Computational analysis of endometrial photocoagulation with diffusing optical device.

Computational analysis of endometrial photocoagulation with diffusing optical device Jinhee Kwon,1 Chang-Yong Lee,2,3 Junghwan Oh,1,3 and Hyun Wook Kang1,3,* 1

Department of Biomedical Engineering, Pukyong National University, Busan 608-737, South Korea Department of Mechanical Engineering, Pukyong National University, Busan 608-737, South Korea 3 Center for Marine-Integrated Biomedical Technology, Pukyong National University, Busan 608-737, South Korea * [email protected] 2

Abstract: A balloon-catheter optical diffuser for endometrial treatment was evaluated with computational thermal analysis. Various catheter materials and dimensions were implemented to identify the optimal design for the device. Spatial and temporal development of temperature during 30-sec irradiation of 532-nm light demonstrated thermal insulation effects of polyurethane on temperature increase up to 384 K, facilitating the irreversible denaturation. The current model revealed the degree of thermal coagulation 13% thicker than experimental results possibly due to lack of tissue dynamics and light intensity distribution. In combination with photon distribution, the analytical simulation can be a feasible tool to optimize the new optical diffuser for efficient and safe endometrial treatment. ©2013 Optical Society of America OCIS codes: (000.4430) Numerical approximation and analysis; (120.6810) Thermal effects; (170.1610) Clinical applications; (170.3890) Medical optics instrumentation; (170.4440) ObGyn.

References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

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Received 30 Jul 2013; revised 8 Oct 2013; accepted 8 Oct 2013; published 14 Oct 2013

(C) 2013 OSA 1 November 2013 | Vol. 4, No. 11 | DOI:10.1364/BOE.4.002450 | BIOMEDICAL OPTICS EXPRESS 2450

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1. Introduction Abnormal uterine bleeding (AUB), also called menorrhagia, is a common clinical problem accounting for 12% of all gynecological outpatient referrals in women of reproductive age [1–3]. AUB is typically defined as the cyclical loss of more than 80 ml of blood over general menstruation cycles [1,4]. Potential etiology of AUB includes local pathology such as hormonal imbalance, dysfunction of the ovaries, uterine fibroids, or infection [3,4]. Treatments of AUB have been achieved with various methods including medication, endometrial destruction, and hysterectomy [4–6]. Due to sudden hormonal changes, drug treatment often causes side-effects such as loss of estrogen and dyspareunia, merely providing ephemeral relief [7]. Although hysterectomy has been opted for a definitive global treatment, the procedure is quite costly and causes a lengthy convalescence with psychological effects. Thus, hysterectomy is usually pursued only when either medical therapy or ablative endometrium fails [6,8]. As an alternative treatment to medication and hysterectomy, endometrial destruction techniques have become increasingly popular in gynecology [1]. The aim of the techniques is to specifically coagulate or ablate approximately 3 mm thick endometrial tissue in uterus leading to cell necrosis without any subjacent damage to myometrium [9]. In particular, the second-generation techniques such as thermal balloon endometrial ablation (TBEA) and microwave endometrial ablation have recently been promoted as a safer and less invasive tool than the first-generation techniques of rollerball ablation and transcervical resection that require general anesthesia [4,8–11]. Among the ablative techniques, the TBEA treatment is generally performed under local anesthesia and without direct visualization of the uterus [11]. In addition, the TBEA techniques are associated with many clinical advantages including significantly less trauma, short post-operative length of stay, rapid recovery time, and cost effectiveness [6,9,10]. In order to accomplish less invasive and more efficient endometrial coagulation, various laser wavelengths including 1064 nm, 1320 nm, and 2.12 μm have also been applied as laser-assisted TBEA treatments [12]. Light absorption by the endometrial

