random Access Memory), a ROM (Read Only Memory), a hard disk, or the like. The communication unit 4 exchanges signals with other computers and devices. A portable recording medium or the like can be connected to the communication unit 4.

  The input / output I / F 5 can be connected to user interface devices such as the display device 6 and the input device 7. The display device 6 displays a screen corresponding to drawing data processed by a CPU 2 or a GPU (Graphics Processing Unit) (not shown) such as an LCD (Liquid Crystal Display) or a CRT (Cathode Ray Tube) display. Device. The input device 7 is a device that receives an input of a user operation such as a keyboard and a mouse. The display device 6 and the input device 7 may be integrated and realized as a touch panel. The hardware configuration of the simulator 1 is not limited.

  FIG. 4 is a diagram conceptually illustrating a processing configuration example of the biological tissue simulation apparatus 1 in the first embodiment. As shown in FIG. 4, the simulator 1 includes an arrangement unit 11, a particle control unit 12, a model information holding unit 13, a force calculation unit 14, a position update unit 15, and the like. Each of these processing units is realized, for example, by executing a program stored in the memory 3 by the CPU 2. The program is installed from a portable recording medium such as a CD (Compact Disc) or a memory card or another computer on the network via the communication unit 4 or the input / output I / F 5 and is stored in the memory 3. It may be stored.

  The placement unit 11 executes (S11) described above. The placement unit 11 executes (S11) using information input by a user operation using the input device 7 or information acquired via the communication unit 4. Specifically, the information indicates the required number of each cell model and the initial arrangement of each cell model, and is held in a model information holding unit 13 described later.

  The particle control unit 12 executes (S12) described above.

  The model information holding unit 13 is provided for each cell model including a mother cell model, a daughter cell model, and a non-dividing cell model, and each virtual particle model including a first virtual particle model and a second virtual particle model in a simulation space. Each holds model information including a position and a model type. The model type indicates a cell type indicated by each model or a particle model instead of a cell model. It is desirable that the model information of each cell model further includes information indicating the size of the cell. The model information of each virtual particle model may further include information indicating the size of the particle.

  The force calculation unit 14 executes (S13) and (S14) described above. That is, the force calculation unit 14 calculates the first interparticle force acting between the cell models and the second interparticle force acting between the mother cell model and the virtual particle model. As described above, the virtual particle model has no effect on the daughter cell model and the non-dividing cell model, and therefore, between the daughter cell model and the virtual particle model, and between the non-dividing cell model and the virtual particle model. The interparticle force acting on is not calculated.

  The position update unit 15 executes (S15), (S16), and (S17) described above. That is, the position update unit 15 updates the position information of the model information related to each cell model and each virtual particle model held in the model information holding unit 13.

[Operation and Effect of First Embodiment]
In an actual living tissue, the shape of the mother cell layer is not unchanged. For example, it is known that the concavo-convex shape of the basal layer in human epidermal tissue changes with aging. It is also known that the dermal papilla tissue in the hair atrophy during the regression phase. In order to correctly simulate the behavior of such a mother cell layer, it is necessary to simulate the behavior of each mother cell such as a basal cell or hair matrix cell. Therefore, as shown in the first embodiment, it is conceivable that the mother cell is also treated as a particle model like a daughter cell or a non-dividing cell and is displaced by the interparticle force from other cells.

  The present inventors have a problem that simply by treating the mother cell as a particle model, the shape of the mother cell layer collapses from the original shape in the living tissue, and the behavior of the mother cell cannot be simulated correctly. Obtained. For example, in an original living tissue, the mother cell layer is formed so that the mother cells do not overlap in the thickness direction. However, in the above simple simulation method, the mother cells overlap and the mother cell layer breaks down. For example, when replaced with skin tissue, the mother cell layer corresponding to the basal layer does not have daughter cells corresponding to spinous cells or non-dividing cells corresponding to dermal structures such as fibroblasts and extracellular matrix. In the simple simulation method described above, daughter cells (spinous cells) and non-dividing cells (dermis structure) enter the mother cell layer, and the mother cell layer breaks down.

  Therefore, the present inventors have come up with the idea of using a virtual particle model that does not represent a cell. By further studying the present inventors, two virtual particle models (a first virtual particle model and a second virtual particle model) are positioned at a position sandwiching the mother cell model in the thickness direction of the mother cell layer. By arranging a set of virtual particle models), each virtual particle model does not affect the daughter cell model and non-dividing cell model, but exerts a force on the mother cell model. We found that the behavior can be simulated.

  Specifically, in the first embodiment, each cell model representing a mother cell, a daughter cell, and a non-dividing cell is arranged in the simulation space according to the positional characteristics of each cell, and does not represent a cell. Two sets of virtual particle models are arranged for each mother cell model at a position sandwiching the mother cell model in the thickness direction of the mother cell layer. The position of each mother cell model includes the first interparticle force generated between the mother cell model and the other mother cell model, the daughter cell model, and the non-dividing cell model, the mother cell model, and the first virtual model. It is updated by the displacement calculated by using the second interparticle force generated between the particle model and the second virtual particle model. The position of each daughter cell model and each non-dividing cell model is updated by the displacement calculated using the first interparticle force, and the position of each virtual particle model is the displacement calculated using the second interparticle force. Updated by

  As a result, each mother cell model moves with the interparticle force generated from the positional relationship with the other cell models, while the interparticle force between each of the two virtual particle models facing each other through the mother cell model. That movement will be suppressed. Therefore, according to the second embodiment, the shape of the mother cell layer can be changed by moving the mother cell model, and the shape of the mother cell layer is prevented from being broken by suppressing the movement of the mother cell model. be able to. That is, according to the second embodiment, the behavior of the mother cell can be accurately simulated.

