Multivariate Nonlinear Regression Model of Laser Fusion in vitro Skin Tissue Incision Performance Based on Response Surface Methodology

Fig. 7. Three-dimensional surface maps and contour maps showing the effects of factor interactions on peak temperature of in vitro skin tissue incision. (a)-(b) Spot movement speed and laser power; (c)-(d) laser frequency and laser power; (e)-(f) laser frequency and spot movement speed

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Fig. 8. Fusion morphology of in vitro skin tissue at optimized parameters. (a) Front view; (b) back view; (c) cross-section

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Table 1. Horizontal coding and real value table of laser welding parameters
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Table 1. Horizontal coding and real value table of laser welding parameters
Weldingparameter Encodingvalue Coding level
-1 0 1
P /W X₁ 3 3.5 4
v /(mm·s^-1) X₂ 150 200 250
F /Hz X₃ 50 100 150

Table 2. Experimental laser welding parameters and results

View table

Table 2. Experimental laser welding parameters and results

Number	X₁	X₂	X₃	σ_b /(N·cm^-2)	T /℃
1234567891011121314151617	0 1 0 1 1 0 0-1-1 0-1 0 1 0 0-1 0	1 0-1 1-1 0 1-1 1 0 0-1 0 0 0 0 0	1-1-1 0 0 0-1 0 0 0-1 1 1 0 0 1 0	38.127.440.229.035.743.637.520.127.744.726.028.844.545.840.422.845.0	49.054.050.053.558.053.549.042.039.853.740.753.356.453.153.540.854.0

Table 3. Variance analysis for the tensile strength of in vitro skin tissue incision

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Table 3. Variance analysis for the tensile strength of in vitro skin tissue incision

Source	Sum of squares	Degree of freedom	Mean square	F value	p-value (P'>F)	Source
Model	1081.59	9	120.18	8.170	0.0056	Significant
X₁	200.00	1	200.00	13.600	0.0078	Significant
X₂	7.03	1	7.03	0.480	0.5115	-
X₃	1.20	1	1.20	0.082	0.7833	-
X₁X₂	51.12	1	51.12	3.480	0.1045	Significant
X₁X₃	103.02	1	103.02	7.010	0.0331	-
X₂X₃	36.00	1	36.00	2.450	0.1616	-
$\begin{matrix} {X_{1}}^{2} \end{matrix}$	497.96	1	497.96	33.870	0.0007	Significant
$\begin{matrix} {X_{2}}^{2} \end{matrix}$	101.09	1	101.09	6.880	0.0343	Significant
$\begin{matrix} {X_{3}}^{2} \end{matrix}$	34.20	1	34.20	2.330	0.1711	-
Residual	102.93	7	14.70	-	-	-
Lack of fit	85.13	3	28.38	6.380	0.0527	Not significant
Pure error	17.80	4	4.45	-	-	-
Total deviation	1184.52	16	-	-	-	-

Table 4. Variance analysis for peak temperature of in vitro skin tissue incision

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Table 4. Variance analysis for peak temperature of in vitro skin tissue incision

Source	Sum of squares	Degree of freedom	Mean square	F value	p-value (P'>F)	Source
Model	547.15	9	60.79	508.43	<0.0001	Significant
X₁	429.25	1	429.25	3589.86	<0.0001	Significant
X₂	18.00	1	18.00	150.54	<0.0001	Significant
X₃	4.21	1	4.21	35.17	0.0006	Significant
X₁X₂	1.32	1	1.32	11.06	0.0127	Significant
X₁X₃	1.32	1	1.32	11.06	0.0127	Significant
X₂X₃	2.72	1	2.72	22.77	0.0020	Significant
$\begin{matrix} X_{1}^{2} \end{matrix}$	60.56	1	60.56	506.48	<0.0001	Significant
$\begin{matrix} X_{2}^{2} \end{matrix}$	8.76	1	8.76	73.27	<0.0001	Significant
$\begin{matrix} X_{3}^{2} \end{matrix}$	13.53	1	13.53	113.14	<0.0001	Significant
Residual	0.84	7	0.12	-	-	-
Lack of fit	0.41	3	0.14	-	0.4028	Not significant
Pure error	0.43	4	0.11	-	-	-
Total deviation	547.98	16	-	-	-	-

Table 5. Tensile strength and peak temperature response values for single factor effect

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Table 5. Tensile strength and peak temperature response values for single factor effect

Factorencoding value	σ_b /(N·cm^-2)			T /℃
Factorencoding value	P	v	F	P	v	F
-1.00	24.15	31.20	32.77	40.82	50.83	48.43
-0.75	30.35	33.91	34.50	44.39	51.22	49.52
-0.50	35.13	35.92	35.76	47.46	51.39	50.35
-0.25	38.50	37.21	36.56	50.04	51.35	50.92
0	40.46	37.80	36.89	52.12	51.08	51.23
0.25	41.00	37.68	36.75	53.70	50.60	51.28
0.50	40.13	36.86	36.15	54.79	49.89	51.07
0.75	37.85	35.32	35.08	55.38	48.97	50.60
1.00	34.15	33.08	33.55	55.48	47.83	49.87

Table 6. Tensile strength and peak temperature of experimental samples incision
View table
Table 6. Tensile strength and peak temperature of experimental samples incision
Sample number σ_b /(N·cm^-2) T /℃
1 43.9 55.0
2 44.7 54.5
3 42.3 56.3
4 42.1 55.6
5 46.5 55.4
6 43.2 56.0
7 44.1 54.5
8 44.0 56.7
9 42.1 55.3
10 43.5 55.0
Average value 43.6 55.4
Predicted value 44.8 55.3

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Liu Qimeng, Huang Jun, Wang Kehong, Zhou Qi. Multivariate Nonlinear Regression Model of Laser Fusion in vitro Skin Tissue Incision Performance Based on Response Surface Methodology[J]. Chinese Journal of Lasers, 2018, 45(8): 807002

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Paper Information

Category: biomedical photonics and laser medicine

Received: Dec. 11, 2017

Accepted: --

Published Online: Aug. 11, 2018

The Author Email: Jun Huang (huangjun0061@126.com)

DOI:10.3788/CJL201845.0807002

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Horizontal coding and real value table of laser welding parameters

Table 1. Horizontal coding and real value table of laser welding parameters

Table 2. Experimental laser welding parameters and results

Table 2. Experimental laser welding parameters and results

Table 3. Variance analysis for the tensile strength of in vitro skin tissue incision

Table 3. Variance analysis for the tensile strength of in vitro skin tissue incision

Table 4. Variance analysis for peak temperature of in vitro skin tissue incision

Table 4. Variance analysis for peak temperature of in vitro skin tissue incision

Table 5. Tensile strength and peak temperature response values for single factor effect

Table 5. Tensile strength and peak temperature response values for single factor effect

Table 6. Tensile strength and peak temperature of experimental samples incision

Table 6. Tensile strength and peak temperature of experimental samples incision