Temperature Regime of Biological Tissue under Photodynamic Therapy

Transcription

1 ISSN , Biophysics, 0, Vol. 57, No., pp Pleiades Publishing, Inc., 0. Original Russian Text V.V. Barun, A.P. Ivanov, 0, published in Biofizika, 0, Vol. 57, No., pp COMPLEX SYSTEMS BIOPHYSICS Temperature Regime of Biological Tissue under Photodynamic Therapy V. V. Barun and A. P. Ivanov Stepanov Institute of Physics, National Academy of Sciences of Belarus, Minsk, 007 Belarus Received April 4, 0; in final form, July 9, 0 Abstract An analytical model is proposed to calculate heating of human skin cover under laser light action of photodynamic therapy. A photosensitizer of «Fotolon» is taken as an example. Temperatures of skin surface and of deep dermis regions are studied as a function of time under pulsed and stationary irradiation of skin surface at the wavelength of 665 nm corresponding to the maximum of the photosensitizer absorption band. It is shown that, under the action of a short light pulse, the photosensitizer can lead to an essential temperature rise of dermis due to a considerable increase in its absorption coefficient. However, this rise does not destruct tissue cells because of the short action. Under stationary irradiation, the photosensitizer concentration has a low effect on the temperature regime of tissue. This is related with the specific features in heating of the medium by red light, where the main thermal process in skin is heat transfer over tissue volume from epidermis having a substantially larger absorption coefficient than that of dermis in the said spectral range. The role of blood perfusion in dermis and its effect on the temperature regime of tissue are evaluated. Keywords: biological tissues, photodynamic therapy, photosensitizer, «Fotolon», temperature, heating, skin, epidermis, dermis, blood. DOI: 0.34/S INTRODUCTION At the present time various techniques of photodynamic therapy (PDT) are widely used in clinical and laboratory practice for treating oncological and other human diseases [ 4]. Therewith first a photosensitizer (PS) is introduced into biotissue, usually intravenously. In a time constituting from several to tens of hours, PS is selectively accumulated in tumor, where its content exceeds several times the PS concentration in healthy tissue [5]. This occurs mainly at the expense of quicker excretion of PS from healthy cells of tissue as compared with tumor ones [6]. Then the pathological region is irradiated with continuous or pulsed light with power or energy density on skin surface, respectively, 0. W/cm or 00 J/cm [6, 7]. The duration of irradiation with a stationary laser beam is varied from several to tens of minutes [6]. As a result PS selectively absorbs light, launching several mechanisms [6 9] of the action of radiation on biotissue. As the main ones there appear photochemical mechanisms formation of singlet oxygen and free radicals, and also radiation-less transmission of absorbed energy to nearby cells of tissue. Singlet oxygen is toxic for tumor cells and leads to their necrosis or death. Destruction of the tumor may be promoted also by elevated temperature in consequence of absorption by Editor s Note: I certify that this is the closest possible equivalent of the original publication with all its factual statements and terminology, phrasing and style. A.G. PS of the irradiating light and heating of tissue. Methods have been developed of laser-induced hyperthermia [6], applied autonomously or supplementing the procedures of PDT and promoting tissue necrosis. On the other hand, the patient may experience painful sensations upon strong heating of tissue. Thus if for a duration of several minutes the temperature in the tumor zone constitutes on the order of 45 C, there occurs death of cancer cells, while if above 60 C there takes place denaturation of proteins and collagen, leading to damage of healthy regions of tissue. Therefore for understanding the prevalent mechanism of PDT, removing possible painful sensations of the patient and choosing the optimal duration of irradiation it is important to estimate the temperature growth of biotissue containing PS upon its laser irradiation. At that it is topical to use analytical (rather than numerical) methods of investigation of the thermal regime of biotissue, not requiring application of complex algorithms and computer codes for calculations. To experimentally study the spatiotemporal distribution of biotissue heating emerging in consequence of laser light absorption it is extremely complicated. For this it is required to implant sensors of local temperature, to control and in a reproducible way change the optothermophysical parameters of the medium with the aim of transposing the results of single measurements onto other patients, and also to actualize a series of other technical and medical arrangements. Therefore below the temperature regime of biotissue is 98