  Hereinafter, the details of the first embodiment will be described. Hereinafter, as a detailed embodiment, a biological tissue simulation method (simulation method) and a biological tissue simulation device (simulator) in the second embodiment and the third embodiment are exemplified. The following description will focus on the content different from the first embodiment described above, and the same content as in the first embodiment will be omitted as appropriate.

[Second Embodiment]
[Biological tissue simulation method]
A simulation method in the second embodiment will be described with reference to FIGS.
FIG. 5 shows steps involved in mother cell division in the simulation method according to the second embodiment. The simulation method in the second embodiment further includes the steps shown in FIGS. 5 and 6 in addition to the steps shown in the first embodiment. The simulation method in the second embodiment is executed by at least one computer such as the simulator 1 in the second embodiment.

  (S51) is a step (S51) of executing any one of the first division pattern, the second division pattern, and the third division pattern at a predetermined frequency and a predetermined ratio. (S51), when executed at the predetermined frequency, selects an original mother cell model that divides from a plurality of mother cell models, determines any one division pattern so as to follow the predetermined ratio, The determined division pattern is executed on the selected mother cell model.

In the first division pattern, two daughter cell models are generated from the original mother cell model and the original mother cell model is deleted.
In the second division pattern, two mother cell models are generated from the original mother cell model. In the second division pattern, the original mother cell model may be one mother cell model after division, or the original mother cell model may be deleted and two mother cell models may be added. That is, the second division pattern may be executed as generation of one new mother cell model, or may be executed as deletion of the original mother cell model and generation of two new mother cell models.
In the third division pattern, a mother cell model and a daughter cell model are generated from the original mother cell model. In the third division pattern, the original mother cell model may be directly used as one mother cell model after division, or the original mother cell model is deleted and new mother cell models and daughter cell models are added. . That is, the third division pattern may be executed as generation of a new daughter cell model, or may be executed as deletion of the original mother cell model and generation of a new mother cell model and a new daughter cell model. .

  The mother cell is known to have three division patterns as described above, and the frequency of division of the mother cell and the generation rate of the division pattern according to the target biological tissue are known. For example, assuming that the time required for epidermis turnover is in the range of about 28 to 60 days, the frequency of division of basal cells (division rate) in human epidermal tissue is about 0.1 to 0.8 per day. It is assumed that it is about once. Moreover, based on verification in mice, it is known that the generation rate of basal cell division patterns is 84% for the third division pattern and 8% for the first and second division patterns (Nature). 446: 185-189, 2007). Based on such knowledge, the predetermined frequency and the predetermined ratio are set. The predetermined frequency and the predetermined ratio may be set in advance or may be adjusted by a user input operation or the like.

  In the second division pattern, one mother cell model divides into two mother cell models. Therefore, when two new mother cell models are placed at or near the original mother cell model, Overlap will increase. Therefore, (S51) may further include enlarging the size of the target mother cell model before the execution of the second division pattern (not shown). In this way, the overlap of the mother cell models immediately after division can be reduced, and the behavior of the mother cells can be simulated more accurately.

  The position immediately after the division in the cell model generated by division as described above is set at or near the position of the mother cell model of the division source. However, since the daughter cell model generated by division needs to escape from the mother cell layer, it is desirable that the daughter cell model is arranged on the side where another daughter cell model exists rather than the position of the mother cell model of the division source. When the cell model has a volume, the size of the cell model immediately after division may be set smaller than the standard, and may gradually be set to a standard size as time elapses from division.

  When the division pattern executed in (S51) is the first division pattern (S52; YES), (S53) is executed. (S53) is a step of deleting the first virtual particle model and the second virtual particle model associated with the deleted mother cell model when the mother cell model is deleted. Deletion of the mother cell model and the virtual particle model can be realized by deleting each corresponding software object or by setting a flag indicating deletion to each software.

  (S54) is a step of generating a third virtual particle model at the position of the deleted mother cell model. The third virtual particle model does not represent a cell forming a living tissue, but is a software object that is virtually provided for calculation in order to control the behavior of each cell model. As will be described later, the third virtual particle model is different from the first virtual particle model and the second virtual particle model in that the third virtual particle model is deleted due to the distance relationship with the adjacent mother cell model. Therefore, the third virtual particle model has information indicating a model type and a position in the software space that can be distinguished from the cell model, the first virtual particle model, and the second virtual particle model. Moreover, the 3rd virtual particle model may have the information which shows a magnitude | size similarly to a 1st virtual particle model and a 2nd virtual particle model, and does not need to have a magnitude | size (it may be zero volume). .

  Next, when the split pattern executed in (S51) is the second split pattern (S52; NO, S55: YES), (S56) is executed. (S56) is a step similar to (S12) shown in FIG. 1, and is a step of generating a first virtual particle model and a second virtual particle model corresponding to one mother cell model.

  (S57) is a step of maintaining the correspondence between the mother cell model and the first virtual particle model and the second virtual particle model generated in (S56). Although not shown, the simulation method in the second embodiment further includes (S57) executed after (S12) in addition to the steps shown in FIG. Using the correspondence relationship held in (S57), (S53 specifies the first virtual particle model and the second virtual particle model to be deleted.