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tissue typically gives rise to heat, resulting in permanent thermal damage to the endometrium layer once the tissue temperature reaches around 338 K or above [13,14]. However, highly localized tissue coagulation with these wavelengths was quite difficult to predict the degree of thermal damage in uterine tissue and often require high surgical skills for clinicians to achieve the successful removal of the targeted endometrium [12,15]. In our previous study, a novel balloon-catheter diffusing device was designed and experimentally evaluated in association with visible wavelength 532 nm as a new surgical tool to efficiently and safely treat an endometrial cell layer [13]. Due to high rate of light absorption by the endometrium in uterus, the wavelength showed a capability of rapid tissue coagulation with minimal injury to the peripheral tissue in vitro and in vivo. The design of light diffusion through the fiber also helped induce the uniform distribution of the laser light, facilitating consistent coagulative necrosis [13]. However, the underlying mechanisms of temperature growth and distribution in tissue during photocoagulation are still poorly understood. No analytical approach for endometrial treatment has been conducted particularly with continuous laser irradiation. The appropriate selection of the biocompatible catheter material is also required to overtly define the design specifications of the balloon catheter device and to identify the critical design factors during heat generation and accumulation. Additionally, the degree of tissue thermal denaturation during and after laser irradiation should be evaluated and predicted to ensure the efficacy and safety of the new lase-assisted procedure. In an attempt to enhance the clinical feasibility of endometrial photocoagulation as well as to optimize the new design of a balloon-catheter diffusing optical device, the current study developed a computational thermal model of photocoagulation in endometrial tissue. Spatial and temporal distribution of the temperature field generated during 532-nm laser treatment was evaluated as a function of thermal property and thickness of the catheter material. The physical role of the balloon-catheter during the laser irradiation was assessed to explore whether or not heat accumulation could be augmented. Additionally, the degree of thermal coagulative necrosis was identified with the Arrhenius integral to predict the thermal penetration depth into the irradiated tissue. The simulated results on thermal damage were then compared with the experimental data in association with the balloon-catheter-assisted diffusing optical device in order to validate the current thermal model. 2. Methods Due to high light absorption of uterine tissue with profuse hemoglobin, a visible wavelength of 532 nm was selected to induce photocoagulation for endometrial treatment. The input power was 120 W in a continuous wave (cw) mode, and various irradiation times were tested: 10, 20, and 30 sec. For the uniform delivery of laser light, a 600 μm core diameter fiber was micro-machined with a 30 W CO2 laser [16]. The top image in Fig. 1(a) illustrates the primary light diffusion from the 25 mm distal end of the micro-machined optical fiber. The bottom image in Fig. 1(a) depicts an integrated balloon-catheter device, where the diffusing optical fiber was inserted into. Saline was filled inside the balloon for catheter inflation, and the diameter of the distended balloon-catheter was 30 mm, based upon the preliminary measurements [13]. Although the laser light diffused in all directions, light absorption was assumed to occur at the interface between the balloon-catheter and tissue surface. An optical-thermal-damage model was developed to simulate the spatial and temporal distribution of transient temperature in tissue during laser irradiation by using COMSOL finite-element modeling software (v3.7, COMSOL Inc., Burlington, Massachusetts, USA). The degree of the thermal damage in tissue was evaluated with the temperature distribution after uniform light diffusion. Based upon the design of the integrated balloon-catheter diffusing device (Fig. 1(a); bottom), the geometry of the thermal model was constructed as shown in Fig. 1(b). The 50-mm long integrated device with a 600-μm core diameter diffusing fiber inserted was initially made contact with the targeted tissue. Inside the catheter, saline (at

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room temperature) was filled to distend the balloon catheter up to 15 mm away from the diffusing optical fiber. In turn, laser light diffused through saline environment, reaching the tissue and eventually initiating light absorption. As both device and light propagation were radially symmetric, the tissue geometry was simplified to 2-D (two dimensional) one with cylindrical coordinates (radial r and axial z). The axial length of the fiber for light diffusion was set at 25 mm, and the radial distance between fiber and catheter was 15 mm as the diameter of the catheter was 30 mm. It was assumed that neither saline nor balloon-catheter material absorbed the 532-nm light (i.e. negligible light absorption of less than 4% [13]) and the incident laser power was uniformly distributed (i.e. r- and z-axis) over the inner surface of the catheter. In addition, heat generation was solely limited to the interface between the catheter and tissue surfaces, which yielded a 35-mm long line heat source (along z-axis) in the thermal model (Fig. 1(b)). The thickness of the distended balloon-catheter was assumed to be constant over the tissue surface.

