Optimal design of illuminant for improving intraoperative color appearance of organs

Abstract

When surgeons evaluate the condition of organs and make diagnoses, color difference is an important information despite its subtleness. Yielding clearer views of blood circulation holds the key to successful surgeries such as transplants and anastomosis. Optimization of surgical illuminant is one approach to clearer views. Our previous study focused on computer simulation to enhance color difference. In the present study, we improved the simulation method by applying a color appearance model CIECAM02 and we realized an optimized illuminant based on the simulation. In an evaluation experiment comparing the optimal illuminant with the conventional illuminant, 14 LEDs fixed to the light unit were spectrally adjusted to demonstrate the two illuminants. Using a rat cecum, we observed the color differences under two conditions: normal blood flow and restricted blood flow. The color difference under the optimal illuminant was greater than under the conventional illuminant and the effectiveness of the optimal illuminant was confirmed.

Appendix: formula of CIECAM02

As a first step to calculate color difference, tri-stimulus values were modified to the CAT 02 space, R, G, B, which is one of the color uniformity spaces, and written as follows:

$$\begin{aligned} \left[ {\begin{array}{*{20}{c}} R \\ G \\ B \end{array}} \right] & ={M_{{\text{CAT}}02}}\left[ {\begin{array}{*{20}{c}} X \\ Y \\ Z \end{array}} \right], \\ {M_{{\text{CAT}}02}} & =\left[ {\begin{array}{*{20}{c}} {0.733}&{0.430}&{ - 0.162} \\ { - 0.704}&{1.698}&{0.0061} \\ {0.003}&{0.0136}&{0.983} \end{array}} \right]. \\ \end{aligned}$$

(4)

The D factor for adaption degree is defined as follows:

$$D~=~F~\left[ {1 - \frac{1}{{3.6}}{e^{\left( {\frac{{ - \left( {{L_A}+42} \right)}}{{92}}} \right)}}} \right].$$

(5)

The adaption luminance ${L_{\text{A}}}$ is defined as illumination luminance divided by 5$\pi$. In this paper, we set ${L_A}={\text{20,000}}~{\text{lx}}$ and $F=1$. Then D is given by 0.87. Using the CAT02 uniform space value and the D factor, we define the full chromatic adaption transform as follows:

$$\begin{gathered} {R_{\text{C}}}~=\left[ {\left( {{Y_{\text{W}}} \cdot D/{R_{\text{W}}}} \right)+\left( {1 - D} \right)} \right]R \hfill \\ {G_{\text{C}}}~=\left[ {\left( {{Y_{\text{W}}} \cdot D/{G_{\text{W}}}} \right)+\left( {1 - D} \right)} \right]G \hfill \\ {B_{\text{C}}}~=\left[ {\left( {{Y_{\text{W}}} \cdot D/{B_{\text{W}}}} \right)+\left( {1 - D} \right)} \right]B. \hfill \\ \end{gathered}$$

(6)

where ${R_{\text{W}}},\;{G_{\text{W}}},\;{B_{\text{W}}}$ are CAT02 values of illumination. The full chromatic adaption values are converted to the Hunt–Pointer–Estevez space before the post-adaption nonlinear response compression as follows:

$$\begin{aligned} \left[ {\begin{array}{*{20}{c}} {{R^{\prime} }} \\ {G^{\prime} } \\ {B^{\prime} } \end{array}} \right] & ={M_{{\text{HPE}}}}{M_{{\text{CAT}}02}}^{{ - 1}}\left[ {\begin{array}{*{20}{c}} {{R_C}} \\ {{G_C}} \\ {{B_C}} \end{array}} \right] \\ {M_{{\text{HPE}}}} & =\left[ {\begin{array}{*{20}{c}} {0.390}&{0.689}&{ -\,0.0787} \\ { -\,0.230}&{1.183}&{0.0464} \\ {0.000}&{0.000}&{0.000} \end{array}} \right] \\ {M_{{\text{CAT}}{{02}^{-1}}}} & =\left[ {\begin{array}{*{20}{c}} {1.01}&{ -\,0.279}&{0.183} \\ {0.454}&{0.474}&{0.0721} \\ { -\,0.00927}&{ -\,0.00570}&{1.02} \end{array}} \right]. \\ \end{aligned}$$

(7)