  FIG. 6 shows steps related to position update of the simulation method according to the second embodiment. In the simulation method according to the second embodiment, the steps shown in FIG. 6 are sequentially executed for each cell model and each virtual particle model. Also in FIG. 6, as in FIG. 1, the simulation method in the second embodiment is simply shown by a flowchart for convenience of explanation. The simulation method in the second embodiment is not limited to the contents shown in FIGS.

(S61) is the same as (S13) shown in FIG.
(S62) is the same as (S14) shown in FIG.

  (S63) is a step of calculating a third interparticle force acting between the third virtual particle model and each cell model including the mother cell model, the daughter cell model, and the non-dividing cell model. In other words, (S63) is the third interparticle force between the mother cell model and the third virtual particle model, the third interparticle force between the daughter cell model and the third virtual particle model, and non-dividing. A third interparticle force between the cell model and the third virtual particle model is calculated. In order to reduce the amount of calculation, it is desirable that the combination of each cell model for which the force between the third particles is obtained and the third virtual particle model is a combination having an interparticle distance of a predetermined value or less. For the calculation of the third interparticle force, a method similar to that described in Patent Document 1 described above may be used.

  (S64) determines the positions of the daughter cell model and the non-dividing cell model by the displacement calculated using the first interparticle force calculated in (S61) and the third interparticle force calculated in (S63). It is a process of updating.

  (S65) is calculated by using the first interparticle force obtained in (S61), the second interparticle force obtained in (S62), and the third interparticle force obtained in (S63). This is a step of updating the position of the mother cell model.

  (S66) is the same as (S17) shown in FIG.

  (S67) is a step of updating the position of the third virtual particle model by the displacement calculated using the third interparticle force obtained in (S63).

  (S68) is a step of calculating the distance between the third virtual particle model and the mother cell model. In order to reduce the amount of calculation, it is desirable to limit the combinations of the third virtual particle model and the mother cell model whose distance is to be obtained to those adjacent to each other.

  When there is a third virtual particle model in which the distance calculated in (S68) is equal to or less than a predetermined threshold (S69; YES), (S70) is executed for the third virtual particle model. (S70) is a step of deleting the third virtual particle model whose distance from the mother cell model is a predetermined threshold value or less. The predetermined threshold here is set to, for example, 1 to 0.5 times the diameter of the mother cell model.

  The execution order of the steps in the simulation method is not limited to the order shown in FIG. The execution order of the steps can be changed within a range that does not hinder the contents. For example, the execution order of (S61), (S62), and (S63) is arbitrary and may be executed in parallel. The same applies to (S64), (S65), (S66), and (S67). Moreover, (S68) to (S70) may be executed at an arbitrary timing for each third virtual particle model independently of the position update.

[Biological tissue simulation device]
FIG. 7 is a diagram conceptually illustrating a processing configuration example of the biological tissue simulation apparatus 1 in the second embodiment. As shown in FIG. 7, the simulator 1 further includes a division processing unit 16 in addition to the configuration of the first embodiment. Similarly to the other processing units, the division processing unit 16 is realized by executing a program stored in the memory 3 by the CPU 2.

  The division processing unit 16 executes the above (S51). The division processing unit 16 holds the predetermined frequency and the predetermined ratio in advance. The predetermined frequency and the predetermined ratio may be changed by a user input operation or the like. When deleting the mother cell model by executing the first division pattern, the division processing unit 16 deletes the model information of the mother cell model held in the model information holding unit 13 or adds the model information to the model information. Add a deletion flag.

  Furthermore, when the division processing unit 16 decides to execute the second division pattern, the division processing unit 16 may enlarge the size of the mother cell model to be divided before the execution of the second division pattern. In this way, the overlap of the mother cell models immediately after division can be reduced, and the behavior of the mother cells can be simulated more accurately.

  The model information holding unit 13 includes a mother cell model, a correspondence relationship between the first virtual particle model and the second virtual particle model generated corresponding to the mother cell model, and a simulation space for the third virtual particle model. The model information including the position and the model type is further held. For example, the model information holding unit 13 holds the identification information of the mother cell model, the first virtual particle model, and the second virtual particle model in association with each other.

  The particle control unit 12 executes (S53), (S54), and (S68) to (S70). That is, when the mother cell model is deleted, the particle control unit 12 deletes the first virtual particle model and the second virtual particle model associated with the deleted mother cell model, and deletes the deleted mother cell model. A third virtual particle model is generated at the position. At this time, the particle control unit 12 specifies the first virtual particle model and the second virtual particle model to be deleted based on the correspondence relationship held in the model information holding unit 13 and holds the first virtual particle model in the model information holding unit 13. The model information of each identified virtual particle model is deleted. In generating the third virtual particle model, the particle control unit 12 adds the model information of the third virtual particle model to the model information holding unit 13.

  Furthermore, the particle control unit 12 deletes the third virtual particle model according to the distance between the third virtual particle model and the mother cell model. This process is the same as (S68) to (S70) described above.

  The force calculation unit 14 further executes (S63) described above.

  The position update unit 15 executes (S64), (S65), (S66), and (S67) described above.

[Operations and effects in the second embodiment]
As described above, in the second embodiment, the three division patterns of the mother cell model are executed at a predetermined frequency and a predetermined ratio. Thereby, it is possible to simulate the division of the mother cell in accordance with the knowledge regarding the division of the mother cell as described above.

  However, simply dividing the mother cell model in order to accurately simulate the division of the mother cell causes a problem that the shape of the mother cell layer collapses from the original shape in the living tissue. For example, when two daughter cell models are generated from the original mother cell model and the original mother cell model is deleted (in the case of the first division pattern), it is generated in order not to disturb the shape of the mother cell layer. It is necessary to push up the two daughter cell models and to fill the gap created by deleting the original mother cell model with other mother cell models.