2 TEMPERATURE REGIME OF TISSUE IN PHOTODYNAMIC THERAPY 99 investigated theoretically by the method of modeling irradiation through skin. It is obvious that tissue heating in PDT depends on the properties of source and conditions of irradiation, structure of biological tissue, concentration and depth distribution of its components absorbing and scattering the light, thermophysical characteristics, type of PS. Known are a large number of PS used in PDT. As a rule, the y possess noticeable bands of light absorption in the near ultraviolet and blue regions of spectrum at wavelengths λ nm and in the red region at λ nm [, 4 6]. Light with λ nm penetrates into tissue very superficially [0] to fractions of a millimeter and can be used in noninvasive (without surgical intervention) PDT of only near-surface regions of tissue. Usually the known and newly created PS are destined for work in the red spectral interval. Below for estimates of the temperature regime we will restrict ourselves by way of example to consideration of PS Fotolon (on the basis of chlorin e6), developed in the Institute of Physics, NAS Belarus [, ], industrially produced by OAO Belmedpreparaty and widely applied in PDT in clinics. In this way, the aim of the given work presents as an investigation of the influence of PS absorption on biotissue heating upon pulsed and stationary irradiation of skin surface. For this we collate quantitative data on spatiotemporal distribution of temperature in a medium containing PS and without it. OPTOTHERMOPHYSICAL MODEL OF SKIN Above it has been noted that the temperature regime of biotissue upon laser illumination depends on its structural, optical and thermophysical parameters. The structural and optical characteristics permit quantitatively setting the source function of the heat conduction equation, while structural and thermophysical ones, describing heat transfer over the medium and calculating the spatiotemporal distributions of temperature. In the given work use was made of a skin model [3]. It was built as a result of critical analysis and selection of published works of various investigators and own calculations of the authors. Let us briefly enumerate the main parameters of the model. Skin is multilayered. Outside there is a corneal layer of mm thickness, then epidermis and derma, containing respectively a pigment melanin and blood vessels capillaries. Epidermis has a thickness of mm, while derma, 4 mm. Let us take that microvessels have a constant diameter D, the magnitude of which resides in the interval cm, while the length of any capillary to its bend is far greater than D. Such an element of capillary can be represented in the form of a long cylinder. A capillary net is a system of microvessels chaotically distributed in space. More detailed information on the structure of the skin cover can be found in [4, 5]. The component composition of skin is sufficiently complex. However from the point of view of light propagation in tissue and subsequent heating thereof it is important to know the properties only of manifested optically native chromophores that scatter and absorb light, and also the characteristics of PS absorption. To the natural components of skin one can relate the basis tissue, hemoglobin derivates contained in blood erythrocytes, melanin. Detailed data on their concentration and spectral properties can be picked up from works [0, 4 7]. The absorption spectra of PS Fotolon were measured in whole blood [8 0] by a method of multiple light scattering at concentrations of this PS in the range mg/ml. Let us underscore the importance of staging the experiments exactly in whole blood, because these spectra depend on the medium in which PS is [8 0], and also the necessity of using the indicated method, inasmuch as for whole blood it is practically impossible to neglect the contribution of multiple scattering. Data [8 0] were included into the