ln
⁢

g
⁡
(
r
)

(
2
)

From the edge information on the cells included in the cell population C1 in the captured image, the position of center mass of these cells are calculated. For all combinations that are pairs of cells selected from among the cells, a histogram where the distance between the positions of center mass is on the abscissa is generated. Based on the frequencies (the number of times) of distances between the positions of center mass calculated from the histogram, the radial distribution function g(r) is obtained. The obtained radial distribution function g(r) is introduced into the potential function w(r) of the above expression (2). Accordingly, the profile of the potential function w(r) can be obtained.

As shown in FIG. 2, part(b), the quadratic curve fitting is applied to the profile of the potential function w(r). Here, a quadratic curve is fitted using the least-square method, thereby obtaining the following expression (3). As a result, according to the following expression (3), r₀is calculated as the average distance, and k is calculated as the spring constant.

[Expression 3]

w(r)|_r=r₀˜k(r−r₀)²+w₀ (3)

The hexagonal order parameter is an index that represents the degree to which an arrangement of cells resembles a regular hexagon. The hexagonal order parameter is obtained based on six central angles of a hexagon formed of six cells closest to one cell from among the plurality of cells around which the six cells are centered. The hexagonal order parameter has a value ranging from zero to one. It can be evaluated that the closer the hexagonal order parameter is to one, the closer to a regular hexagon the arrangement of cells is. For example, the index calculation unit 11 calculates the hexagonal order parameter as described below.

FIG. 3 illustrates a hexagonal order parameter Q₆. According to the following expressions (4) and (5), the hexagonal order parameter Qⁱ₆is calculated for any cell i. For the cells included in the cell population C1, the average of the hexagonal order parameter s Qⁱ₆is taken, thereby calculating the hexagonal order parameter Q₆. As shown in FIG. 3, θ_ijis the central angle centered at any cell i, and N(i) are six cells closest to any cell i.

$\begin{matrix} [Expression 4] &  \\ q_{6}^{i} = \frac{1}{6} \sum_{j \in N (i)} e^{i 6 θ_{ij}} & (4) \end{matrix}$

$\begin{matrix} [Expression 5] &  \\ Q_{6}^{i} = {❘ q_{6}^{i} ❘}^{2} \in [0, 1] & (5) \end{matrix}$

FIG. 4, part(a) is a photograph showing a captured image of the low-quality cell population C1. FIG. 4, part(b) is a photograph showing a captured image of the high-quality cell population C1. As shown in FIGS. 4, part(a) and 4, part(b), it is found that the finally desired quality of the cell population C1 is orderly arrangement (alignment) of small cells. The average distance r₀, the spring constant k, and the hexagonal order parameter Q₆can be regarded as indices based on fundamental theories of colloid physics and crystal physics, with respect to such a quality.

Returning to FIG. 1, the evaluation unit 12 executes an evaluation process of evaluating the cell population C1, on the basis of the indices calculated by the index calculation unit 11. In a case where the indices include the average distance r₀, the evaluation unit 12 may evaluate that the smaller the average distance r₀is, the higher the quality of the cell population C1 is (the denser the multiple cells are), or may evaluate that the cell population C1 has a high quality if the average distance r₀is equal to or less than a threshold. In a case where the indices include the spring constant k, the evaluation unit 12 may evaluate that the larger the spring constant k is, the higher the quality of the cell population C1 is (the distances between cells are uniform), or may evaluate that the cell population C1 has a high quality if the spring constant k is equal to or larger than a threshold. In a case where the indices include the hexagonal order parameter Q₆, the evaluation unit 12 may evaluate that the closer to one the hexagonal order parameter Q₆is, the higher the quality of the cell population C1 is (the arrangement of cells is close to a regular hexagon), or may evaluate that the cell population C1 has a high quality if the hexagonal order parameter Q₆is equal to or larger than a threshold.

The evaluation unit 12 executes an OVL calculation process of calculating an overlapping coefficient (hereinafter called “OVL”) that represents the overlapping degree of the Gaussian distributions determined based on the values of indices and error components thereof. The OVL has a value equal to or larger than zero and equal to or less than one. If the OVL is zero, it represents that the Gaussian distributions are completely separated. If the OVL is one, it represents that the Gaussian distributions completely overlap. Hereinafter, the OVL calculation process and the evaluation by OVL are specifically described while exemplifying a case where the OVLs of parameters A and B that are two freely selected indices are compared and evaluated.