  FIG. 8 is a diagram conceptually showing the operation effect of the third virtual particle model. In FIG. 8, M1, M2, and M3 represent mother cell models, and two daughter cell models generated by dividing the mother cell model M2 in the first division pattern are denoted by D1 and D2. As shown in FIG. 8, even in a simple method, the daughter cell models D1 and D2 after division are pushed upward by the repulsive force from the mother cell models M1 and M2 and the attractive force from other daughter cell models. It may be possible to simulate what is done. However, the gap generated by pushing up the daughter cell models M1 and M2 and deleting the original mother cell model M3 is not filled, or it takes a considerable time to fill the gap. This is because the interparticle force does not act between the mother cell models M1 and M2 due to the gap. If the gap exists for a long time, another daughter cell model enters the gap and the mother cell layer collapses from its original shape.

  Therefore, the present inventors have come up with the idea of using a virtual particle model (third virtual particle model) that does not represent cells instead of the deleted mother cell model. The present inventors have further studied, and this third virtual particle model exerts a force (third interparticle force) on the mother cell model, daughter cell model, and non-dividing cell model, and the mother It was found that by destroying the cell model when the distance between the cell model and the cell model decreases, the mother cell layer can be prevented from collapsing while correctly simulating the division of the mother cell.

  Specifically, in the second embodiment, when the mother cell model is deleted, the third virtual particle model is arranged at the position of the deleted mother cell model, as shown in the lower part of the drawing of FIG. Is done. The third virtual particle model exerts a force (a third interparticle force) on the mother cell model, the daughter cell model, and the non-dividing cell model, and the position of each mother cell model is the first interparticle force and the second particle. In addition to the inter-force, it is updated by the displacement based on the third inter-particle force working with the third virtual particle model. Thereby, the said clearance gap produced by execution of a 1st division | segmentation pattern can be filled up with the attractive force of the 3rd particle | grain force which acts between a 3rd virtual particle model and a mother cell model.

  Furthermore, in the second embodiment, when the distance between the third virtual particle model and the mother cell model is equal to or less than a predetermined threshold, the third virtual particle model is deleted. That the distance between the third virtual particle model and the mother cell model is equal to or smaller than a predetermined threshold means that interparticle force acts between the mother cell models existing at positions sandwiching the third virtual particle model. Means that. That is, when the interparticle force acts between the mother cell models, the third virtual particle model becomes unnecessary, and therefore the unnecessary third virtual particle model is deleted in the second embodiment.

  As described above, according to the second embodiment, it is possible to correctly simulate the behavior of the mother cell including the division of the mother cell.

[Third Embodiment]
Hereinafter, the biological tissue simulation method and biological tissue simulation apparatus according to the third embodiment will be described. In the third embodiment, at least the mother cell model has information indicating the size.
[Biological tissue simulation method]
A simulation method in the third embodiment will be described with reference to FIG.
FIG. 9 shows steps related to size control of the simulation method according to the third embodiment. The simulation method in the third embodiment further includes the steps shown in FIG. 9 in addition to the steps shown in the first embodiment and the second embodiment. The simulation method in the third embodiment is executed by at least one computer such as the simulator 1 in the third embodiment.

  Each step shown in FIG. 9 is executed for each mother cell model. In this simulation method, (S91) and (S92) can be continuously executed for each mother cell model. In this case, this simulation method can execute (S91) and (S92) for each mother cell model in parallel. In the present simulation method, (S92) may be executed after (S91) is executed for all mother cell models.

  (S91) is a step of calculating the number density related to the mother cell model based on the distance between the mother cell model and the surrounding mother cell model. The calculated number density indicates the number of mother cell models existing in the unit range. For example, (S91) calculates the distance between each of the surrounding mother cell models for a certain mother cell model, and calculates the sum of the calculated distances as the number density of the mother cell model. In the surrounding mother cell model, another mother cell model is set in which the interparticle distance from the mother cell model for which the number density is calculated is equal to or less than a predetermined threshold. In this case, the predetermined threshold can be set to a maximum of 2 dr or less, preferably in a range of 1.1 to 1.5 dr. Here, dr represents a reference distance related to a combination of a mother cell model to be calculated and surrounding mother cell models.

  (S92) is a step of changing the size of each mother cell model based on the number density calculated in (S91). Specifically, (S92) determines the size of each mother cell model so that the number density calculated at each time is constant. Therefore, (S92) reduces the size of the mother cell model as the calculated number density increases, and increases the size of the mother cell model as the calculated number density decreases.

[Biological tissue simulation device]
FIG. 10 is a diagram conceptually illustrating a processing configuration example of the biological tissue simulation apparatus 1 in the third embodiment. As shown in FIG. 10, the simulator 1 further includes a density calculation unit 17 and a size control unit 18 in addition to the configuration of the second embodiment. The density calculation unit 17 and the size control unit 18 are realized by executing a program stored in the memory 3 by the CPU 2, similarly to the other processing units.

  The model information holding unit 13 holds model information including information indicating the size in addition to the position and the model type for at least the mother cell model. The model information holding unit 13 may hold model information that further includes information indicating the size of the daughter cell model and the non-dividing cell model.

The density calculation unit 17 executes (S91) described above.
The size control unit 18 executes (S92) described above. The size control unit 18 updates the size information of the model information of the mother cell model held in the model information holding unit 13.