optical part of model [3]. The maximum of the absorption band of PS Fotolon falls on λ = 665 nm and constitutes roughly cm in the above-indicated interval of concentrations. These values in the order of magnitude are commensurate with the absorption index of blood. Therefore for evaluating the temperature regime of tissue it is important to take into account the influence of additional absorption of PS on the characteristics of the light field in the medium (source function of the heat problem) and on the degree of its heating. Data on the thermophysical properties of skin determining the heat transfer over tissue that are necessary for solving the considered problem can be taken from the thermophysical part of model [3]. These include the heat capacity of the medium c, its density ρ, coefficient of thermal conductivity κ or thermal diffusivity η, parameters of heat emission α between blood and basis tissue and convective heat exchange h at the interface of skin surrounding medium, rate v of blood perfusion measured in s and giving the blood volume passing in s through unit volume of basis tissue. In the literature simple approximate formula are proposed for calculating parameters c, ρ, κ and consequently η = κ/cρ, connecting their values with volume concentration C w of water in tissue. For example, according to [, ], c =.5C w, () ρ = /(0.066C w ), () κ = 0.0ρ(0.45C w ), (3) where c, ρ and κ have dimension respectively J/(g K), g/cm 3 and W/(cm K). Somewhat dissimilar formula are proposed in work [6], but they give practically the same values of c, ρ, κ as () (3), and the same depen- BIOPHYSICS Vol. 57 No. 0

3 00 BARUN and IVANOV dence thereof on C w. However coefficient η determining heat transfer in the medium weakly depends on water concentration. Upon changing C w in the limits typical of soft tissues, the η values remain roughly constant [6, 3] and equal to the thermal diffusivity coefficient of water. Product cρ enters as a multiplier into the source function (see below). Its variations for soft tissues during estimation of medium temperature we will further neglect. On the whole let us note that the thermophysical characteristics of biotissues are far less variable than the optical ones. This is understandable, because the basic component of tissues is presented by water. Therefore for estimates of the temperature regime the cρ, κ and η parameters for all skin layers can be put constant and equal, as in water, 4. J/(cm 3 K); W/(cm K) and cm /s respectively. Usually parameter h = 0.4 cm [3]. For α values in [3, 6] the following estimate was obtained: α = 9.7 ηc v ( C v )/D, where C v is volume concentration of capillaries (fraction of tissue volume occupied by blood). The perfusion rate v depends on a series of factors and for skin changes in an interval of roughly c [6, 4, 5]. SOLUTION OF HEAT CONDUCTION EQUATION An analytical solution of the problem of biotissue heating under the action of laser radiation was obtained in a series of works [6, 6 9]. These results are used blow as applied to taking into account the tissue heating in consequence of additional PS light absorption. Let us note that comparison with numerical methods [30] executed in [6] has shown acceptable correspondence of the obtained temperature distributions in biotissue. Let us consider a two-layer medium consisting of epidermis and depth-uniform derma, i.e. neglect the influence of the corneal layer [9] (inasmuch as its optical thickness is small). Let us analyze the kinetics of the thermal field for two cases: illumination by a short light pulse and time-stationary beam of radiation. Therewith we will consider a linear problem, i.e. assume that tissue heating does not change either the structure of the medium or its optical and thermophysical characteristics. Illumination by a short laser pulse. In work [8] it is shown that the temperature of medium, in small moments of time t after irradiation (on the order of 50 ms and less depending on radius r 0 of the beam), does not depend on r 0. Mathematically this signifies that in short pulse illumination it is possible to investigate tissue heating from at δ(t) pulse infinitely broad in space. The physical cause is presented by that in a small time t the heat «has no time» to get out of the irradiation zone in the radial direction. The characteristic time of radial diffusion can be estimated by formula τ r = /(.4η) [6, 8]. At r 