FIGS. 5, part(a) and 5, part(b) are graphs for illustrating OVL comparison and evaluation. In the graph shown in FIG. 5, part(a), the parameter A is on the abscissa, and the parameter B is on the ordinate. On the graph, a plurality of data points are plotted. For example, for (A₁, B₁), Gaussian distributions GA₁and GB₁determined from the values A₁and B₁and the error components are obtained. For example, for (A₂, B₂), Gaussian distributions GA₂and GB₂determined from the values A₂and B₂and the error components are obtained. In the diagram, line segments expanding centered at data points are error bars that represent error components (this also analogously applies to other diagrams). Note that the error components of the average distance r₀and the spring constant k include errors occurring in the fitting process (fitting errors). The error components of the hexagonal order parameter Q₆include at least any one of the standard deviation and the standard error.

From the overlap of Gaussian distributions GA₁and GA₂, A_OVLthat is the OVL of the parameter A is calculated in association with the parameter difference A_diff(=|A₂−A₁|). From the overlap of Gaussian distributions GB₁and GB₂, B_OVL, that is the OVL of the parameter B is calculated in association with the parameter difference B_diff(=|B₂−B₁|). Such calculation of A_OVLand B_OVLis executed for all the data points on the graph.

To allow the parameter A and the parameter B to be compared with each other with reference to the same criterion, a linear relationship between them is assumed, and from the gradient, change in parameter B with change in parameter A by one is obtained. A parameter #B (#B=B/slope) obtained by criterion correction of the parameter B in such a way as to change by one when the parameter A changes by one is defined. As shown in FIG. 5(b), when a graph where the parameter differences A_diffand #B_diffare on the abscissa and A_OVLand B_OVLare on the ordinate is created, it can be, for example, evaluated to be a sensitive index such that the OVL is small (in the diagram, the parameter B where the OVL plunges with increase in difference) and the errors do not overlap.

In a case where the OVLs of three or more parameters are compared and evaluated, a reference parameter may be defined, criterion correction based on the reference parameter may be applied to the three parameters, and then evaluation may be performed. For example, in a case where the OVLs of the average distance r₀, the spring constant k and the hexagonal order parameter Q₆are compared and evaluated, first, each of them is compared and evaluated with the density (described later) of cells of the cell population C1. Based on each comparison and evaluation result, the OVLs of the average distance r₀, the spring constant k and the hexagonal order parameter Q₆may be compared and evaluated.

Alternatively, in a case where the OVLs of three or more parameters are compared and evaluated, evaluation may be performed by calculating the ascending order of the OVLs of these parameters. For example, in a case where the OVLs of the average distance r₀, the spring constant k and the hexagonal order parameter Q₆are compared and evaluated, first, the OVLs of the average distance r₀and the spring constant k are compared and evaluated. The OVL of the average distance r₀and the hexagonal order parameter Q₆is compared and evaluated. The OVL of the hexagonal order parameter Q₆and the spring constant k is compared and evaluated. Accordingly, the average distance r₀, the spring constant k and the hexagonal order parameter Q₆may be compared and evaluated by calculating the ascending order of OVLs.

FIG. 6 shows a cell evaluation program P1. As shown in FIG. 6, the cell evaluation program P1 is a program for evaluating the quality of the cell population C1, and is stored in a storage unit 13 of the computer 10. The cell evaluation program P1 includes an index calculation module P11, and an evaluation module P12. The index calculation module P11 causes the computer 10 to execute the index calculation process described above. The evaluation module P12 causes the computer 10 to execute the evaluation process and the OVL calculation process described above.

The cell evaluation program P1 may be fixedly recorded in a tangible recording medium, such as a CD-ROM, a DVD-ROM or a semiconductor memory, for example, and be provided. Alternatively, the cell evaluation program P1 may be provided as a data signal superimposed on carrier waves, via a communication network.

As shown in FIG. 1, the display unit 20 displays at least any one of a captured image by the phase-contrast microscope 2, a calculation result of indices by the index calculation unit 11, and an evaluation result of the cell population C1 by the evaluation unit 12. For example, a display or the like may be used as the display unit 20. The operation unit 30 allows an operator to perform various operations on the cell evaluation device 1. For example, a mouse, a keyboard or the like may be used as the operation unit 30.

Next, the cell evaluation method (an operation method of the cell evaluation device 1) that evaluates the quality of the cell population C1 using the cell evaluation device 1 is described.