[Operations and effects in the third embodiment]
In the third embodiment, for each mother cell model, the number density is calculated based on the distance from the surrounding mother cell models, and the size of each mother cell model is reduced as the number density increases, Enlarged as density decreases. Thus, according to the third embodiment, the size of each mother cell model is controlled such that the number density of the mother cell model is constant. In other words, the size of each mother cell model is such that when there is a gap, the size of the surrounding mother cell model temporarily increases, and when the interval is narrowed, the size of the surrounding mother cell model temporarily decreases. Is controlled.

  Therefore, the gap between the mother cell models generated according to the division of the mother cell model can be filled more easily, and the collapse of the mother cell layer can be surely prevented, and thus the behavior of the mother cell can be correctly simulated. it can.

[Supplement]
In the above description, the output mode of the simulation contents in each embodiment is not particularly mentioned. The simulation content can be output in various ways. Information relating to each cell model such as model information held in the model information holding unit 13 may be output in the form of display, printing, file output, or the like, or each cell model may be drawn to indicate the shape of the cell model Drawing data for drawing as an element may be generated, and display or printing may be performed based on the drawing data. In this case, only each cell model is the target of the drawing element, and each virtual particle model is not the target of the drawing element.

  Examples will be given below to describe the above-described embodiment in more detail. The present invention is not limited in any way by the following examples.

  In the following examples, the above-described embodiments are applied to simulation of human epidermal tissue. In the following examples, the mother cell corresponds to a basal cell, the daughter cell corresponds to a spiny cell, and the non-dividing cell corresponds to a unit obtained by modeling a dermal tissue as a particle model. Hereinafter, the particle model of the unit corresponding to the non-dividing cell is referred to as a dermal cell model. In human epidermal tissue, a basal layer corresponding to the mother cell layer is formed so that basal cells and pigment cells (melanocytes) do not overlap in the thickness direction.

In (S12) and (S56), the first virtual particle model is disposed on the spinous layer, and the second virtual particle model is disposed on the dermis tissue side.
In this embodiment, each cell model including the basal cell model, spiny cell model, and dermal cell model has a position (center of gravity position) in the simulation space, a model type, and a particle diameter of the cell. On the other hand, in this embodiment, each virtual particle model including the first virtual particle model, the second virtual particle model, and the third virtual particle model is defined as a particle having no volume.

  By the way, the above-mentioned first interparticle force, second interparticle force, and third interparticle force are composed of at least one of a volume force and a spring force acting between cell models and between a cell model and a virtual particle model. The body force is a force that works in proportion to the volume of the object (particle model), and changes according to the distance between adjacent particle models. The spring force also changes according to the distance between adjacent particle models. A repulsive force acts between particle models that are closer to each other than a distance at which they are in a stable state (inter-particle reference distance). However, as the separation distance increases, the volume force and spring force between the particle models are no longer negligible.

  For the calculation of the force between particles, a method similar to that described in Patent Document 1 described above may be used. For example, the interparticle force is calculated using the interparticle coefficient between the volume force and the spring force, the distance (ddr), and the reference distance (dr0) between adjacent particle models. The distance (ddr) is a distance between particles, and is calculated as, for example, a Euclidean distance between centroid positions. The reference distance (dr0) is a distance at which the repulsive force and the attractive force acting between the particle models are switched, can be calculated based on the particle size and the particle shape, and is equal to the particle diameter in the case of spheres having the same diameter. The inter-particle coefficient is set in accordance with the magnitude of the mutual force necessary to make a minute displacement from the reference distance (dr0). The reference distance (dr0) and the distance (ddr) can be determined according to the combination of target particle models, and may be determined in advance for each model type.

Specifically, the volume force between the particle models can be calculated as F in the following equation (1), and the spring force between the particle models can be calculated as f in the following equation (2). In the following formula, k and k ′ represent interparticle coefficients.

In this embodiment, the interparticle force is calculated as follows.
The first interparticle force acting on the basal cell model is derived from the volume force and spring force between other basal cell models, the volume force between spiny cell models, and the volume force between dermal cell models. Calculated. Thus, in this embodiment, no spring force is applied between the basal cell model, the spinous cell model, and the dermal cell model.

  On the other hand, in this embodiment, since each virtual particle model is defined as having no volume, no volume force acts between the virtual particle model and the cell model. That is, the second interparticle force acting on the basal cell model is calculated from the spring force between the first virtual particle model and the second virtual particle model. The third interparticle force acting on the basal cell model is calculated from the spring force between the third virtual particle model.

  The first interparticle force acting on the spinous cell model is calculated from the bulk force and the spring force with the other spinous cell model and the bulk force with the basal cell model. The distance between the spinous cell model and the dermal cell model is the distance where the interparticle force does not work because the basal cell model is sandwiched, so here the volume force between the spinous cell model and the dermal cell model And spring force was excluded. Further, the first virtual particle model and the second virtual particle model are defined to exert a force only on the basal cell model, and as a result, the second interparticle force does not reach the spiny cell model. The third interparticle force acting on the spinous cell model is calculated from the spring force between the third virtual particle model.

  The first interparticle force acting on the dermis cell model is calculated from the body force and spring force between the other dermis cell models and the body force between the basal cell models. The second interparticle force does not reach the dermal cell model. The third interparticle force acting on the dermal cell model is calculated from the spring force between the third virtual particle model.

  According to the present embodiment, the space between the cell models is maintained by the volume force, and the collapse of the shape of the basal layer can be prevented by the spring force.