Fig. 1. Diffusing optical fiber for endometrial photocoagulation: (a) image of 25 mm-long micro-machined fiber tip (top) and schematic of balloon catheter-assisted diffusing device (bottom) and (b) geometry of bovine liver model with diffusing light delivery balloon catheter for thermal simulation

Since the optical properties for uterine endometrium at 532 nm were not available, bovine liver tissue with comparable light absorption was utilized instead for the computation study [17]. In fact, based upon hemoglobin spectra [18] and the absorption coefficient of myometrium measured at 630 nm [19], the absorption coefficient for uterine tissue at 532 nm could theoretically be scaled to be around 15.8 cm−1 (i.e. the average value between HbO2 and Hb). In addition, our previous studies (in vitro bovine liver and in vivo caprine uterus [13]) demonstrated the equivalent degree of coagulative necrosis (i.e. 2~3 mm) possibly due to similarly glandular tissue structure and profuse blood vessels. The liver tissue was considered homogeneous and isotropic, and its thickness was set at 30 mm, creating the sufficient physical range for temperature distribution. The effect of the catheter thickness on the peak temperature generation was investigated in order to identify the optimal design for endometrial photocoagulation. The physical role of the balloon-catheter was also assessed by simulating temperature distribution with and without the presence of the catheter. The thermal model solved the time-dependent partial differential equations that were incorporated with nonlinear boundary conditions as well as thermal and optical properties of the tissue and the catheter material. The thermal properties of all the materials used for the current simulation are listed in Table 1.

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Table 1. Thermal properties of materials used in simulation Material

K (W/m·K)

ρ (kg/m3)

c (J/kg·K)

α (m2/s)

Saline

0.63

990

4200

1.53

Liver tissue

0.513

1050

3600

1.36

Polyurethane

0.03

374

1155.1

6.94

Reference

× 10 × 10−7 × 10−8 −7

[20] [17] [21]

The light propagation in liver tissue was described by Beer’s law in a radial direction (i.e. independent of z-axis in Fig. 1(b)). Upon the light absorption by the tissue, the incident optical energy was immediately converted into thermal energy [14,17]. Assuming the uniform generation of heat along the z-axis at the tissue interface, the localized heat source, Qext (W/m3) induced by the laser light in scattering media was expressed as a function of radial position r in cylindrical tissue as follows [22]: Qext (r ) =

μa P0 As

exp (− μa + μ s' ) ⋅ r 

(1)

where P0 (W) was the incident laser power on tissue, As (m2) the active surface area of the catheter, μa (cm−1) the absorption coefficient, and μs' (cm−1) the reduced scattering coefficient of the liver tissue. Despite that the laser light diffused out in all directions, heat generation occurred only at the tissue interface (Fig. 1(b)). Thus, P0 represented the radiant power solely penetrating through the active surface area of the catheter, As (i.e. 0.003 m2 = 2π × 15 mm × 35 mm) that made contact merely with the tissue surface, by disregarding the top and bottom hemispheres of the catheter (i.e. P0 = 76% × input laser power of 120 W). Both absorption and reduced scattering coefficients for the bovine liver were assumed to be constant during laser-induced heat accumulation [17]. Spatial and temporal responses of the temperature generated in tissue were governed by the bio-heat transfer equation [17,23]. Due to in vitro test conditions and negligible metabolic heat compared to the laser-induced heat, neither heat gain from metabolism nor convective cooling due to blood perfusion was assumed. All of thermal and mechanical properties of the tissue were also assumed to be constant. Therefore, the governing equations were rewritten in the Laplace form for a cylindrical model with symmetry in both tissue and catheter as follows [23,24]:

( ρ c) L

∂TL 1 ∂  ∂T = kL r L  ∂t r ∂r  ∂r

( ρ c)C

 ∂  ∂TL  + ∂z  k L ∂z  

∂TC 1 ∂  ∂T = kC r C  r ∂r  ∂t ∂r

  + Qext 

 ∂  ∂TC   + ∂z  kC ∂z    

(2)