First, the cell population C1 mounted on the culture dish 5 is imaged by the phase-contrast microscope 2. Image processing is applied by the image processing device 3 to a captured image by phase-contrast microscope 2, thereby obtaining edge information on each cell included in the captured image.

Subsequently, the cell evaluation device 1 evaluates the quality of the cell population C1 on the basis of the edge information on the captured image obtained by the image processing device 3. That is, the index calculation unit 11 executes the index calculation process described above to calculate indices that include the average distance r₀, the spring constant k and the hexagonal order parameter Q₆(index calculation step). Based on the calculated indices, the evaluation process described above is executed by the evaluation unit 12 to evaluate the cell population C1 (evaluation step). For the calculated indices, the OVL calculation process described above is executed by the evaluation unit 12 to calculate the OVL (overlap coefficient calculation step). The display unit 20 is then caused to display at least any one of the captured image, the calculated indices, the calculated OVL, and the evaluation result of the cell population C1.

FIG. 7, part(a) is a graph showing the relationship between the density d and the good cell ratio. FIG. 7, part(b) is a graph showing the relationship between the spring constant k and the good cell ratio. The density d is the degree of sparseness and denseness of the cells in the cell population C1, and is an index represented by the following expression (6) in a case where the average value of the areas of single cells is assumed as S_A. The good cell ratio is the ratio of cells that have good quality in the cell population C1. The error component of the density d includes at least any one of the standard deviation, the standard error, and the measurement error of the cell area S_A.

d=1/S_A (6)

As shown in FIGS. 7, part(a) and 7, part(b), both the density d and the spring constant k positively correlate with the good cell ratio. In particular, the spring constant k has a smaller error component than the density d. Accordingly, for evaluation of the cell population C1, it can be understood that the spring constant k is sensitive and the reliability as an index is high.

FIG. 8, part(a) is a graph showing the relationship between the density d and the spring constant k. FIG. 8, part(b) is a graph for comparing and evaluating the OVL of the density d and the OVL of the spring constant k. The abscissa of FIG. 8, part(b) is the density difference d_diffand the spring constant difference k_diff. The criterion correction is applied to any of the density difference d_diffand the spring constant difference k_diff. As shown in FIG. 8, part(a), it can be understood that the error component of the spring constant k is small in comparison with the density d. As shown in FIG. 8, part(b), it can be understood that the OVL of the spring constant k is significantly small in comparison with the density d and the spring constant k is a sensitive index. Accordingly, for evaluation of the cell population C1, it can be understood that the spring constant k is sensitive and the reliability as an index is high.

FIG. 9, part(a) is a graph showing the relationship between the density d and the average distance r₀. FIG. 9, part(b) is a graph for comparing and evaluating the OVL of the density d and the OVL of the average distance r₀. The abscissa of FIG. 9, part(b) is the density difference d_diffand the average distance difference r_{0_diff}. The criterion correction is applied to any of the density difference d_diffand the average distance difference r_{0_diff}. As shown in FIG. 9, part(b), it can be understood that for evaluation of the cell population C1, the OVL of the average distance r₀is often small in comparison with the density d, and the distance is a sensitive index.

As described above, the cell evaluation method, the cell evaluation device 1, and the cell evaluation program P1 according to this embodiment calculate the index including the average distance r₀, the spring constant k and the hexagonal order parameter Q₆, and evaluate the cell population C1 on the basis of the indices. The finally desired quality of the cell population C1 is orderly arrangement (alignment) of small cells. Consequently, according to this embodiment, the indices based on the collective order is applied to evaluation, and it can be numerically quantified and grasped whether small cells are orderly arranged in the cell population C1. The indices are allowed to have correlation with the quality, and quantitative meaning can be given between the indices and the quality.

Consequently, according to this embodiment, the quality of the cell population C1 can be quantitatively evaluated. According to this embodiment, the quality of the cell population C1 can be non-destructively evaluated only from the captured image, it can be clearly identified whether the cell population C1 has a high quality or low quality, and the quality can be numerically quantified. According to this embodiment, a quantitative standard technique for a two-dimensional cell population using a statistical physics method can be provided. This embodiment is expected for an operation as a quantitative standard in general ophthalmic diagnosis. The cell evaluation program P1 according to this embodiment can be applied as a process management program for a cell culture platform for transplantation.