0 = mm, τ r 70 ms. Apart of that, the role of epidermis in heat transfer over derma is confined in this case only to absorption of a part of the light flux incident on the skin surface [9]. In other words, epidermis can be regarded as a spectral filter attenuating the radiation in derma. From the physical point of view the said is conditioned by sufficiently large values of time τ η (see below). In derma the main part of light energy will be engulfed by blood. Therefore capillaries will heat more strongly that the basis tissue surrounding them. Until heat starts «running over» the entire tissue, the most rapidly proceeding process will be energy exchange between capillaries and basis tissue. Their temperature kinetics as a function of depth z is described, according to [6, 6, 7], by formulae r 0 A ΔT ( t, F( t, A G( t, zβ, ) τ = , η (4) A ΔT ( t, F( t, A G( t, zβ, ) τ = η (5) τ η τ h Here ΔT and ΔT are the excesses of tissue and blood temperatures over the human normal temperature. Everywhere subscript relates to basis tissue, to blood. F( t, t --- t z = exp exp( βerfc τ η τ η tη (6) + ( βerfc --- t z exp , τ η tη G( t, zβ, ) --- t τ η ( βz )erfc --- t z = exp exp τ η tη (7) t --- z t z exp exp erfc , τ η t η η τ η tη A = A 0 ( W) + A 0 W, (8) A = A 0 ( W) + A 0 W, W() t + exp( τ α /t)[ I 0 ( τ α /t) + I ( τ α /t)]. (9) Coefficients A 0,0 = μ a, γp 0 /(cρ), A 0 = ( C v )A 0 + C v A 0 ; P 0 laser pulse energy density on the surface of derma; γ accounts of the change in radiation density under the air skin interface [6, 3]; I 0, I, erfc(x) respectively modified Bessel functions of zero and first order, additional probability integral; τ α = D /(9.7η), τ η = /(β η), τ h = /(h η). Included in (4) (8) are optical parameters: β = 3μ a μ e ' depth index of attenuation of tissue; μ a its absorption index; μ a = μ a,b + C PS μ PS absorption index of blood with PS, where μ a,b and μ PS absorption indexes of respectively τ η τ h BIOPHYSICS Vol. 57 No. 0

4 TEMPERATURE REGIME OF TISSUE IN PHOTODYNAMIC THERAPY 0 ΔT, K ΔT, K (a) ΔT, K ΔT, K (b) t, s t, s Fig.. Dependences of excess of the temperature of blood (curves ) and basis tissue () over normal temperature on time after action of broad δ(t) laser pulse upon introduction of PS with C PS = mg/ml (solid curves) and without it (dashed), z = 0 (a) and 0. cm (b), C v = 0.0. blood proper, cm, and PS, ml/(mg cm), C PS specific mass concentration of PS, mg/ml; μ e ' = μ e ( g) effective attenuation index, where μ e = μ a + μ s attenuation index, μ s scattering index; g mean cosine of the indicatrix of scattering of elementary volume, and also the above-indicated thermophysical characteristics. The optical characteristics are phenomenological quantities. The give averaged information on the optical properties of the components entering into the elementary volume of tissue, and are determined by means of additive summation of the optical parameters of the components. A number of quantities indicated above have a distinct physical sense. Coefficients A 0,0 characterize the energy absorbed at the layer surface by unit volume in case the layer consisted only of basis tissue or only of blood vessels. Value A 0 gives energy absorbed by unit volume of the layer at z = 0. Parameters τ α, τ η and τ h are characteristic times of one or another process on condition that it is prevalent in time: τ α time of equilibration of the temperature of blood and basis tissue, τ η time of equilibration of the temperature over tissue thickness, τ h time of heat exchange of skin surface with external medium. Therefore, even conducting no calculations by formulae (4) and (5), one can obtain certain information about thermal processes in tissue on the basis of analysis of the indicated temporal parameters. Before studying the regularities of temperature kinetics by (4) and (5), let us indicate that given the presence of PS the derma presents a three-component absorbing medium. Therein the elementary volume absorption index μ a = ( C v )μ a + C v μ a. (0) Above it has been noted that in the quality of PS in calculations we have considered Fotolon. It has three absorption bands in the visible region of the spectrum [8, 0]. In PDT use is made of the long-wavelength band nm. Calculations were executed for τ = 665 nm, corresponding to the absorption maximum of the PS. The concentration of the latter in blood was chosen equal to C PS = mg/ml. Though