(3)

where the subscripts L and C represent liver tissue and catheter, ρ (kg/m3) is the density, c (J/kg·K) the specific heat at constant pressure, T (K) the temperature dependent on time and position, t (sec) time, and k (W/m·K) the thermal conductivity. The initial condition was T(r, z, 0) = 293 K, and the external surface of the tissue was insulated (i.e. Neumann boundary condition: n ⋅ k ⋅∇T = 0 where n is the normal direction of the heat flux). The rate process of thermal damage in liver tissue was mathematically estimated by chemical reaction theory. As damage represents a decrease in critical concentration of tissue chemical components, the transformation rate into coagulated state can be described by the Arrhenius integral [17,22]. Then, the dimensionless parameter indicative of the level of damage, Ω was rewritten from the Arrhenius integral as follows: #194563 - $15.00 USD



τp  − Ea  Ω (r , t ) = Af  exp   dt 0  R ⋅ T (r , t ) 

(4)

where Af (1/s) is the frequency factor, Ea (J/mol) the denaturation activation energy, R (J/mol·K) the universal gas constant of 8.314, T (K) the absolute temperature in tissue, and τp (sec) the duration of photocoagulation, which was 30 sec for the damage model. Ω = 1 represents the irreversible thermal damage that occurred in tissue with its corresponding temperature of approximately 338 K [22–25]. The values of optical properties at 532 nm and rate constants for the liver tissue used in the current model were listed in Table 2 [17,25]. Table 2. Values of parameters used for thermal damage model Parameter

Value

References

Absorption coefficient (μa, cm−1)

10.9

[17]

Reduced scattering coefficient (μs', cm−1)

11.9

Frequency factor (Af, 1/s) Activation energy (Ea, J/mol) Universal gas constant (R, J/mol·K)

7.39

[17]

× 10 × 105

2.577

8.314

−39

[25] [25] [25]

To validate the current thermal damage model with coagulation lesions, in vitro laser experiments were performed with liver tissue and a diffusing optical fiber. Figure 2 shows a schematic diagram of the experimental set-up. Initially, a 10-mm thick liver specimen was prepared from a slaughter house and placed in a cylindrical tissue holder (7 cm in diameter) representative of a human uterus. According to the simulation results, polyurethane material was found to be optimal for experimental validations. A 0.5-mm thick layer of polyurethane catheter was superimposed over the tissue surface to identify the effect of thermal insulation on tissue temperature. The holder was entirely submerged in saline maintained at approximately 293 K in order to emulate the balloon-catheter distended with saline. A customized 532-nm laser was implemented for 30-sec laser photocoagulation, and the input power of 120 W was delivered through a diffusing optical fiber with the average irradiance of 2.8 W/cm2. The fiber tip was placed 15 mm above the tissue surface to mimic the distended balloon-catheter with a radius of 15 mm. The thickness of the catheter was approximately 0.5 mm, based upon the simulation results.

Fig. 2. In vitro experimental set-up with diffusing optical fiber for validating computational model of endometrial photocoagulation (L: lens, M: mirror, and AO: acousto-optic)

Ten specimens of the liver tissue were tested (N = 10). Post-experimentally, the coagulated tissue was cross-sectioned and imaged, and the radial depth (i.e. into the tissue) of the tissue coagulation was measured ten times for each tissue with image processing software (Image J, National Institute of Health, MD, USA). Discoloration of the liver tissue corresponded to irreversible tissue denaturation during photocoagulation. A two-tailed Student’s t-test was performed for analysis with statistical significance when p < 0.05.

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3. Results

Figure 3 exhibits the physical correlation of catheter thickness with the peak temperature generated at the polyurethane catheter-tissue interface after 30-sec laser irradiation. It should be noted that 0 mm thickness represents no catheter case and saline at room temperature was assumed to surround both the optical diffuser and the tissue surface. The peak temperature initially increased with the thickness, but the corresponding peak temperature became saturated as the catheter thickness approached around 0.5 mm. Approximately 384 K of the peak temperature was invariably maintained with the catheter thickness increasing from 0.5 to 1 mm. Therefore, a 0.5-mm layer of polyurethane was considered optimal for the balloon catheter, which was selected and utilized for the rest of the numerical calculations.