Since corneal endothelial cells having once reduced does not naturally recover, effective treatment is required. As treatment for corneal endothelial dysfunction, “corneal endothelial cell injection therapy” that transfers corneal endothelial cells in a state of a suspension has been proposed in recent years. According to the cell evaluation device 1 in this embodiment, in a quality management process for cultured cells used for the treatment, only microscopic observation without staining with a cell marker allows quality management and cell selection before transfer.

In this embodiment, the OVLs of indices are calculated. Accordingly, the sensitivities of indices can be grasped using the OVLs. By evaluating the cell population C1 on the basis of the OVLs besides the indices, the quantitative quality evaluation of the cell population C1 can be more accurately performed.

In this embodiment, the average distance r₀, the spring constant k and the hexagonal order parameter Q₆are calculated as the indices. However, not all of them are necessarily adopted as indices. At least any one of the average distance r₀, the spring constant k and the hexagonal order parameter Q₆may be adopted as an index. The indices are not limited to the average distance r₀, the spring constant k and the hexagonal order parameter Q₆, and may include other parameters. For example, the indices may further include any of the density d, the hexagonal cell ratio, the aspect ratio, the number of adjacent cells, and the film thickness (reflectance). The hexagonal cell ratio, the aspect ratio, the number of adjacent cells, and the film thickness (reflectance) can be calculated by a publicly known method. Furthermore, at least any one of parameters included as indices may be appropriately selected.

This embodiment can be used to evaluate the cell population C1 in a drug candidate substance in development of an ophthalmic therapeutic drug, for example. As described above, by applying this embodiment to evaluation of the cell population C1 in the drug candidate substance, the time of verifying the effectiveness and safety of the drug candidate substance can be reduced.

Second Embodiment

Next, a second embodiment is described. In the description of this embodiment, differences from the first embodiment are described, and redundant description is omitted.

FIG. 10 is a configuration diagram showing a cell evaluation device 50 according to the second embodiment. As shown in FIG. 10, the cell evaluation device 50 in this embodiment is, for example, a device used as an ophthalmic ocular test device, and includes at least a specular microscope 60, a computer 70, a display unit 20, and an operation unit 30.

The specular microscope 60 images a cell population that are endothelial tissue including a plurality of corneal endothelial cells of an eye of a patient 80, and obtains a specular image as a captured image. The specular microscope 60 outputs the specular image to the computer 70.

The computer 70 may be configured in a manner analogous to that of the computer 10 (see FIG. 1) in terms of a physical configuration. The computer 70 includes an image processing unit 71, an index calculation unit 72 and an evaluation unit 73, as a functional configuration.

The image processing unit 71 extracts edge information pertaining to contours of a plurality of corneal endothelial cells included in a cell population in the specular image taken by the specular microscope 60, by a publicly known image processing method. The image processing unit 71 outputs the extracted edge information to the index calculation unit 72. The index calculation unit 72 executes the index calculation process described above on the basis of the edge information on the specular image input from the image processing unit 71. Accordingly, the index calculation unit 72 calculates indices that include at least “average distance r₀,” “spring constant k” and “hexagonal order parameter Q₆.” The evaluation unit 73 executes the evaluation process described above, on the basis of the indices calculated by the index calculation unit 72, and evaluates the cell population. The evaluation unit 73 executes the OVL calculation process, and calculates the OVL, which is an index.

FIG. 11 shows photographs taken by specular microscopy indicating images including a plurality of corneal endothelial cells. FIG. 11, part(a) shows a low-quality cell population, and FIG. 11, part(b) shows a high-quality cell population. As shown in FIGS. 11, part(a) and 11, part(b), it is found that the finally desired quality of the cell population including a plurality of corneal endothelial cells is orderly arrangement (alignment) of small cells in a manner analogous to that of the first embodiment.

Next, the cell evaluation method (an operation method of the cell evaluation device 50) that evaluates the quality of the cell population using the cell evaluation device 50 is described.

First, the cell population including the corneal endothelial cells of the patient 80 is imaged by the specular microscope 60. Image processing is applied by the image processing unit 71 to the specular image taken by the specular microscope 60, edge information on each corneal endothelial cell included in the specular image is obtained. Based on the edge information on the obtained specular image, the index calculation step described above is executed by the index calculation unit 72 to calculate the indices (index calculation step). Based on the calculated indices, the evaluation process described above is executed by the evaluation unit 73 to evaluate the cell population (evaluation step). For the calculated indices, the OVL calculation process described above is executed by the evaluation unit 12 to calculate the OVL (overlap coefficient calculation step). The display unit 20 is then caused to display at least any one of the specular image, the calculated indices, the calculated OVL, and the evaluation result of the cell population.

