Ultrasonic Peeling. The Bauman Moscow State Technical University, Russia,

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1 V. M. Gorshkova Ultrasonic Peeling The Bauman Moscow State Technical University, ussia, ABSTACT The article suggests a mathematical descrition o eeling by ultrasound technologies. INTODUCTION Ultrasonic eeling can be reerred to the surace eeling which is atraumatic because the corneal layer (dead cells) is eeled rom the skin surace. A decrease in thickness o the corneal layer ermits to remove hyerkeratosis regions, to increase living corneal layers thickness, to imrove a skin tint (color) and to clear hyerigmented regions. The ultrasonic eeling technology has been develoed in the Bauman Moscow State Technical University. During ultrasonic eeling the ultrasonic vibration eect is roduced on the system o a harmaceutical substance in solution (gel, cream) (antisetics or α - hydroxy-acids o low concentration) and a biological tissue o the skin (corneal layer and eidermis). Flow characteristics o solutions can be shown as: where shear stress; shear rate. ( ) It is known [] that this relation is similar to one shown in Fig.. μ - viscosity μ Δ d d. I d& γ const, the luid is Newtonian and tgα d d& γ const in the d region o abnormal low ( ) i.e. shear stress is a unction o shear rate.

2 Fig.. Flow curves I, III Newtonian low; II abnormal low a) b) Fig.. Viscosity and shear rate relation in Newtonian low (a) and in general case (b), see designations in Fig.. An investigation o the low o non-newtonian luids is a very intricate theoretical and alication roblem, which has not been solved till now. Let н be maximum shear rate, which can arise in the system. Obviously ( ) d As it ollows rom Fig., Fig.. Note that the area under the curve ( γ) d and relation looks like low curves shown in d& γ d & d& γ can be calculated by the equation

3 ( ) d Let us consider now an equivalent rectangle s γ & d * (which area equals ( ) γ & d * d ), thereore elation between shear stress and shear rate, being realized to the maximum in the system, is an aarent viscosity: d μ * Thereore, within the н range o variation the antisetic solution can be aroximately considered as Newtonian luid, i.e. that low curves are constant). Viscosity can be calculated as: & γ (& γ ) () * d ( & γ ) d & γ d const (bearing in mind Note, that and * are determined by the low curve coniguration. Now let us consider the luid low, when cavitation rocess is caused by an ultrasonic vibration transmitter. esting luid, lying on the surace (corneal) skin layer is exosed to ultrasonic eect by means o an ultrasonic generator and a tool, which results in ormation o microbubbles, i.e. cavitation. Let us analyze roerties o a cavitating bubble and its inluence on luid roerties. Let us consider a cavern (bubble), and denote: P-ressure, created by the surrounding luid on the cavern; P н - ressure o saturated vaors in the cavern; P г ressure o gases (rom air) ; - surace

4 tension coeicient. For simlicity the cavern is assumed to be a shere. Thereore, equilibrium o the bubble in the luid is given by the equation: P н Where - shere radius. From gas dynamics it is known that temerature ºС ence, it is obvious that i P <, the cavern exands. í Ã In view o the Boyle s law ressures and cavern radius, resectively. Thereore, P BT, where <Bconst ; T- г P >, the cavern comresses, i н г н Where Thus, P н н н, where P, - initial gas I the gas state variation law is adiabatic ( const ), thereore - seciic heat ratio), thereore., γ γ (γ ence, the cavern varies its radius under the action o an outside orce ( T ),. 4

5 In case o the Claeyron s law ( ) BT T, The cavern critical radius is BT k, and the critical ressure is BT P k. In the isothermal case: k ; ( ) T, ; k 4 In the adiabatic case: ( ) T γ, ; k ; 4 k Note that the bubble critical radius can be ound roviding: ( ), T, P кр P() кр The resence o caverns makes luid comressible. The latter means that its density deends on ressure. Aroximately this deendence can be considered to be a linear one. This act is theoretically and exerimentally validated in []. ence, as a result o interaction o corneal layer cells and microbubbles, the latter collase, thereore the overressure (microlocal ressure) is created in the region o their eect, which results in eeling o dead (corneal layer) cells. 5

6 There are a lot o imerections such as cracks (irregularities) on the skin surace (corneal layer). When illed with luid, air remains in cracks. Besides, enetrating through the surace o the luid due to diusion, gases are dissolved therein, cavitation is develoed. For the sake o simlicity the cavern is resumed to be a shere. Fluid is ractically incomressible and at the initial oint o time is at rest. Suose that the luid motion is irrotational and the luid is isotroic and homogeneous. Moreover, the bubble moves only along the radius. Denote Δ d ϕ u ; d ϕ r d dt ϕ, where () - cavern radius at the oint o time t. t By virtue o the above assumtions a rictionless liquid and a viscous luid behaves identically. Thus, du u dt r ρ () t, where t - ressure on the cavern wall at the oint o time t; ρ - gas density; luid ressure in a remote oint. Suose that the bubble is illed with erect gas, i.e. t υ BT where υ - saturation ressure deending on temerature. Thereore, ρ du dt ru BT, υ ( T ), where (, T )- outside orce (ultrasonic) acting on the cavern radius variation. Obviously, three situations are ossible: ) (, T ) at, i.e. there is an equilibrium; k ) (, T ) > at - cavern growth; k ) (, T ) < at cavern collase. k 6

7 Let us determine the critical value o, when k, hence, k BT, thereore k 4 ( υ)k Thus, the dynamic conditions o the bubble collase have been ound. ence, as a result o interaction o corneal layer cells and microbubbles the latter collase, thereore, in the region o ultrasonic eect the overressure is created, which results in eeling o keratinized (dead) cells. It is known that the corneal layer is an unwettable surace. Note that a criterion or high quality eeling is wettability o surace, which can be described by the ollowing conditions: let be surace tension at the skin-air interace, surace tension at the skin-solution interace, - surace tension o solution-air, and θ - contact angle. Condition o the surace wettability is as ollows: cosθ I θ < 9 the surace is wettable, i θ > 9 the surace is unwettable. Thereore, uon carrying out the ultrasonic eeling the skin surace becomes wettable which ermits to draw a conclusion about the eiciency o ultrasonic eeling. eerences. Vinogradov G.V., Malkin A.Ya. Polymer heology.-m.: Chemistry, Gorshkova V.M. Develoment o Technology and Tools or Ultrasonic Imregnation o the Pharmaceutical Substance into the Vascular Wall. Ph.D. thesis M Nikolaev G.A., Loshchilov V.I. Ultrasonic Technology in Surgery - M.: Medicine, 98 7

8 4. Alication o Ultrasonic in Medicine. Basic Physics/ Under the Editorshi o K. ill - М.: Mir, Ernandes E.I. Cosmetic Peeling: Theoretical and Practical Asects. Collected articles. Publishing ouse Cosmetics and Medicine ; М. -.4 V.M. Gorshkova. Ph. D. (Eng),Ass ro. o «Chemistry», senior researcher o «Medical and Technical Inormation Technologies» Deartment o the Bauman Moscow State Technical University. Author o about ublication in the ield o medical engineering and technology. 8