[Size control of mother cell model]
In this example, the size control of the mother cell model in the third embodiment can be executed as follows.

For example, the distance between the mother cell model and a certain surrounding mother cell model can be calculated by the following equation.
Distance = (1.3dr / ddr) -1
Here, dr indicates a reference distance related to a combination of a mother cell model to be calculated and surrounding mother cell models, and ddr indicates a distance between particles (distance between centroids) of the combination. The reference distance will be described in detail in the example section. Thus, in this embodiment, the distance between the mother cell model calculated for size control of the mother cell model and a surrounding mother cell model is a value calculated using the interparticle distance. is there.

The sum of the plurality of distances calculated by the above formula for each surrounding mother cell model is calculated as the number density of the mother cell model. Then, the cell diameter of the mother cell model can be calculated by the following equation.
r = dr + (1.5−number density) × 0.1 dr
Here, r indicates the cell diameter of the mother cell model.

According to this specific example, the size of the mother cell model is set larger as the number density is smaller, and smaller as the number density is larger.
The calculation method of the number density of the mother cell model and the calculation method of the cell diameter from the number density are not limited to the above formula, and the weight of the particles closer to each other is increased based on the idea that the closer the particles, the greater the influence. To be determined. Therefore, the above calculation formula can also be changed as follows. Specifically, “1.3” in the calculation formula for the distance can be changed in the range of 1 dr to 2 dr under the idea of the calculation range of the number density, and “1.5” in the calculation formula for the cell diameter. "Is an average value of number density, so it should be determined by trial calculation." 0.1 "is the degree of strength of the force. If it is too weak, the effect is small, and if it is too large, it becomes unstable. Can be changed in the range of 1 to 1.

[Initial placement of mother cell model]
In order to more accurately simulate the change in the shape of the mother cell layer, it is desirable that the initial arrangement of the mother cell model is determined as follows. In other words, the simulation method according to the embodiment further includes determining each interval between the adjacent mother cell models in the initial arrangement of the mother cell model with a random number. Further, in the simulator 1 in the embodiment, the placement unit 11 determines each interval between other mother cell models adjacent to each other in the initial placement of the mother cell model using a random number.

  In this embodiment, the basal cell models as mother cell models are arranged on a flat surface, and the vertical and horizontal intervals on the plane between adjacent basal cell models are the particles of the basal cell model. Randomly determined within a range of 10% (0.1 dx) or less of the diameter. Due to the initial arrangement of the basal cell model, asperities of the basal layer were formed in a more natural shape as a result of the simulation. However, the range of the interval determined by the random number is not limited to 0.1 dx, and can be set in the range of 0.01 dx to 0.5 dx depending on the nature of the living tissue to be simulated.

  11 and 12 are diagrams showing simulation results in the present example. In this example, the initial shape of the basal layer is set to a flat surface as described above, and as shown in each of the above-described embodiments, the position movement of each cell model and the division of the basal cell model are simulated. It was. The division of the basal cell model was set at a frequency of 0.2 times per day.

  As a result, as shown in FIG. 11, according to the present example, the number of basal cells was divided until 45 days and the number of basal cells was increased to 5% from 45 days to 55 days. When the number of basal cells was set to be constant after the 55th day, it was simulated that a concavo-convex shape was formed in the basal layer from around the 55th day, and that the concavo-convex shape changed with time. Furthermore, it was verified that the uneven shape of the basal layer could be simulated in this way, and that the original shape of the basal layer in the epidermal tissue was maintained without breaking the basal layer even around the 135th day.

  FIG. 12 shows the height and number density of the basal cell model. The height of the basal cell model means the degree of separation from the dermis in the direction from the dermis to the skin surface. In FIG. 12, it is difficult to visually recognize because of the gray scale, but according to the present embodiment, the concavo-convex shape of the basal layer can be simulated, and the basal cell model overlaps in the layer thickness direction. It was verified that no collapse occurred.

  Thus, according to this embodiment, the behavior of basal cells in human epidermal tissue can be correctly simulated. Therefore, the simulation of the formation process of the unevenness of the base layer in this embodiment can be used for skin care, aging care, and the like.

  In addition, in the some flowchart used by the above-mentioned description, although several process (process) is described in order, the execution order of the process performed by each embodiment is not restrict | limited to the order of the description. In each embodiment, the order of the illustrated steps can be changed within a range that does not hinder the contents. Moreover, each above-mentioned embodiment can be combined in the range in which the content does not conflict.

  Part or all of the above embodiments can be specified as follows. However, each above-mentioned embodiment is not restrict | limited to the following description.

<1> A behavior of a living tissue formed by mother cells having division ability, daughter cells generated by division of the mother cells, and non-dividing cells existing on the opposite side of the daughter cells through the mother cell layer is at least 1 In a biological tissue simulation method simulated by two computers,
A mother cell model representing the mother cell, a daughter cell model representing the daughter cell, and a non-dividing cell model representing the non-dividing cell according to the positional characteristics of the mother cell, the daughter cell, and the non-dividing cell. Place it in the simulation space as a particle model,
Generating a first virtual particle model and a second virtual particle model that do not exert any force on the daughter cell model and the non-dividing cell model at a position sandwiching the mother cell model in the thickness direction of the mother cell layer;
Calculating a first interparticle force acting between cell models including the mother cell model, the daughter cell model and the non-dividing cell model;
Calculating a second interparticle force acting between the mother cell model and the first virtual particle model and the second virtual particle model;
Update the position of the daughter cell model and the non-dividing cell model by the displacement calculated using the force between the first particles,
Update the position of the mother cell model by the displacement calculated using the first interparticle force and the second interparticle force,
Updating the positions of the first virtual particle model and the second virtual particle model according to the displacement calculated using the force between the second particles;
A biological tissue simulation method.