FIG. 12 shows an example of a display of the display unit 20. As shown in FIG. 12, for example, a specular image 61 taken by the specular microscope 60, a chart 62 where the names, values and OVL of the indices are associated with each other, and various icon buttons, are displayed on the display unit 20. The indices here include the spring constant k, the average distance r₀, the hexagonal order parameter Q₆, the density d, the hexagonal cell ratio, the aspect ratio, the number of adjacent cells, and the film thickness. According to such a display, the cell population can be easily evaluated and diagnosed.

FIG. 13, part(a) is a graph showing the relationship between the density d and the good cell ratio. FIG. 13, part(b) is a graph showing the relationship between the spring constant k and the good cell ratio. In this embodiment, the density d is a degree of sparseness and denseness of a plurality of cells in a cell population including corneal endothelial cells, and the good cell ratio is a ratio of good qualities in the cell population including the corneal endothelial cells. As shown in FIGS. 13, part(a) and 13, part(b), both the density d and the spring constant k positively correlate with the good cell ratio. In particular, the spring constant k has a smaller error component than the density d. Accordingly, for evaluation of the cell population including corneal endothelial cells, it can be understood that the spring constant k is sensitive and the reliability as an index is high.

FIG. 14, part(a) is a graph showing the relationship between the density d and the spring constant k. FIG. 14, part(b) is a graph for comparing and evaluating the OVL of the density d and the OVL of the spring constant k. The abscissa of FIG. 14, part(b) is the density difference d_diffand the spring constant difference k_diff. The criterion correction is applied to any of the density difference d_diffand the spring constant difference k_diff. As shown in FIG. 14, part(a), it can be understood that the error component of the spring constant k is small in comparison with the density d. As shown in FIG. 14, part(b), it can be understood that the OVL of the spring constant k is significantly small in comparison with the density d and the constant is a sensitive index. Accordingly, for evaluation of the cell population including corneal endothelial cells, it can be understood that the spring constant k is sensitive and the reliability as an index is high.

FIG. 15, part(a) is a graph showing the relationship between the density d and the average distance r₀. FIG. 15, part(b) is a graph for comparing and evaluating the OVL of the density d and the OVL of the average distance r₀. The abscissa of FIG. 15, part(b) is the density difference d_diffand the average distance difference r_{0_diff}. The criterion correction is applied to any of the density difference d_diffand the average distance difference r_{0_diff}. As shown in FIG. 15, part(b), it can be understood that for evaluation of the cell population including corneal endothelial cells, the OVL of the average distance r₀is often small in comparison with the density d, and the distance is a sensitive index.

The evaluation unit 73 may predict the quality of a cell population later than a time point when the captured image is captured, on the basis of the indices calculated by the index calculation unit 72. That is, in the evaluation step described above, based on the indices calculated by the index calculation step described above, the quality of a cell population is predicted at a point in time later than when the specular image is captured. Accordingly, prognostication of the cell population can be supported. In this embodiment, as described below, for example, in particular, prognostication after cell injection therapy of corneal endothelial cells can also be supported.

FIG. 16 shows states of corneal endothelial cells of six patients after corneal transplant. In FIG. 16, the transplant time point is adopted as the reference (zero month). FIG. 16, part(a) is a graph showing the relationship between the density d of corneal endothelial cells of each patient and time. FIG. 16, part(b) is a graph showing the relationship between the density d at the three-month time point and the spring constant k at the three-month time point with respect to the corneal endothelial cells of each patient. FIG. 16, part(c) is a graph showing the relationship between the density d at the 24-month time point and the spring constant k at the three-month time point with respect to the corneal endothelial cells of each patient. FIG. 16, part(d) is a graph for comparing and evaluating the OVL of the density d at the three-month time point and the OVL of the spring constant k at the three-month time point with respect to the corneal endothelial cells of each patient. FIG. 16, part(e) is a graph for comparing and evaluating the OVL of the density d at the 24-month time point and the OVL of the spring constant k at the three-month time point with respect to the corneal endothelial cells of each patient. The abscissa axes of FIGS. 16, part(d) and 16, part(e) are the density difference d_diffand the spring constant difference k_diff. The criterion correction is applied to any of the density difference d_diffand the spring constant difference k_diff.