this value of C PS exceeds the usually introduced concentrations of Fotolon [5], the below-presented values of tissue temperature give an upper estimate of the degree of medium heating. In Fig. we present the results of calculations of growth of the temperature of blood and derma given the presence of PS and without it, on the skin surface and at a depth of mm upon irradiation by a δ(t)-pulse with energy density 5 J/cm. It is seen that blood temperature at small t is significantly greater than basis tissue temperature. However this excess takes place not for long, on the order of fractions of ms, while with growth of time these temperatures get closer and in roughly ms become identical. Mathematically this is connected with that A and A in (4) and (5) turn into A 0. From the indicated moment the medium behaves as one-component, and the growth of its temperature is described by formula ΔT( t, A 0 F ( t, z ) A 0G( t, zβ, ) τ = η () The availability of PS leads to that in the near-surface layers of derma (Figs. a and b) the blood temperature strongly increases. In the depth of medium, in consequence of additional PS light absorption, the radiation intensity will weaken more strongly, which τ η τ h BIOPHYSICS Vol. 57 No. 0

5 0 BARUN and IVANOV will lead to a decrease in heating of both blood and derma. At the expense of this the temperature of basis tissue at 0. cm depth is somewhat lower with PS available than without it. Then, in consequence of heat exchange with the more heated blood, the basis tissue temperature rises. At the considered density of incident energy the blood temperature growth in the initial time moments is larger than 0 K. However this does not lead to irreversible effects in tissue because of short-term thermal action. For example, by estimates [6] the indicated effects start to take place upon heating to 60 C for a duration of at least 6 s. Let us note that for determination of the fraction of tissue cells «having survived» as a result of thermal action, it is convenient to use the Arrhenius relationship [6, 3], which connects the relative number of undamaged cells with the duration of heating, temperature of tissue and its thermodynamic and thermophysical parameters. Upon increasing the energy density P 0 it is necessary to take into account this relationship and the possible irreversible impacts of heat on tissue. In other words, the Arrhenius equation can be used for estimating the boundaries of applicability of formulae (4) and (5), which, recall, were obtained under assumption of independence of the tissue properties of the irradiation parameters. Let us indicate that these formulae do not contain the rate v of blood perfusion in derma. The v values start influencing the thermal regime of tissue after tens of seconds [4] elapsed from the onset of action, and in irradiation of skin by a short light pulse they may be disregarded. In this way, relationships (4) (9) give an analytical solution of the problem of biotissue heating by a short laser pulse in PDT. Let us note that formulae (4) (9) were written down for the case of skin irradiation by a δ(t)-pulse infinitely broad over space and therefore do not contain its duration Δt. At a finite value of Δt one should calculate an integral of convolution type: ΔT t ( ) ( t, = u( t τ)g ( ), ( τ, dτ, 0 () where u(t) is the temporal form of irradiation pulse, G (), Green function for basis tissue (blood) in medium irradiation with an infinitely broad δ(t)- pulse. It analytical form is presented in [8] for onelayer medium and in [9] for a multilayered type of skin. In order not to complicate the test, we will not present the quite cumbersome analytical writing of Green functions G (),. For this one can turn to works [8, 9]. If the light pulse has the shape of a unit step in time, then u() t = at t Δt 0 at t > Δt. () As seen from Fig., after equilibration of temperatures of basis tissue and blood the biotissue irradiated by the δ(t)-pulse heats more strongly with PS available than without it. From analysis of the general properties of the heat conduction equation in biotissue [6 8] it follows that this situation will be preserved also at a finite value of Δt, as long as Δt τ α (the shortest of characteristic times τ α, τ η and τ h ) and τ r. Usually τ α τ r, because D r 0. Let D = 0 μm (typical average diameter of capillaries). Then τ α 80 μs. In this way, in the case of pulse irradiation