For nonlinear compression, parameters k, ${F_L}$, n, and ${N_{bb}}$ which are related to the surrounding environment are calculated using the following formulae:

$$\begin{aligned} k & =1/\left( {5{L_{\text{A}}}+1} \right) \\ {F_{\text{L}}} & =0.2{k^4}\left( {5{L_{\text{A}}}} \right)+0.1{\left( {1 - {k^4}} \right)^2}{\left( {5{L_A}} \right)^{1/3}} \\ n & ={Y_{\text{b}}}/{Y_{\text{w}}} \\ {N_{{\text{bb}}}} & ={N_{{\text{cb}}}}=0.7125{\left( {1/n} \right)^{0.2}}. \\ \end{aligned}$$

(8)

Using these parameters, we express the nonlinear compression as follows:

$$\begin{aligned} {R^\prime }_{a} & =\frac{{400{{\left( {{F_L}{R^\prime }/100} \right)}^{0.42}}}}{{27.13+{{\left( {{F_L}{R^\prime }/100} \right)}^{0.42}}}}+0.1 \\ {G^\prime }_{a} & =\frac{{400{{\left( {{F_L}{G^\prime }/100} \right)}^{0.42}}}}{{27.13+{{\left( {{F_L}{G^\prime }/100} \right)}^{0.42}}}}+0.1 \\ {B^\prime }_{a} & =\frac{{400{{\left( {{F_L}{B^\prime }/100} \right)}^{0.42}}}}{{27.13+{{\left( {{F_L}{B^\prime }/100} \right)}^{0.42}}}}+0.1. \\ \end{aligned}$$

(9)

Preliminary Cartesian coordinates a, b are calculated to obtain hue angle h:

$$\begin{aligned} a & =R_{{\text{a}}}^{\prime } - 12G_{a}^{\prime } - 2B_{a}^{\prime }~/~11 \\ b~ & =\left( {1/9} \right)\left( {R_{{\text{a}}}^{\prime }+G_{{\text{a}}}^{\prime } - 2B_{{\text{a}}}^{\prime }} \right) \\ h & =~{\tan ^{-1}}\left( {b/a} \right). \\ \end{aligned}$$

(10)

The achromatic response A is defined as follows:

$$A=\left[ {2R_{{\text{a}}}^{\prime }+\left( {1/20} \right)B_{{\text{a}}}^{\prime } - 0.305} \right]{N_{{\text{bb}}}}.$$

(11)

Using these values, we calculate target lightness J under the illuminant as follows:

$$J=100{\left( {A/{A_{\text{W}}}} \right)^{c\left( {1.48+\sqrt n } \right)}},$$

(12)

where ${A_{\text{W}}}$ is the achromatic response of the illuminant. In this paper, we set c to 0.69 corresponding to an average environment. The chroma value C and the colorfulness value M are calculated as follows:

$$\begin{aligned} C & ={t^{0.9}}\sqrt {J/100} {\left( {1.64 - {{0.29}^n}} \right)^{0.73}} \\ t & =~\frac{{\left( {50000/13} \right){N_c}{N_{cb}}{e_t}{{\left( {{a^2}+{b^2}} \right)}^{1/2}}}}{{R_{Z}^{\prime }+G_{Z}^{\prime }+\left( {21/20} \right)B_{Z}^{\prime }}} \\ M & =CF_{L}^{{0.25}}. \\ \end{aligned}$$

(13)

The parameters for coefficients values, ${c_1}$, ${c_2}$, and ${K_L}$, are defined as uniform color space values: ${c_1}=0.007,\;{c_2}=0.0228,\;{K_L}=1.00$. Color differences by CIECAM02 are defined as follows:

$$\begin{gathered} {J^\prime }~=\frac{{\left( {1+100{c_1}} \right)J}}{{1+{c_1}J}} \hfill \\ {a_M}^{\prime }={M^\prime }\cos \left( h \right) \hfill \\ {b_M}^{\prime }=M{~^\prime }\sin \left( h \right) \hfill \\ {M^\prime }=\left( {1/{c_2}} \right)\ln \left( {1+{c_2}M} \right). \hfill \\ \end{gathered}$$

(14)

Color difference value in the CIECAM02 color appearance model is defined using lightness value J′ and Cartesian coordinates ${a_M}^{\prime }$, ${b_M}^{\prime }~$as follows:

$$\Delta {E^\prime }={({(\Delta {J^\prime }/{K_L})^2}+\Delta {a^\prime }_{M}+\Delta {b^\prime }_{M})^{1/2}}.$$

(15)