Fig. 3. Effect of polyurethane catheter thickness on peak temperature generation at tissue interface

Figure 4 displays the transient temperature distribution during 30-sec irradiation. Each color represents an isothermal region, and the diffusing optical fiber was positioned at r = 0 mm. The laser-induced temperature was originated from the catheter-tissue interface (i.e. outer black line), and the resultant heat diffusion radially and uniformly proceeded to the saline, catheter, and tissue respectively (i.e. top and 3D views in Fig. 4(a)). Due to the geometrical symmetry, the cross-sectional view of the model was captured progressively at three different irradiation times in Fig. 4(b). After 30 sec, the peak temperature of the liver tissue reached 384 K whereas that of the saline-catheter interface merely approached 306 K. White arrows represent the direction of conductive heat flux during heat accumulation (along r-axis), indicating that the uniform temperature was developed along the area where the tissue was irradiated (i.e. 35 mm line heat source along z-axis). The thermal penetration depth radially into the tissue was 1.5 fold, compared with that into the saline (i.e. 7.3 mm for tissue vs. 4.8 mm for saline).

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Fig. 4. Spatial distribution of temperature during 30-sec photocoagulation assisted with polyurethane catheter: (a) top and three-dimensional views of temperature distribution at tissue-catheter interface after 30 sec and (b) cross-sectional view (along z-axis) of temperature increase and heat flux propagation at various irradiation times. Note that a color legend is on the right side.

Figure 5 presents the spatial distribution of temperature without (Fig. 5(a)) and with a 0.5mm thick polyurethane balloon-catheter (Fig. 5(b)) for three irradiation times. Red dashed, green dotted, and blue solid lines corresponds to 10, 20, and 30 sec respectively. A gray dotted line in the middle of each graph shows the tissue surface where the laser-induced heat was generated. In the case of no catheter applied (i.e. saline), the maximum tissue temperature reached up to 350 K (after 30 sec irradiation), and the temperature was almost symmetrically distributed in a radial direction (r-axis), in that both saline and liver tissue had almost equivalent thermal properties (Table 1). On the other hand, with the catheter applied, the maximum temperature dramatically increased up to 384 K, and three distinct temperature regions existed, corresponding to each material. The temperature inside the tissue exponentially decreased in a radial distance whereas a sharp temperature decline occurred within the catheter from 384 K to 306 K. Thus, saline showed a relatively slower temperature decrease along r-axis in comparison with the tissue region.

Fig. 5. Spatial and temporal distribution of temperature as function of various irradiation times (10, 20, and 30 sec): (a) without and (b) with polyurethane balloon catheter. Note that radial distance represents the direction of r-axis and the dotted lines indicate the tissue surface.

Figure 6(a) demonstrates the temporal development of temperature along the z-axis (i.e. fiber axis) with the presence of a polyurethane catheter on tissue. Red dashed, green dotted, and blue solid lines represent different irradiation times of 10, 20, and 30 sec respectively. Primarily, rapid temperature increase was initiated at a rate of 5.5 K/sec, maintaining the constant peak temperature of 348 K along the entire heat source. However, the increase rate gradually decreased with irradiation time down to 1.6 K/sec in association with an around

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10% narrower region of the constant peak temperature. Both proximal and distal ends of the heat source induced the rapid temperature reduction due to their boundary conditions. Figure 6(b) shows the temperature variations at four different locations: tissue interface (red hollow rhombus; interface between tissue and catheter), 1 mm in tissue (cyan solid square; 1 mm away from the tissue-catheter interface into tissue), saline interface (green hollow circle; interface between saline and catheter), and 1 mm in saline (blue asterisk; 1 mm away from the saline-catheter interface into saline). The temperature changes took place during and after 30sec laser irradiation, and the temperature of each point was measured from the middle of the heat source. Overall, each temperature was modulated with the laser irradiation. The temperatures for tissue interface and 1 mm in tissue promptly increased during the irradiation but exponentially decreased once the irradiation ended. The average temperature increase during 30 sec irradiation for tissue interface was approximately 1.7 fold (i.e. 3 K/s for tissue interface vs. 1.8 K/s for 1 mm in tissue) On the other hand, the temperatures for saline interface as well as 1 mm in saline showed the minimal increase of up to 13 K (i.e. temperature of 306 K) even during and after the irradiation, indicating that a substantial temperature drop existed within the balloon-catheter situating between the saline and tissue.