the PS absorption will lead to growth of biotissue temperature at Δt 0 μs. Analogous estimates are easy to obtain also at other values of D. Stationary illumination. Let us consider a Gaussian incident beam of radius r 0 (by level /e 0.4), creating in its center on skin surface an illuminance E 0. The temporal thermal process practically at once proceeds as in a one-component medium, so that G (), = G δ,, but absorption is determined by relationship (0). Analogously to () we obtain that the temperature excess in this case ΔT( t, z, r) = G δ ( τ, z, r) dτ. Here r is distance from beam axis, G δ ( t, z, r) = G δ, ( t, r 0 exp{ r /[ 4( r 0 /8 + ηt) ]} ( r 0 /8 + ηt) t 0 (3) (4) is a Green function of the problem of medium heating by a δ(t)-pulse of radius r 0. Let us note that in (5) the spatial coordinates r and z are separated. The reasons of this are discussed in [8, 33]. Apart of that, the parameters of light absorption and scattering by tissue enter only into the Green function G δ,. Therefore it has a different form for epidermis and derma, while the dependence on r is identical for these two layers of skin. As shown in [9], in continuous irradiation one may not use the approximation of one-layer medium for studying skin heating, but it is necessary to take into account different characteristics of absorption of epidermis and derma. The given fact will be also illustrated below in considering Fig.. Let us briefly indicate also the procedure of evaluating the role of blood perfusion in the thermal regime of skin. For a multilayered medium obtaining an analytical solution of the heat conduction equation in this case has no success. However for uniform derma the account of blood flow rate reduces simply to multiplying the right-hand part of (3) by exp( vt) [34]. Perfusion, obviously, leads to a decrease in the degree of heating obtained without its consideration. Let us find for a uniform medium the relationship of temperatures calculated with account BIOPHYSICS Vol. 57 No. 0

6 TEMPERATURE REGIME OF TISSUE IN PHOTODYNAMIC THERAPY 03 (a) 3 (b) t, s t, s.00 (c) 3.00 (d) t, s t, s Fig.. Dependences of ΔT on time after beginning irradiation with a stationary laser beam of radius r 0 = 0.5 (curves ), 0.5 () and cm (3) upon introduction of PS with C PS = mg/ml (solid curves) and without it (symbols), z = 0 (a, b) and 0. cm (c, d), f m = 0.08 (a, c) and 0.0 (b, d), C v = and without account of heat transfer by moving blood. Let us transpose the values of the indicated relationship onto the case of two-layer tissue. Understandably, this is an assumption, but from physical considerations it is clear that it is lawful for approximate estimates of the thermal regime. Let us note that an advantage of such a procedure presents as retention of the analytical form of solution of (4), (5). In Fig. we present the time dependences of the degree of tissue heating in the center (r = 0) of a light beam of different sizes, creating on the skin surface an illuminance E 0 = 0. W/cm. This power density roughly corresponds to that usually used in PDT. Cases (a) and (c) correspond to a volume concentration f m of melanin in epidermis 0.08, while (b) and (d) f m = 0.0. Solid curves give ΔT with PS available at concentration C PS = mg/ml, while symbols without it. Let us note first that the increment of temperature with time at small t is linear and does not depend on the size of the light spot, just as it follows from the general properties of solution of heat conduction equation [8]. The larger the r 0, the later this dependence is violated. The influence of bean radius starts manifesting itself after hundreds of milliseconds elapsed from the onset of light action. As it follows from Fig., at f m = 0.08 on the temperature of skin surface (a) and deep layers of derma (b) PS has practically not influence, though its concentration is chosen quite large and it noticeable increases the derma absorption index (7). The physical cause of such a peculiarity of the thermal regime of tissue presents as that both its surface and inner regions are heated prevalently at the expense of heat transfer from epidermis. Firstly, it noticeable weakens the light reaching derma. Secondly, its absorption index at λ = 665 nm roughly by an order exceeds the μ a of derma [4 6, 9], so that the absorption of radiation in derma only weakly tells on the temperature regime of tissue. Epidermis in the indicated spectral interval plays a role of a peculiar «stove» [9] providing heating BIOPHYSICS Vol. 57 No. 0

