Modified Beer-Lambert Law for Nd∶YAG Laser Transmission in Blood

Xiaoxi Dong; Yaqun Kong; Huijuan Yin; Weinan Dong; Jizhi Zhao; Jichun Yang

doi:10.3788/LOP202259.0617023

Journals >Laser & Optoelectronics Progress >Volume 59 >Issue 6 >Page 0617023 > Article

Laser & Optoelectronics Progress
Vol. 59, Issue 6, 0617023 (2022)

Modified Beer-Lambert Law for Nd∶YAG Laser Transmission in Blood

Xiaoxi Dong¹, Yaqun Kong², Huijuan Yin¹, Weinan Dong¹, Jizhi Zhao³, and Jichun Yang^1、*

Author Affiliations

¹Institute of Biomedical Engineering, Chinese Academy of Medical Sciences & Peking Union Medical College, Tianjin 300192, China

²Beijing Friendship Hospital, Capital Medical University, Beijing 100050, China

³Peking Union Medical College Hospital, Chinese Academy of Medical Sciences & Peking Union Medical College, Beijing 100730, China

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DOI: 10.3788/LOP202259.0617023 Cite this Article Set citation alerts

Xiaoxi Dong, Yaqun Kong, Huijuan Yin, Weinan Dong, Jizhi Zhao, Jichun Yang. Modified Beer-Lambert Law for Nd∶YAG Laser Transmission in Blood[J]. Laser & Optoelectronics Progress, 2022, 59(6): 0617023 Copy Citation Text

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Fig. 1. Transmitted laser energy detecting system of Nd∶YAG. (a) Schematic diagram of system; (b) principle of detection

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Comparison between theoretical value and real detected value. (a) Relationship between detected depth and target depth; (b) relationship between geometry-dependent factor and detected depth

Fig. 2. Comparison between theoretical value and real detected value. (a) Relationship between detected depth and target depth; (b) relationship between geometry-dependent factor and detected depth

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Fig. 3. Residual analysis of geometry-dependent factor and detected depth by four fitting methods. (a) Linear regression residual; (b) log regression residual; (c) index regression residual; (d) power regression residual

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Fig. 4. Relationship between laser decay and depth in blood

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Blood sort	Proportion in venous blood /%^［22］	$μ_{a}$ /cm^{-1［19，22‐23］}	$μ_{s}^{'}$ /cm^{-1［21，24‐25］}
Oxygenated blood	58.78	3.02	3.41
Deoxygenated blood	41.22	0.28	6.61
Venous blood	‒	1.89	4.73

Table 1. Optical properties of blood

Target thickness /mm	Scale of transferpettor /μL	Theoretical thickness /mm	Detected thickness /mm	Transmitted laser intensity /V	$R_{r e a l}$ /%
0	0	0	0	1.40±0.02	—
1.00	195	0.99	0.95±0.02	0.97±0.09	30.86
1.25	245	1.24	1.15±0.02	0.87±0.04	38.35
1.50	295	1.49	1.37±0.03	0.58±0.03	58.73
1.75	345	1.75	1.65±0.05	0.43±0.02	69.21
2.00	395	2.00	1.87±0.08	0.32±0.06	77.41

Table 2. Selected scales of transferpettor, theoretical thickness and transmitted laser intensity

Name	Formula	a	b	R²
Linear fitting	$G (d) = a d + b$	1.0699	-0.7651	0.9295
Log fitting	$G (d) = a l n d + b$	1.6200	0.2534	0.9139
Index fitting	$G (d) = a e x p (b d)$	0.1902	-0.1024	0.8873
Power fitting	$G (d) = a d^{b}$	0.3808	1.8219	0.6289

Table 3. Parameters and regression decision coefficient for the fitting of geometry-dependent factor

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