Fig. 6. Computation of temperature increase: (a) axial distribution (along z-axis) of temperature at catheter-tissue interface for various irradiation times and (b) transient temperature changes during and after photocoagulation at various locations

The laser-induced temperature was compared with its corresponding thermal coagulation in tissue (Fig. 7). Based upon the accumulated temperature after 30-sec irradiation (Fig. 7(a)), the Arrhenius integral was calculated to identify the physical extent of irreversible thermal damage occurring in tissue where Ω = 1. Figure 7(b) presents various iso-surfaces of thermal denaturation corresponding to the temperature map in Fig. 7(a), and the coagulated lesion was rather radially extended into the tissue. Figure 7(c) shows a magnified image captured from the areas partially including saline, catheter, and tissue in Fig. 7(b). The thickness of the simulated coagulative necrosis, defined by Ω = 1, was measured to be 2.3 ± 0.3 mm (i.e. top in Fig. 7(c); ten measurements along the surface) with the corresponding temperature of approximately 338 K. In vitro validation tests also confirmed the comparable extent of coagulation lesions in the tissue. (i.e. bottom in Fig. 7(c)). Damage was defined as discoloration of the liver tissue, indicative of the complete thermal denaturation whereas red color represents the intact tissue. After 30-sec irradiation, thermal damage was uniformly created inside the tissue, and slight (less than 150 μm thick) carbonization was visually observed at the catheter-tissue interface. Based upon the discolored lesions, the laser-assisted coagulation thickness measured from all the samples was estimated to be 2.6 ± 0.2 mm, which was 13% thicker than the simulated result (p = 0.02).

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Fig. 7. Thermal effect of 30-sec photocoagulation with polyurethane balloon catheter: (a) peak temperature map, (b) corresponding thermal damage with log10 of Arrhenius integral, and (c) comparison between simulated thermal coagulation (Ω = 1; top) and experimental result (bottom)

4. Discussion

The goal of this study was assessment of spatiotemporal temperature distribution and evaluation of potential design improvements for endometrial photocoagulation assisted with a balloon-catheter diffusing optical device. The primary focus of the computational model was the estimation of laser-induced coagulative necrosis below vaporization threshold in order to comprehend the photocoagulation process and to ensure the safety of the endometrial treatment. In turn, the end-point of irreversible thermal denaturation was determined by the coagulation threshold estimated solely with the Arrhenius value (Ω = 1) corresponding to the temperature at around 338 K. Apparently, no thermal confinement occurred during the laser treatment, in that the laser irradiation time (order of seconds in continuous mode) was excessively longer than thermal relaxation time (i.e. τth = 1/4α·(μa + μs) = 300 ms) in liver tissue. Thus, light absorption and heat deposition accompanied simultaneous thermal diffusion radially to the peripheral tissue, resulting in relatively steady temperature increase in comparison with the pulsed laser irradiation [14,17]. In addition, as thermal simulation was achieved by heat conduction equations, thermal mapping plainly led to progressive temperature increase in tissue and vividly delineated the margin of thermal lesion in the modeling essentially similar to the experimental results (Fig. 7). The application of a polyurethane layer played a significant role as a thermal barrier in effectively insulating laser-induced heat at the catheter-tissue interface (Fig. 5). It is conceived that the augmented thermal insulation resulted from 45% smaller thermal diffusivity of polyurethane compared to that of saline (i.e. 6.94 × 10−8 m2/s for polyurethane vs. 1.53 × 10−7 m2/s for saline). The lower ratio of dynamic thermal conduction to heat capacity in tissue could lead to the higher rate of heat deposition. The sharp temperature drop along the polyurethane layer (Fig. 5(b)) also evidenced that most of the thermal energy generated during light absorption was substantially confined to the catheter-tissue interface without significant radial heat conduction inside the catheter. In turn, with minimal heat loss to the saline, the accumulated thermal energy inside the polyurethane layer entailed more rapid temperature development in tissue, eventually reaching higher peak temperature (Fig. 6). Accordingly, the superior insulation effect of polyurethane can shorten operation time to