7 04 BARUN and IVANOV with a narrow beam (small r 0 ) the role of blood flow rate is insignificant. Upon increasing r 0 the growth of derma temperature may noticeable decline up to two times as dependent on v. As noted, the data in Figs. and 3 were obtained for Gaussian light beams of different sizes r 0. Using the same methodology as that presented above, it is possible to simply go over to other radial profiles of irradiation (see, for example, [35]) v 0 3, /s Fig. 3. Dependences of ΔT in stationary regime on rate v of blood perfusion at r 0 = 0.5 (curves ) and cm (), z = 0. cm, f m = 0.08, C v = of the entire medium in whole. If now one investigates the tissue thermal regime at a smaller concentration f m (Figs. b and d), we obtain that in this case indeed there become manifest the differences in tissue temperatures with PS and without it (let us pay attention to the logarithmic scale along the ordinate axis). From the said it follows, in particular, that in stationary irradiation to build noninvasive techniques of disclosing tumor regions where PS is accumulated and determining its concentration in tissue, for example by thermal images of skin surface, is difficult. Analogous invasive techniques based on insertion into tissue of local temperature sensors also appear of low promise. Let us note also that upon decreasing f m the heating of medium proceeds on the whole more weakly, though in derma more light is absorbed. This also testifies to an important role of epidermis in heat transfer during tissue irradiation in the red spectral interval. From Fig. it follows that the temperature regime of the tissue stabilizes in several minutes after the onset of irradiation. The particular time of commencement of a stationary regime depends on the radius r 0 of the laser beam and the coordinate z. Obviously, the larger the r 0, the stronger the heating, because a growing light power is supplied into the medium. Apart of that, the growth of temperature is directly proportional to E 0. Let us note that at the chosen irradiation parameters (r 0 in the range 0.5 cm and E 0 = 0. W/cm ) the tissue temperature may grow by several degrees. Hence follows the importance of controlling exactly these parameters both for optimization of the hyperthermia regime and for non-admission of tissue destruction because of thermal action. In Fig. 3 shown is the influence of blood perfusion rate on the stationary temperature of derma at a depth of mm. The values of v varied in the above-indicated limits typical of skin. It is seen that upon irradiation CONCLUSIONS For analysis of the thermal regime of biotissues in PDT use has been made of an analytical technique based on the earlier performed works of the authors. It has allowed writing down the final formulae for estimation of medium temperature growth simply by accounting PS absorption upon varying the other optical characteristics of skin and irradiation parameters. As distinct from the widely applied various numerical procedures of soling this problem, the proposed formulae do not require creation of complicated algorithms and computer codes for calculations and allow investigators, engineers and practicing physicians to simply enough solve particular physical, medical and biophysical tasks. In the work in the capacity of example we have chosen PS Fotolon. The reasons for this are several. Firstly, it is often used in PDT in clinical conditions. Secondly, its biomedical characteristics, spectral properties of absorption and conditions of application are typical of also other PS of the chlorin series. Thirdly, and this is perhaps the main thing, experimental investigations have been executed on its absorption band in whole blood precisely in the medium where it is used in PDT. For other PS one feels an obvious shortage of analogous data. The main conclusion of the executed work is a substantial difference in the influence of PS light absorption on tissue heating upon pulsed and stationary irradiation with red light. In the former case, at a duration of irradiation on the order of 0 μs and less, the temperature of basis tissue and blood, on the whole, grows with increasing PS concentration, while in the latter at an irradiation time more than 0 ms practically does not depend on it. This is connected with the specific optical properties of skin layers and PS in the indicated spectral interval and peculiarities of heat transfer in multilayered tissue. By means of concrete calculations it is shown that under stationary irradiation the heating of tissue is ensured by epidermis, playing at the expense of its absorption properties the role of a peculiar «thermoelement». Therewith the optical parameters of derma, where PS is usually contained, bear a secondary character. It is shown that under stationary irradiation of skin surface with power density E 0 = 0. W/cm the growth of biotissue temperature may reach several degrees BIOPHYSICS Vol. 57 No. 0