As shown in FIG. 16, part(a), at the three-month time point, there is no difference between the densities d of all the patients. However, at the 24-month time point, the densities d of some patients significantly decrease. As shown in FIG. 16, part(d), at the three-month time point, it shows that the OVL of the density d is high and the sensitivity for evaluation of the cell population is low. As shown in FIG. 16, part(e), it shows that at the 24-month time point when reduction in density d becomes actually prominent, the OVL decreases, and the sensitivity for the evaluation of the cell population increases. Accordingly, at the three-month time point, in a case where the cell population is evaluated with the density d being adopted as an index, it shows that reduction in cell quality and tissue quality in long-term prognosis cannot be determined.

Meanwhile, as shown in FIGS. 16, part(b) and 16, part(c), the error component of the spring constant k at the three-month time point is smaller than the error components of the densities d at the three-month time point and the 24-month time point. As shown in FIG. 16, part(d), at the three-month time point, it shows that the OVL of the spring constant k is sufficiently low and the sensitivity for evaluation of the cell population is high. That is, at the three-month time point, by evaluating the cell population with the spring constant k being adopted as an index, even reduction in cell quality and tissue quality in long-term prognosis that cannot be determined from the density d can be predicted. Consequently, in a case where the cell population is evaluated with the spring constant k being adopted as an index, for example, through follow-up at the three-month time point, a cell population having a high possibility that the quality decreases in long-term prognosis can be separated. As for prediction of the cell quality and tissue quality in long-term prognosis, with respect to certain cells, it can be assumed that an analogous result can be obtained even with the average distance r₀and the hexagonal order parameter Q₆being adopted as indices.

As described above, this embodiment also exerts advantageous effects analogous to those in the first embodiment, that is, advantageous effects of allowing the quality of the cell population to be quantitatively evaluated and the like. In this embodiment, the prediction of the onset and development of dysfunction of a corneal endothelium due to a medicine, an ophthalmic operation, contact lenses and the like can be achieved. Application to general ophthalmic corneal endothelial diagnosis, for example, in a screening examination before an ophthalmic operation, a contact lens examination for outpatients and the like can be achieved.

FIG. 17, part(a) is a graph showing the relationship between the density d and the good cell ratio in vitro (cultured cells) according to the first embodiment. FIG. 17, part(b) is a graph showing the relationship between the spring constant k and the good cell ratio in vitro according to the first embodiment. The density d is a degree of sparseness and denseness of a plurality of cells in the cell population C1 including corneal endothelial cells. The good cell ratio is the ratio of cells that have good quality in the cell population C1 including corneal endothelial cells. In the diagram, r²is a coefficient of determination.

As shown in FIGS. 17, part(a) and 17, part(b), both the density d and the spring constant k strongly, positively correlate with the good cell ratio. Accordingly, for evaluation of the cell population C1, it can be understood that the spring constant k has a high reliability as an index (to the same extent as that of the density).

FIG. 18 is a graph showing the relationship between the density d and the spring constant k in vitro according to the first embodiment. As shown in FIG. 18, since the density d and the spring constant k strongly, positively correlate with each other, it shows that the spring constant k can be used in a manner analogous to that of the density d, in evaluation of the cell population C1.

FIG. 19 is a graph showing the relationship between the density d and the average distance r₀in vitro according to the first embodiment. As shown in FIG. 19, since the density d and the average distance r₀strongly, positively correlate with each other, it shows that the average distance r₀can be used in a manner analogous to that of the density d, in evaluation of the cell population C1.

FIG. 20, part(a) is a graph showing the relationship between the density d and the good cell ratio in vivo (restored cornea) according to the second embodiment. FIG. 20, part(b) is a graph showing the relationship between the spring constant k and the good cell ratio according to a second embodiment. As shown in FIGS. 20, part(a) and 20, part(b), both the density d and the spring constant k positively correlate with the good cell ratio. Accordingly, for evaluation of the cell population C1, it can be understood that the spring constant k is sensitive and the reliability as an index is high.

FIG. 21 is a graph showing the relationship between the density d and the spring constant k in vivo according to the second embodiment. Since the density d and the spring constant k strongly, positively correlate with each other, it shows that the spring constant k can be used in a manner analogous to that of the density d, in evaluation of the cell population C1 including corneal endothelial cells.