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potentially less than 1 min, which is preferable to surgical gynecologists for AUB treatments [13]. The maximum peak temperature at the catheter-tissue interface was achieved when the catheter thickness became 0.5 mm or above (Fig. 3). A characteristic length scale for temperature elevation in a cylindrical geometry is the thermal diffusion length, lD = 2(ατ)1/2, where τ (sec) is the irradiation time. Based upon the thermal property of polyurethane and 30sec laser irradiation, the calculated thermal diffusion length was 2.9 mm, which is thinner than the optimal catheter thickness from the model. Thus, thermal energy can be mostly accumulated and maintained inside the catheter without substantial conductive loss throughout the medium. During balloon-catheter distention, the catheter should be able to physically tolerate the saline weight as one of the design factors for catheter dimensions [13]. In fact, according to the preliminary measurements, the physical balloon inflation caused a 1 mm thick catheter to thin down to approximately 0.5 mm due to five-fold catheter volume increase. The current findings revealed that the initial catheter thickness could be limited by thermal and mechanical capabilities of the distended catheter during laser treatment. Therefore, the favorable catheter thickness should be carefully estimated and selected in consideration of the internal balloon pressure and size of the balloon-catheter used for photocoagulation.

Fig. 8. Dynamic effects of light scattering: (a) temperature-dependent variations in thermal damage (log10 Ω) and (b) corresponding distribution of temperature and Arrhenius integral

Computational evaluation of coagulation necrosis was conducted with the Arrhenius integral that defines the thermal damage zone in tissue [22,26]. Although both theoretical and experimental coagulation (less than 3 mm) was still safe to protect the myometrium underneath the endometrium (typically 5 mm thick [13]) for maintaining fertility, the degree of experimental thermal injury was more complicated with 13% thicker coagulation zone (Fig. 7(c)). It is conceived that the apparent discrepancy in coagulative necrosis could arise from dynamic variations in optical properties of the liver tissue during laser irradiation. In order to roughly examine the role of the property variations, the dynamic optical scattering was implemented and incorporated into the model by means of the Arrhenius damage integral as a scaling factor between fully native and fully coagulated tissues [27]. After complete tissue coagulation, μs' was assumed to increase by seven fold (i.e. 83.3 cm−1) in comparison with the native tissue [28]. Figure 8(a) showed the logarithmic correlation of the Arrhenius integral with temperature changes, which was used to scale μs' during the simulation. The corresponding temperature and Arrhenius integral were computed to demonstrate the thermal effects of the dynamic scattering on the irradiated tissue (Fig. 8(b)). The resultant degree of thermal damage became 2.8 ± 0.4 mm, which was 22% and 8% thicker than the previous numerical and experimental results, respectively. Thus, the increased thermal lesions confirmed that incorporating the dynamic tissue effects into the model could refine better the degree of coagulative necrosis during the photocoagulation. To further enhance the accuracy

