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Research Papers

# Potassium Titanyl Phosphate Laser Tissue Ablation: Development and Experimental Validation of a New Numerical Model

[+] Author and Article Information
Hossam Elkhalil

Department of Biomedical Engineering, University of Minnesota, Minneapolis, MN 55455; Department of Biomedical Engineering, Jordan University of Science and Technology, Irbid, 21110, Jordan

Taner Akkin

Department of Biomedical Engineering, University of Minnesota, Minneapolis, MN 55455

John Pearce

Department of Electrical and Computer Engineering, University of Texas, Austin, TX 78712

John Bischof1

Department of Biomedical Engineering, University of Minnesota, Minneapolis, MN 55455; Department of Mechanical Engineering and Urologic Surgery, University of Minnesota, Minneapolis, MN 55455bischof@umn.edu

This condition is satisfied when the optical penetration depth ($δ=1/μa$) is much larger than the heat penetration depth during the laser pulse ($Lon=4αton$), where ton is the laser pulse duration.

Muscle protein denaturation is a complex endothermic kinetic process, which can act as a heat sink during tissue heating. This process is represented by an excess specific heat Cp ex which can be integrated to yield the latent heat of denaturation [40-41]. In order to assess the importance of this latent heat as a heat sink, a comparison with collagen denaturation was made. Specifically, during collagenous tissue heating, the latent heat of denaturation had only a small effect (1 to 2 °C) on the temperature profiles [40]. Since the latent heat is 8.66 mJ/kg for collagen and is only 2.85 mJ/kg for muscle, we therefore elected to neglect the latent heat of denaturation in our model.

Tissue fragmentation experimentally observed in our study indicated an explosive laser-tissue interaction process; therefore, the high fluence region was used for the Eab calculation.

Assuming that the optical penetration depth of the CO2 laser is 20 μm, the power densities at the tissue surface are between 1.25 and 3.5 × 109  W/cm3 . Similarly, taking the optical penetration depth of the KTP laser as 1000 μm, the volume power density at the surface is about 8 × 107  W/cm3 . Since our laser pulse duration was on the order of 100 ns, which is one order of magnitude smaller than the 2 μs CO2 laser pulse, this two orders of magnitude decrease in the power density will still be enough to induce phase explosion.

1

Corresponding author.

J Biomech Eng 134(10), 101002 (Oct 01, 2012) (13 pages) doi:10.1115/1.4007452 History: Received February 17, 2012; Revised August 03, 2012; Posted September 27, 2012; Published October 01, 2012; Online October 01, 2012

## Abstract

The photoselective vaporization of prostate (PVP) green light (532 nm) laser is increasingly being used as an alternative to the transurethral resection of prostate (TURP) for treatment of benign prostatic hyperplasia (BPH) in older patients and those who are poor surgical candidates. In order to achieve the goals of increased tissue removal volume (i.e., “ablation” in the engineering sense) and reduced collateral thermal damage during the PVP green light treatment, a two dimensional computational model for laser tissue ablation based on available parameters in the literature has been developed and compared to experiments. The model is based on the control volume finite difference and the enthalpy method with a mechanistically defined energy necessary to ablate (i.e., physically remove) a volume of tissue (i.e., energy of ablation Eab ). The model was able to capture the general trends experimentally observed in terms of ablation and coagulation areas, their ratio (therapeutic index (TI)), and the ablation rate (AR) (mm3 /s). The model and experiment were in good agreement at a smaller working distance (WD) (distance from the tissue in mm) and a larger scanning speed (SS) (laser scan speed in mm/s). However, the model and experiment deviated somewhat with a larger WD and a smaller SS; this is most likely due to optical shielding and heat diffusion in the laser scanning direction, which are neglected in the model. This model is a useful first step in the mechanistic prediction of PVP based BPH laser tissue ablation. Future modeling efforts should focus on optical shielding, heat diffusion in the laser scanning direction (i.e., including 3D effects), convective heat losses at the tissue boundary, and the dynamic optical, thermal, and coagulation properties of BPH tissue.

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## Figures

Figure 14

Schematic diagram clarifying the laser beam shape and divergence. The left panel shows a beam at the fiber tip that has a beam radius of R1 ; this radius changes to R2 , which depends on the value of the beam divergence angle (θ) when the beam travels a distance WD along the optical axis. The right panel shows the launch radial position of the photon (r1 ) and the laser intensity profile at the fiber tip. When the laser beam diverges, the radial photon position becomes r2 and the laser intensity profile expands.

Figure 9

Ablation rate (AR = ablation area/scanning speed) measured by the experiment and the model at scanning speeds (SSs) of 0.5, 1, 2, and 4 mm/s and working distances (WDs) of (a) 0, (b) 2, and (c) 5 mm. The experimental data are represented as mean ± SD. The number of samples used was n = 5.

Figure 15

Laser intensity calculated for a diverged laser beam over WD = 4 mm using the actual Gaussian beam determined based on Eq. 2 and the simulated photon energy distribution based on Eqs. 9,10,11

Figure 10

Intensity profile of the laser beam at (a) a working distance (WD) = 10 mm, and (b) at a working distance (WD) = 20 mm

Figure 11

Laser beam spot radius measured by Eq. 1 versus the working distance (WD). The data at the higher WD was linearly fitted with R2  > 0.99.

Figure 12

Flow chart showing the Monte Carlo simulation (MC) setup that was used in our model. The MC simulation involved launching N photons whose positions depended on the divergence angle and the beam shape. Energy deposition was calculated at the new photon position, and the Roulette concept was applied to properly terminate photons [35].

Figure 1

(a) Schematic diagram showing the experimental setup for the in vitro tissue ablation with laser fiber scanning in the y direction at different working distances (WDs) and scanning speeds (SSs). (b) Schematic diagram showing the induced wounds and a middle point cross section that was used to analyze and assess the ablation outcome. The black region represents the ablated (removed) tissue and the white region represents the coagulated tissue.

Figure 2

Schematic diagram of the computational model showing the model components and its inputs and outputs

Figure 3

(a) 3-D domain and control volume setup, and (b) 2-D domain and control volume setup

Figure 4

Digital images of cross section (left panel) and top section (right panel) views for a laser induced wound showing ablation and coagulation areas

Figure 5

Ablation depth per pulse (mm) as a function of the natural logarithm of the laser fluence per pulse (J/mm2 ) of porcine skin. The data were calculated based on the mass loss data obtained from Ref. [43]. The slopes of the fitting correspond to two mass loss mechanisms: desiccation and ablation.

Figure 6

Ablation areas measured by the experiment and the model at scanning speeds of 0.5, 1, 2, and 4 mm/s and working distances of (a) 0, (b) 2, and (c) 5 mm. The experimental data are represented as mean ± SD. The number of samples used was n = 5.

Figure 7

Coagulation areas measured by the experiment and the model at scanning speeds of 0.5, 1, 2, and 4 mm/s and working distances of (a) 0, (b) 2, and (c) 5 mm. The experimental data are represented as mean ± SD. The number of samples used was n = 5.

Figure 8

Therapeutic index (TI = ablation area/coagulation area) measured by the experiment and the model at scanning speeds (SSs) of 0.5, 1, 2, and 4 mm/s and working distances (WDs) of (a) 0, (b) 2, and (c) 5 mm. The experimental data are represented as mean ± SD. The number of samples used was n = 5.

Figure 13

Schematic diagram showing the divergence angle (θ) and the azimuthal angle (Ψ)

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