Mathematical models of laser-induced tissue thermal damage

Figures & data

Table I.  Collected kinetic coefficients for representative thermal damage processes.

	Process parameters
Process	A (s^−1)	Ea (J mole^−1)	RCEM	Tcrit (°C)	Notes
Collagen changes
Maitland [35]	1.77 × 10^56	3.676 × 10^5		68.2	Rat tail birefringence
Pearce [34]	1.61 × 10^45	3.06 × 10^5		80.4	Rat skin birefringence
Aksan [77]	1.136 × 10^86	5.623 × 10^5		68.1	Rabbit patellar tendon
Miles [78]	6.658 × 10^79	5.21 × 10^5		67.8	Rat tail tendon, DSC
Chen [55–57]	1.46 × 10^66	4.428 × 10^5		76.4	Shrinkage, bovine chordae tendineae
Muscle
Jacques [79]	2.94 × 10^39	2.596 × 10^5	0.732	70.4	Myocardium whitening
Pearce (unpublished)	*4.341 × 10^51	3.365 × 10^5	0.678	67.2	Birefringence loss
Brown [65]	1.98 × 10^106	6.67 × 10^5	0.449	54.6	Microvessels in muscle
Erythrocytes
Lepock [59]	7.6 × 10^66	4.55 × 10^5		82.2	Haemoglobin denaturation
	*1.70 × 10^46	3.04 × 10^5	0.694	70.3	Haemolysis
Przybylska [62]	*1.08 × 10^44	2.908 × 10^5	0.707	71.8	Haemolysis, normal RBCs
	*3.7 × 10^43	2.88 × 10^5	0.708	72.1	Haemolysis, Down's Syndrome
Apoptosis/necrosis
Bhowmick [73]	7.78 × 10^22	1.61 × 10^5	0.824	94.2	H. prostate
McMillan [74]	2.29 × 10^29	1.895 × 10^5	0.797	64.0	Freshly excised tonsil
Cell death
Sapareto [80]	2.84 × 10^99	6.18 × 10^5	0.5	51.4	CHO cells, T > 43°C
Bhowmick [81]	1.66 × 10^91	5.68 × 10^5	0.508	52.1	AT-1 cells < 50°C
	173.5	1.97 × 10^4		186	AT-1 cells > 50°C
Borrelli [82]	2.984 × 10^80	5.064 × 10^5	0.547	55.5	BhK cells
He [83]	4.362 × 10^43	2.875 × 10^5	0.710	71.0	SN12 cells, suspended
	3.153 × 10^47	3.149 × 10^5	0.685	73.1	SN12 cells, attached

*Value for A is estimated from Equation 11(a).

Figure 1. Figurative sketch of actin-myosin geometry that forms the regular structure responsible for the birefringent properties of the sarcomere. (A) Functional sarcomere unit cell (between z-bands). (B) Cross-section in the a-band.

Figure 2. Transient temperatures at the 1σ radius (2.5 mm); at the surface (solid line) and at 2.5 mm depth (lower temperature dashed line).

Table II.  Summary of damage model predictions for the Ho:YAG numerical model example.

	Radius (mm)			Depth (mm)		Damage for T(t) from Figure 2
Process	10%	90%	Δr (mm)	10%	90%	Surface	2.5 mm
CHO cells	5.2	4.4	0.8	Full	4.2	100%	100%
Murine embryoblasts	4.5	4.2	0.3	4.70	3.6	100%	100%
BhK cells	4.7	4.0	0.7	Full	3.4	100%	92%
μVascular	4.5	4.0	0.5	4.5	3.3	100%	88%
Skin burns	4.1	3.6	0.5	3.5	2.8	100%	18%
Muscle birefringence	3.9	3.2	0.7	3.3	2.3	100%	10%
SN12 cells	3.9	3.0	0.9	3.3	2.1	100%	8%
Collagen birefringence	3.1	2.4	0.7	2.1	1.5	70%	0.4%
Apoptosis/necrosis	3.5	2.1	1.4	2.7	1.3	55%	5%
Collagen shrinkage	2.7	1.7*	1.0	1.9	1.0*	40%	0

*Collagen shrinkage at maximum 60%.

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