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

Liu Qimeng; Huang Jun; Wang Kehong; Zhou Qi

doi:10.3788/CJL201845.0807002

Journals >Chinese Journal of Lasers >Volume 45 >Issue 8 >Page 807002 > Article

Chinese Journal of Lasers
Vol. 45, Issue 8, 807002 (2018)

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

Liu Qimeng, Huang Jun^*, Wang Kehong, and Zhou Qi

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[in Chinese]

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DOI: 10.3788/CJL201845.0807002 Cite this Article Set citation alerts

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 Copy Citation Text

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Fig. 1. (a) In vitro biological tissue test sample; (b) experimental setup

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Fig. 2. (a) Measuring peak temperature of incision; (b) measuring tensile strength

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Fig. 3. Peak temperature changing curve of sample during welding

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Fig. 4. Tensile strength dispersion map

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Fig. 5. Peak temperature dispersion map

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Fig. 6. (a) Three-dimensional surface map and (b) contour map showing the effects of laser power and spot movement speed on tensile strength

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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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Weldingparameter	Encodingvalue	Coding level
Weldingparameter	Encodingvalue	-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 1. Horizontal coding and real value table of laser welding parameters

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 2. Experimental laser welding parameters and results

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

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