FIG. 22 is a graph showing the relationship between the density d and the average distance r₀in vivo according to the second embodiment. As shown in FIG. 22, since the density d and the average distance r₀strongly, positively correlate with each other, it shows that the average distance r₀can be used in a manner analogous to that of the density d, in evaluation of the cell population C1 including corneal endothelial cells.

FIG. 23 shows the relationships between in vitro results according to the first embodiment and in vivo results according to the second embodiment. FIG. 23, part(a) is a graph showing the relationship between the density d in vitro according to the first embodiment and the density d in vivo according to the second embodiment. FIG. 23, part(b) is a graph showing the relationship between the spring constant k in vitro according to the first embodiment and the density d in vivo according to the second embodiment. FIG. 23, part(c) is a graph of a result of an ROC analysis where the density d in vitro according to the first embodiment is adopted as a variable, and the density d in vivo according to the second embodiment falling below 2000 is true. FIG. 23, part(d) is a graph of a result of an ROC analysis where the spring constant k in vitro according to the first embodiment is adopted as a variable, and the density d in vivo according to the second embodiment falling below 2000 is true.

As shown in the coefficient of determination and the area under the ROC curve illustrated in FIGS. 23, part(a) to 23, part(d), it shows that the spring constant k has an achievement equivalent to that of the density d. Accordingly, it shows that by using the spring constant k in vitro according to the first embodiment, the density d in vivo according to the second embodiment can be predicted at an accuracy equivalent to that using the density d. That is, it shows that the spring constant k is useful.

The ROC (Receiver Operating Characteristics) analysis is a concept of signal processing. In a case of dichotomy between normality and abnormality using a certain variable, it serves as a measure of classification accuracy of the variable. For example, a case is discussed where a group to be tested is dichotomized into positive and negative using a numerical value obtained from a result of a certain test. In a case where a certain threshold is introduced into the test numerical value, when the value equal to or more than the threshold is determined to be positive and the value less than the threshold is determined to be negative, the ratio of correctly supplementing true reactors as positives (sensitivity), and the ratio of correctly supplementing true non-reactors as negatives (specificity) are obtained. While the threshold is monotonically changed as a parameter, the false-positive rate (=1-specificity) is plotted on the abscissa, and the sensitivity is plotted on the ordinate, a curve is obtained (ROC curve). At this time, the area under the curve can have a value ranging from zero to one, inclusive. As the area under the curve is closer to one, the used variable has a performance of more correctly dichotomizing the group to be tested.

The evaluation unit 12 executes an ROC analysis process of performing the ROC analysis with indices including at least any one of the average distance r₀, the spring constant k and the hexagonal order parameter Q₆being adopted as variables. That is, the ROC analysis process is executed by the evaluation unit 12 with the indices being variables, thereby performing the ROC analysis (ROC analysis step). Accordingly, the indices can be evaluated using the ROC analysis.

FIG. 24 shows states of corneal endothelial cells of 12 patients after corneal transplant. FIG. 24, part(a) is a graph showing the relationship between the density d and time. FIG. 24, part(b) is a graph showing the relationship between the density d at the six-month time point and the density d at the 24-month time point. FIG. 24, part(c) is a graph showing the relationship between the spring constant k at the six-month time point and the density d at the 24-month time point. FIG. 24, part(d) is a graph of an ROC curve of a case with the density d at the 24-month time point equal to or less than 1000, the case being determined with the density d at the six-month time point. FIG. 24, part(e) is a graph of an ROC curve of a case with the density d at the 24-month time point equal to or less than 1000, the case being determined with the spring constant k at the six-month time point. In FIG. 24, part(a), the transition of the density d is represented by a scatter plot and a box-whisker plot.

As shown in FIG. 24, part(a), at the three-month time point, there is no difference between the densities d of all the patients. However, at the 24-month time point, the densities d of some patients significantly decrease. As shown in FIG. 24, part(b), the density d at the six-month time point and the density d at the 24-month time point do not correlate with each other. As shown in FIG. 24, part(c), the spring constant k at the six-month time point and the density d at the 24-month time point weakly correlate with each other. That is, it shows that at the six-month time point, use of the spring constant k instead of the density d can more correctly predict the density d at the 24-month time point.

Meanwhile, as a result of the ROC analysis, as illustrated in FIG. 24, part(d), it shows that in a case where the density d at the six-month time point is used as a variable, the area under the curve is small, and the sensitivity for cell population evaluation is low. As shown in