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of the computation, the temperature-induced changes in optical tissue properties (both absorption and scattering) will be measured. Accordingly, the coagulation dynamics will be incorporated into the computational model to calculate endometrial lesions more precisely. Other explanations for the discrepancy in coagulative necrosis can include variations in thermal sensitivity of tissue possibly associated with the empirical values of both Af and Ea used for the theoretical model. Furthermore, unlike the uniform light distribution implemented for the simplicity of the model (Fig. 1), the intensity of the laser light was experimentally validated to be uneven along the fiber axis [13], which eventually contributed to partial tissue carbonization at the catheter-tissue interface (Fig. 7(c)). The previous in vivo studies also confirmed thicker coagulation with large variations in the extent of coagulation necrosis. However, the model can still make important qualitative predictions about the axial penetration of thermal damage such as the extent of primary damage in various glandular layers. For the sake of the computation accuracy, a more comprehensive approach allowing for not only dynamic thermal responses of uterine tissue and catheter material but also light intensity distribution would refine the computational analysis of endometrial photocoagulation. In addition, the coagulation threshold contingent upon various irradiances and irradiation times will be experimentally determined in order to calculate the damage integrals and obtain the rate constants fitting the experimental data within a range of experimental uncertainties [14,17,22,26]. In light of translating analytical data to in vivo tests even to clinical context, the current simulation model still has various limitations regarding lack of several physical processes for numerical analysis. For instance, in spite of good validation with liver tissue, extensive experimental measurements on human uterine tissue should be implemented to identify the accurate values of optical (i.e. absorption and reduced scattering coefficients at 532 nm) and thermal properties [17], which, thus, can help translate the current model to practical applications. In addition, optical interactions of laser with endometrial tissue should be incorporated into the model to reflect the integrating sphere effect during heat deposition, in that a human uterus with a close volume can be associated with multiple diffuse scattering at the surface of the uterine wall [13,17]. Currently, Monte Carlo simulation is being integrated with the thermal model for the detailed tracking of spatial photon distribution in endometrium. In addition, inconsistencies of the numerical outcomes typically result from inherent chromophore variability, non-uniformity of heat deposition, and irradiance fluctuations due to laser speckling. Accordingly, convective heat loss due to blood perfusion as well as temporal variations of light intensity from a laser source may need more consideration with respect to progressive temperature increase during and after endometrial photocoagulation. Furthermore, visible characterization of thermal lesions in endometrium should be performed in vivo in a quantitative manner to minimize any subjective assessment on comparative lesion measurements. Chronic tissue response should also be investigated to explore the role of the thermal lesions in healing process. To pursue successful clinical applications, further parametric optimization of ballooncatheters and clinical laser settings are under investigation. Due to the anatomical features of human uterus, different geometry as well as physical dimensions of the balloon-catheter should be tested in conjunction with various inflating balloon pressures to refine the clinical validity of the diffuser device. Although the current study utilized the input laser power of 120 W in a continuous mode at 532 nm with the potential treatment time of less than 1 min, a temporal modulation of laser power at near-IR such as 980 nm wavelength with the order of thermal relaxation time (~300 ms) may entail rapid heat deposition along with the desired coagulation necrosis. In fact, a sharper thermal gradient was experimentally observed within 1 sec after light absorption (Fig. 5(b)). As a result, the prompt temperature development owing to efficient energy coupling would help simplify and facilitate the surgical procedures of AUB treatment, which may eventually expect less skill and shorter operation time from gynecological surgeons. Thus, more cost-effective and compact pulsed-diode laser systems

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with relatively lower average power can provide more practical configurations for clinical settings and also render the current method even applicable to treatment of smaller tubular structures such as urethral strictures. Another logical extension to attain the optimal surgical margins along with accurate localization of coagulation necrosis is a visualization approach by integrating the current diffusing device with elasticity imaging. Changes in tissue stiffness induced by denaturation process can be monitored with elasticity imaging during the laser treatment in order to guarantee the safety margins in uterine walls [29]. Therefore, further investigations will use the model to calculate the optimal surgical parameters and to ensure the clinical efficacy and safety of endometrial photocoagulation with various designs of the integrated optical diffusers. 5. Conclusions

Temperature growth and distribution during endometrial photocoagulation with a ballooncatheter optical diffuser were investigated. Due to strong thermal insulation effect of polyurethane with low thermal diffusivity, the application of the catheter during light absorption entailed more rapid temperature increase, which could even facilitate tissue coagulation process, compared to the current AUB treatment modalities. The comparable degree of coagulation necrosis was theoretically as well as experimentally evaluated. The current model can be used to validate the safety of the photocoagulation for various designs of the balloon-catheters. Incorporation of optical interactions, dynamic uterine tissue properties as well as laser intensity distribution into the simulation model is underway to enhance the computational accuracy and eventually to optimize the performance of the designed optical diffuser and clinical configurations with various laser parameters. Acknowledgments

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2012R1A1A1012965).

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