<2> holding a correspondence relationship between the mother cell model and the first virtual particle model and the second virtual particle model generated corresponding to the mother cell model;
Performing a first division pattern that generates two daughter cell models from the mother cell model and deletes the mother cell model;
When the mother cell model is deleted, the first virtual particle model and the second virtual particle model associated with the deleted mother cell model are deleted,
Generating a third virtual particle model at the position of the deleted mother cell model;
Calculating a third interparticle force acting between the third virtual particle model and the cell model;
Update the position of the third virtual particle model by the displacement calculated using the force between the third particles,
Deleting the third virtual particle model according to the distance between the third virtual particle model and the mother cell model;
Further including
Updating the position of the daughter cell model and the non-dividing cell model is performed based on a displacement calculated using the first interparticle force and the third interparticle force,
The update of the position of the mother cell model is performed based on a displacement calculated using the first interparticle force, the second interparticle force, and the third interparticle force.
The biological tissue simulation method according to <1>.
<3> Any one of the first division pattern, a second division pattern that generates two mother cell models from the mother cell model, and a third division pattern that generates a mother cell model and a daughter cell model from the mother cell model One at a predetermined frequency and a predetermined rate,
The biological tissue simulation method according to <2>, further comprising:
<4> Before executing the second division pattern, enlarge the size of the target mother cell model,
The biological tissue simulation method according to <3>, further comprising:
<5> Based on a distance between the mother cell model and a surrounding mother cell model, a number density related to the mother cell model is calculated,
Reducing the size of the mother cell model as the calculated number density increases,
Enlarging the size of the mother cell model as the calculated number density decreases,
The biological tissue simulation method according to any one of <1> to <4>, further including:
<6> The first interparticle force acting on the mother cell model includes a body force and a spring force with another mother cell model, a body force with the daughter cell model, and the non-dividing cell model. Calculated from the body force between
The second interparticle force acting on the mother cell model is calculated from a spring force between the first virtual particle model and the second virtual particle model.
The biological tissue simulation method according to any one of <1> to <5>.
<7> The third interparticle force acting on the mother cell model is calculated from a spring force between the third virtual particle model,
The biological tissue simulation method according to any one of <2> to <4>.
<8> In the initial arrangement of the mother cell model, each interval between adjacent mother cell models is determined by a random number.
The biological tissue simulation method according to any one of <1> to <7>, further including:
<9> A program that causes at least one computer to execute the biological tissue simulation method according to any one of <1> to <8>.
<10> Simulates the behavior of a living tissue formed by mother cells having division ability, daughter cells generated by division of the mother cells, and non-dividing cells existing on the opposite side of the daughter cells through the mother cell layer. In the biological tissue simulation device,
A mother cell model representing the mother cell, a daughter cell model representing the daughter cell, and a non-dividing cell model representing the non-dividing cell according to the positional characteristics of the mother cell, the daughter cell, and the non-dividing cell. An arrangement means for arranging the particle model in the simulation space;
Particle control means for generating a first virtual particle model and a second virtual particle model that do not exert any force on the daughter cell model and the non-dividing cell model at a position sandwiching the mother cell model in the thickness direction of the mother cell layer When,
Each cell model including the mother cell model, daughter cell model, and non-dividing cell model, and each virtual particle model including the first virtual particle model and the second virtual particle model, including a position in the simulation space and a model type Model information holding means for holding each information;
A first interparticle force acting between cell models including the mother cell model, the daughter cell model, and the non-dividing cell model; and the mother cell model and the first virtual particle model and the second virtual particle model. Force calculating means for calculating the force between the second particles acting between,
The positions of the daughter cell model and the non-dividing cell model are updated by the displacement calculated using the first interparticle force, and the first interparticle force and the second interparticle force are used. Position updating means for updating the position of the mother cell model by displacement, and updating the positions of the first virtual particle model and the second virtual particle model by displacement calculated using the second interparticle force; ,
A living tissue simulation apparatus.
<11> a division processing means for executing a first division pattern for generating two daughter cell models from a mother cell model and deleting the mother cell model;
Further comprising
The model information holding means includes a mother cell model, a correspondence relationship between the first virtual particle model and the second virtual particle model generated corresponding to the mother cell model, and a simulation space for the third virtual particle model. Further holding model information including the position and model type in
When the mother cell model is deleted, the particle control unit deletes the first virtual particle model and the second virtual particle model associated with the deleted mother cell model, and the deleted mother cell Generating the third virtual particle model at the position of the model, and deleting the third virtual particle model according to the distance between the third virtual particle model and the mother cell model;
The force calculating means further calculates a third interparticle force acting between the third virtual particle model and the cell model;
The position update means updates the position of the daughter cell model and the non-dividing cell model by a displacement calculated using the first interparticle force and the third interparticle force, and the first interparticle force The position of the mother cell model is updated by the displacement calculated by using the second interparticle force and the third interparticle force, and the displacement is calculated by using the third interparticle force. Update the position of the virtual particle model,
The biological tissue simulation device according to <10>.
<12> The division processing means generates a mother cell model and a daughter cell model from the first cell division model, a second cell division pattern that generates two mother cell models from the mother cell model, and a third cell pattern. Execute any one of the split patterns at a predetermined frequency and a predetermined rate;
The biological tissue simulation device according to <11>.
<13> When the division processing unit decides to execute the second division pattern, it expands the size of the target mother cell model before the execution of the second division pattern.
The biological tissue simulation device according to <12>.
<14> density calculating means for calculating a number density related to the mother cell model based on a distance between the mother cell model and a surrounding mother cell model;
Size control means for reducing the size of the mother cell model with an increase in the calculated number density, and expanding the size of the mother cell model with a decrease in the calculated number density;
The biological tissue simulation device according to any one of <10> to <13>, further comprising:
<15> The arrangement unit determines each interval between adjacent mother cell models by random numbers in the initial arrangement of the mother cell model,
The biological tissue simulation device according to any one of <10> to <14>.