8 TEMPERATURE REGIME OF TISSUE IN PHOTODYNAMIC THERAPY 05 after 3 min elapsed from the beginning of a PDT s?ance. The obtained estimate imposes serious restrictions on further growth of irradiation power. Though blood perfusion leads to a decrease of temperature increment in the stationary regime roughly by.5 times, this may prove insufficient for elimination of probable painful sensations of the patient or destruction of tissue cells and large values of E 0. The revealed regularities ensue from the general approaches of the optics of scattering media and thermophysics, while their concrete interpretation presented in the work for evaluation of the thermal regime of biotissue in PDT may present interest for physicists, medics, biophysicists engaged in optimization and realization of PDT techniques in practice. ACKNOWLEDGMENTS The work was supported by the Belorussian Foundation for Basic Research (F09Vn-00 and F0-067). REFERENCES. Itogi Nauki Tekhn. Ser. Sovr. Probl. Lazer Fiz., Ed. by S. A. Akhmanov, E. B. Chernyaeva (VINITI, Moscow, 990), Vol. 3.. E. F. Stranadko, O. K. Skobelkin, G. N. Vorozhtsov, et al., Ros. Onkolog. Zh., no. 4, 3 (998). 3. E. F. Stranadko, N. A. Markichev, and M. V. Ryabov, Photodynamic Therapy in Treating Malignant Neoplasms of Various Localizations: Physicians Manual (Moscow, 999) [in Russian]. 4. Photomedicine in Gynecology and Reproduction, Ed. by P. Wyss et al. (S. Karger AG, Basel, 000). 5. A. F. Mironov, Soros. Obraz. Zh., no. 8, 3 (996). 6. M. N. Niemz, Laser Tissue Interaction, 3rd edn. (Springer, Berlin, 007). 7. O. V. Borgul, M. A. Kaplan, V. N. Kapinus, et al., Ros. Bioterap. Zh. 6, (007). 8. E. F. Stranadko, Fotobiol. Medits. (), 36 (999). 9. E. F. Stranadko, Ros. Onkolog. Zh., no. 4, 5 (000). 0. V. V. Barun, A. P. Ivanov, A. V. Volotovskaya, and V. S. Ulashchik, Zh. Prikl. Spektrosk. 74 (3), 387 (007).. G. P. Gurinovich, T. E. Zorina, S. B. Melnov, et al., J. Photochem. Photobiol. B 3 (), 5 (99).. G. A. Kostenich, I. N. Zhuravkin, and E. A. Zhavrid, J. Photochem. Photobiol. B (3), (994). 3. V. V. Barun and A. P. Ivanov, Biofizika 49, 5 (004). 4. S. L. Jacques, 5. V. V. Tuchin, Lasers and Fiber Optics in Biomedical Investigations (Izd. Sarat. Un-ta, 998) [in Russian]. 6. V. V. Barun and A. P. Ivanov, Optika Spektrosk. 00 (), 49 (006). 7. A. N. Bashkatov, E. A. Genina, and V. V. Nuchin, J. Innovative Optical Health Res. (), 9 (0). 8. A. Ya. Khairullina, M. V. Parkhots, T. V. Oleinik, et al., Optika Spektrosk. 9 (), 54 (00). 9. M. V. Parkhots, A. Ya. Khairullina, and B. M. Dzhagarov, Optich. Zh. 69 (7), 8 (007). 0. M. V. Parkhots, V. N. Knyukshto, G. A. Isakov, et al., Zh. Prikl. Spektrosk. 70 (6), 86 (003).. M. J. P. Brugmans, J. Kemper, G. H. M. Gijsbergs, et al., Lasers Surg. Med., 587 (99).. B. Choi and A. J. Welch, Lasers Surg. Med. 9, 35 (00). 3. J.-L. Boulnois, Lasers Med. Sci. (), 47 (985). 4. A. J. Welch, E. H. Wissler, and L. A. Priebe, IEEE Trans. Boimed. Eng. 7 (3), 64 (980). 5. L. O. Svaasand, T. Boerslid, and M. Oeveraasen, Lasers Surg. Med. 5 (6), 589 (985). 6. V. V. Barun and A. P. Ivanov, Int. J. Heat Mass Transfer. 46 (7), 343 (003). 7. V. V. Barun and A. P. Ivanov, Biofizika 50, 3 (005). 8. V. V. Barun and A. P. Ivanov, Kvant. Elektron. 34 (), 069 (004). 9. V. V. Barun and A. P. Ivanov, Optika Spektrosk. 07 (6), 959 (009). 30. Yu. N. Shcherbakov, A. N. Yakunin, I. V. Yaroskavskii, and V. V. Tuchin, Optika Spektrosk. 76 (5), 85 (994). 3. V. V. Barun and A. P. Ivanov, Kvant. Elektron. 40 (4), 37 (00). 3. A. J. Welch, IEEE J. Quant. Electron. 0 (), 47 (984). 33. V. V. Barun and A. P. Ivanov, Dikl. NAN Belarusi 49 (5), 48 (005). 34. V. V. Barun and A. P. Ivanov, Inzh.-Fiz. Zh. 78 (3), 5 (005). 35. V. V. Barun and A. P. Ivanov, Inzh.-Fiz. Zh. 78 (4), 8 (005). BIOPHYSICS Vol. 57 No. 0