Confinement of Freezing Front by Laser Irradiation during Cryosurgery

A new methodology to control the freezing front propagation during cryosurgical procedures is studied through the use of numerical techniques. Laser irradiation of a target tissue is explored as a new methodology for localizing heat generation and, thus, confining more accurately the desired cryoinjury region and to protect a thicker superficial layer of tissue. In addition to the irradiation of laser energy, the use of dyes is proposed as a means of localizing heat absorption and increasing the thickness of the protected region. A 2D finite volume numerical code based on the enthalpy method was developed to model the freezing process during cryoprobe cooling of a volume of tissue, while heating was applied to the external boundary protecting the superficial layer of tissue. Laser irradiation was modeled with Beer’s Law, and the energy absorption, which is proportional to the intensity, was taken as a source term in the energy equation. The thermophysical properties of the tissue are modeled as temperature dependent properties of water. Temperature contours resulting from a) constant temperature heating b) and regulated laser irradiation heating of tissue indicate that the latter methodology may be more effective in limiting cryoinjury to a predefined region. Additionally, if dyes are used, the protected area increases in thickness. The most dramatic differences between the two methodologies occur when the cryoprobe is placed near the surface, the effective attenuation coefficient of the material is low, and dyes are injected into the tissue to promote localized absorption of laser irradiated energy. NOMENCLATURE Bi Biot number, Bi=hyo/ks C specific heat (J kg K) d position in the y direction (m) E enthalpy (J) h heat transfer coefficient (W m K) H depth (m) I(y) laser irradiance at a distance y (W m) I laser output irradiance (W m o k thermal conductivity (W m ) -1 K) L latent heat of fusion (J kg) q heat flux (W m) Q heat source, (W m) St Stefan number t time (s) T temperature (C) T∞ temperature of surroundings (C) x coordinate tangential to the surface (m) y coordinate normal to the surface (m) y side of square prism o y dimensionless coordinate, y=y/yo Greek letters α effective attenuation coefficient (m) β ratio of liquid to solid thermal diffusivities δ thickness of dye layer (m) ε laser protection effectiveness coefficient κ ratio of liquid to solid conductivities D interface location ρ density (kg m) 1 Copyright © 2005 by ASME τ dimensionless time, τ=2kst/ρsCsyo Θ dimensionless temperature, =(T-T Θ ∞)/(Tm-T∞) Subscripts cryo cryoprobe d dye i initial value l liquid phase lethal lethal value m phase change s solid phase w heating wall INTRODUCTION Cryoablation of tissue using direct placement of cryoprobes within the tissue is a technique that has been gaining acceptance as a procedure for the treatment of internal cancer. The technique was first proposed by Arnott [1], but the first cryosurgical device for the treatment of internal tissues was presented by Cooper and Lee [2] in 1961. The technique compares favorably with other techniques, such as radical surgery and irradiation of tissue, because of the less traumatic procedure which reduces the blood loss and hospitalization times, which makes it the most recommended procedure for patients that are too ill or too old to undergo major surgery or for those with a very localized disease. Although used for various tissue malignancies, the most successful application of cryosurgery has been for the eradication of prostatic cancer. In 1993, Onik et al. [3], presented preliminary results indicating that ultrasound-guided prostate cryosurgery may be an effective treatment for prostate cancer with minimal associated morbidity. During prostate cancer cryosurgery metal freezing probes, called cryoprobes, are inserted into the tissue and cryogen flows through the probes which are in direct contact with the tissue. These cryoprobes have experienced technological improvements in recent years, [4-6]. Mainly reduction in size and increased ability to control the freezing rate that make possible to increase the number of cryoprobes inserted into the tissue, and also increase the possibility of a successful cryosurgery. The freezing starts as the probes are turned on, and the individual iceballs of each probe end up coalescing to form a larger ice ball. The border of the iceball is monitored with the aid of transrectal ultrasound or by magnetic resonance imaging to make sure that the ice ball does not approach healthy tissue that, if damaged, would produce postoperative complications hindering the success of the cryosurgical procedure. Among the most common postoperative complications, urinary rectal fistula is the most severe. During cryosurgery, the iceball is allowed to approach the rectal wall, but careful attention must be paid not to freeze the rectum. In order to kill all the unhealthy tissue, it may be necessary to allow the ice ball to get very near to the rectal wall without touching it. Other complication that may be very severe is urethral sloughing. In order to avoid this complication, the urethral walls have to be protected from damage by impeding them to freeze during the procedure. With the appearance of the urethral warmer, first proposed by Cohen et al. [7], this complication has reduced significantly. Although cryosurgery is a proven procedure for the eradication of prostatic cancer, the success of the procedure is still very dependent on the experience and good judgment of the surgeon, as he is the person who monitors the growth of the iceball and determines up to what point the ice ball is allowed to grow. The problem is twofold: the surgeon must be sure the complete unhealthy tissue has been lethally damaged but has to guarantee that the delicate urethra and rectum walls have been spared. Additionally, there is concern about the improvement of the monitoring procedure [8]. For the previously stated reasons, the surgeon may resort to treatment planning strategies, such as the optimal placement of cryoprobes to maximize ablation of the prostate while minimizing collateral damage. Efforts to improve the technique by modeling numerically the freezing and assessing the best placement for the cryoprobes have been done by researchers such as Baissalov et al. [9], Rewcastle et al. [10], and Rabin et al. [11]. In order to increase the likelihood of a successful cryosurgery, it would be desirable to devise effective ways to protect certain regions of tissue from being frozen without limiting so severely the application of the cryoprobe. If an artifact is created that guarantees that certain regions will never freeze, no matter how long the application of the cryoprobe is, a great progress may be achieved, as the cryosurgical procedure would become less dependent upon the good judgment of the surgeon. In this scenario is that this investigation proposes the use of laser irradiation as a means to guarantee the protection of superficial layers of tissue that may well represent the urethral or rectum walls. Other investigations, such as those of Rabin et al [12, 13], have proposed the use of so-called cryoheaters, but its effect is the protection of only a very superficial layer of tissue. The present investigation determines the effect achieved by laser irradiation and compares it to the protection achieved by other more conventional means of heating, such as warmers and cryoheaters. PROBLEM DEFINITION The problem studied herein assesses the advantages that regulated laser irradiation heating may have over the conventional constant temperature heating for the protection of tissue during cryosurgical procedures. The computational domain represented by Figure 1 consists of a rectangular body of depth H and width W. Inside this domain, a cryoprobe is placed at x=0 and y=d. The cryoprobe is represented as a rectangular block of dimensions Hcryo by Wcryo, whose surface is at Tcryo. The domain is assumed to be sufficiently deep so that the boundary, y=H, may be assumed to have a zero heat flux boundary condition. The sides of the block, x=0 and x=W, are assumed to be symmetry planes, as the system may be a part of a larger system having a row of cryoprobes separated by a distance 2W and placed all at the same depth. The boundary, y=0, is the heating boundary. Two different types of boundary conditions may be established, depending on the way the heat is being applied through the surface: (a) Uniform constant temperature heating. The top surface is assumed to be in contact with another surface at Tw, and a perfect thermal contact exists between these surfaces, so the boundary condition is T(x,0)=Tw . (b) Natural convection with air and laser irradiation through the surface. The top surface has natural convection 2 Copyright © 2005 by ASME with surroundings at T∞ and the associated convective heat transfer coefficient is h. The mathematical expression of the boundary condition is