1 Biological tissue simulation device (simulator)
2 CPU
3 Memory 4 Communication Unit 6 Display Device 7 Input Device 11 Arrangement Unit 12 Particle Control Unit 13 Model Information Holding Unit 14 Force Calculation Unit 15 Position Update Unit 16 Division Processing Unit 17 Density Calculation Unit 18 Size Control Unit

Claims (7)

The behavior of living tissue formed by mother cells having the ability to divide, daughter cells generated by division of the mother cells, and non-dividing cells existing on the opposite side of the daughter cells through the mother cell layer by at least one computer In the simulated biological tissue simulation method,
A mother cell model representing the mother cell, a daughter cell model representing the daughter cell, and a non-dividing cell model representing the non-dividing cell according to the positional characteristics of the mother cell, the daughter cell, and the non-dividing cell. Place it in the simulation space as a particle model,
Generating a first virtual particle model and a second virtual particle model that do not exert any force on the daughter cell model and the non-dividing cell model at a position sandwiching the mother cell model in the thickness direction of the mother cell layer;
Calculating a first interparticle force acting between cell models including the mother cell model, the daughter cell model and the non-dividing cell model;
Calculating a second interparticle force acting between the mother cell model and the first virtual particle model and the second virtual particle model;
Update the position of the daughter cell model and the non-dividing cell model by the displacement calculated using the force between the first particles,
Update the position of the mother cell model by the displacement calculated using the first interparticle force and the second interparticle force,
Updating the positions of the first virtual particle model and the second virtual particle model according to the displacement calculated using the force between the second particles;
A biological tissue simulation method. Holding a correspondence relationship between the mother cell model and the first virtual particle model and the second virtual particle model generated corresponding to the mother cell model;
Performing a first division pattern that generates two daughter cell models from the mother cell model and deletes the mother cell model;
When the mother cell model is deleted, the first virtual particle model and the second virtual particle model associated with the deleted mother cell model are deleted,
Generating a third virtual particle model at the position of the deleted mother cell model;
Calculating a third interparticle force acting between the third virtual particle model and the cell model;
Update the position of the third virtual particle model by the displacement calculated using the force between the third particles,
Deleting the third virtual particle model according to the distance between the third virtual particle model and the mother cell model;
Further including
Updating the position of the daughter cell model and the non-dividing cell model is performed based on a displacement calculated using the first interparticle force and the third interparticle force,
The update of the position of the mother cell model is performed based on a displacement calculated using the first interparticle force, the second interparticle force, and the third interparticle force.
The biological tissue simulation method according to claim 1. Any one of the first division pattern, a second division pattern for generating two mother cell models from the mother cell model, and a third division pattern for generating a mother cell model and a daughter cell model from the mother cell model is predetermined. Run at a frequency and a predetermined rate,
The biological tissue simulation method according to claim 2, further comprising: Before executing the second division pattern, enlarge the size of the subject mother cell model,
The biological tissue simulation method according to claim 3, further comprising: Based on the distance between the mother cell model and surrounding mother cell models, the number density for the mother cell model is calculated,
Reducing the size of the mother cell model as the calculated number density increases,
Enlarging the size of the mother cell model as the calculated number density decreases,
The biological tissue simulation method according to claim 1, further comprising:   A program for causing at least one computer to execute the biological tissue simulation method according to any one of claims 1 to 5. Biological tissue simulation that mimics the behavior of biological tissue formed by mother cells that have division ability, daughter cells that result from division of the mother cells, and non-dividing cells that exist on the opposite side of the daughter cells through the mother cell layer In the device
A mother cell model representing the mother cell, a daughter cell model representing the daughter cell, and a non-dividing cell model representing the non-dividing cell according to the positional characteristics of the mother cell, the daughter cell, and the non-dividing cell. An arrangement means for arranging the particle model in the simulation space;
Particle control means for generating a first virtual particle model and a second virtual particle model that do not exert any force on the daughter cell model and the non-dividing cell model at a position sandwiching the mother cell model in the thickness direction of the mother cell layer When,
Each cell model including the mother cell model, daughter cell model, and non-dividing cell model, and each virtual particle model including the first virtual particle model and the second virtual particle model, including a position in the simulation space and a model type Model information holding means for holding each information;
A first interparticle force acting between cell models including the mother cell model, the daughter cell model, and the non-dividing cell model; and the mother cell model and the first virtual particle model and the second virtual particle model. Force calculating means for calculating the force between the second particles acting between,
The positions of the daughter cell model and the non-dividing cell model are updated by the displacement calculated using the first interparticle force, and the first interparticle force and the second interparticle force are used. Position updating means for updating the position of the mother cell model by displacement, and updating the positions of the first virtual particle model and the second virtual particle model by displacement calculated using the second interparticle force; ,
A living tissue simulation apparatus.