Thermal analyses of in vitro low frequency sonophoresis

Ultrasonics Sonochemistry 35 (2017) 458–470

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Ultrasonics Sonochemistry journal homepage: www.elsevier.com/locate/ultson

Thermal analyses of in vitro low frequency sonophoresis Peng Han-Min ⇑, Zhu Pan-Cheng, Chen Zhi-Jun State Key Lab of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics & Astronautics, Nanjing 210016, China

a r t i c l e

i n f o

Article history: Received 6 July 2016 Received in revised form 28 October 2016 Accepted 28 October 2016 Available online 2 November 2016 Keywords: Sonophoresis Thermal analyses Low frequency ultrasound FEM Sonochemistry

a b s t r a c t As a type of transdermal drug delivery method, low frequency sonophoresis (LFS) has been investigated during the last twenty years and is currently being attempted in a clinical setting. However, the safety of low frequency ultrasound on humans has not been completely guaranteed with high-intensity ultrasound. Thermal damage, one of the challenges in the LFS process, e.g., burns, epidermal detachment and necrosis of tissues, hinders its widespread applications. To predict and impede the overheating problems in LFS, an acoustic-flow-thermal finite element method (FEM) based on COMSOL Multiphysics software is proposed in this paper to achieve thermal analyses. The temperature distribution and its rising curves in in vitro LFS are obtained by the FEM method and experimental measurements. Both simulated and experimental maximum temperatures are larger than the safety value (e.g., 42 °C on human tissues) when the driving voltage is higher than 40 V (5.5 W input electric power), which proves that the overheating problem really exists in high-intensity ultrasound. Furthermore, the results show that the calculated temperature rising curves in in vitro LFS correspond to the experimental results, proving the effectiveness of this FEM method. In addition, several potential thermal influence factors have been studied, including a duty ratio and amplitude of the driving voltage, and liquid height in the donor, which may be helpful in restraining the temperature increase to limit thermal damage. According to the calculated and experimental results, the former two factors are sensitive to the rise in temperature, but a small scale of liquid volume increase can enhance the permeation of Calcein without obvious temperature change. Hence, the above factors can be synthetically utilized to restrain the rise in temperature with little sacrifice of permeation ability. So this acoustic-flow-thermal FEM method could be applied to an optimized LFS system design and simulating the thermal analyses of LFS in healthy human body in terms of safe thermal limits. Ó 2016 Elsevier B.V. All rights reserved.

1. Introduction Low-frequency sonophoresis (LFS) is a type of transdermal drug delivery system for realizing and enhancing the administration of drugs through the skin via injections and oral route [1–3]. As a major barrier, the stratum corneum (SC) of the skin limits the penetration of substances, but LFS (20–100 kHz) can effectively improve the transdermal permeation of different drugs, including hydrophobic and hydrophilic permeants as well as small and large molecular weight permeants [4–5]. Early in 1995, Mitragotri et al. found that LFS should be more effective (up to three orders of magnitude) than high-frequency sonophoresis (over 1 MHz) in enhancing skin permeability [6–7]. Over the last two decades, many researchers have investigated LFS mechanisms [8–12], various ultrasound or synergistic treatment methods [4,13–15],

⇑ Corresponding author. E-mail address: [email protected] (H.-M. Peng). http://dx.doi.org/10.1016/j.ultsonch.2016.10.027 1350-4177/Ó 2016 Elsevier B.V. All rights reserved.

delivery characteristics of different permeants (e.g., proteins, biopolymers, nanoparticles, and other high-molecular weight drugs or particles) [16], clinical applications [17–18], and so on. Although a number of LFS theories have been studied, the real mechanism is too complicated to fully understand. Until now, researchers have believed that the main ultrasonic effects on LFS include cavitation, acoustic streaming, thermal effects, and bilayer sonophore effect [19], among which cavitation is regarded as the main activity that modifies the SC and contributes to the improvement of transdermal drug delivery [4,10,16]. Currently, to expand the application region of LFS, its safety in humans has been the focus of a large amount of research. Boucaud et al. reported that no modifications were observed in human skin samples when ultrasound intensities were lower than 2.5 W/cm2 at 20 kHz; however, at intensities over 4 W/cm2 in continuous mode or 5.2 W/cm2 in pulsed mode (both in 10 min), obvious histologic damage, such as the detachment of the epidermis and dermal necrosis, was observed [20]. Generally, cavitation and thermal effects are the two main causes of skin or biological tissue

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Nomenclature Latin letters Values or description an the inward normal acceleration on the top surface of the transducer head (m2/s), Eq. (1) and Fig. 6 (measured values) b damping factor in gas–liquid medium, Eq. (5) c speed of sound (m/s), 1450 cc complex acoustic speed, Eq. (1) Cp heat capacity, material parameter d skin thickness, variable D thermal diffusivity of the gas (m2/s), 1.9  105 f the working frequency of ultrasonic transducer [Hz], 21000 F the volume force of acoustic streaming, variable k thermal conductivity, material parameter kTKE the turbulent kinetic energy, variable n the normal vector (unit vector), Eq. (1) p0 initial amplitude of acoustic pressure, variable the total pressure in the flow, variable pF pt total acoustic pressure, variable pb undisturbed pressure in the liquid, p1 + 2rl/R p1 equilibrium pressure in the liquid, =qgz Q heat source, variable Qa heat source from the acoustic attenuation, variable r radial coordinate r, variable R equilibrium radium of cavitation bubbles, variable R0 radius for the Gaussian radii distribution with a maximum value (m), 5  104 [27] R1 minimum bubble radius (m), 5  106 [27] maximum bubble radius (m) 3  103 [27] R2 Rinstant instantaneous bubble radius, variable

modifications: ultrasonic cavitation exists in the drug solution next to the skin and in skin crevices (such as the hair, follicle shafts, and sweat glands ducts). A suitable thermal effect (41
45 °C) can improve molecular diffusion movement, blood flow and metabolism. Nevertheless, the thermal effect in LFS is very difficult to maintain at 41
45 °C, and overheating which often occurs in ultrasonic cavitation induces histologic damage [21], including burns, epidermal detachment and tissue necrosis [21]. Boucaud et al. suggested a safe temperature limit of 42 °C for the skin [22]. Therefore, in LFS, the ultrasound intensity and acoustic exposure time should be synthesized to guarantee the available permeation of transdermal drug delivery, and the maximum temperature in the skin should be approximately 42 °C. Until now, ultrasonic tissue heating problems have been mainly studied at high frequency (P1 MHz) [23], especially for therapeutic ultrasound. Heat generation induced by low-frequency high power ultrasonic horn reactors has been computed by COMSOL, as well [24]. Nevertheless, there are few studies on the thermal effect in LFS, which is a key problem regarding the safety of this technique in clinical applications. In this paper, thermal analyses are completed in in vitro LFS based on the finite element method (FEM) of COMSOL. A computational modeling of the acousticflow-thermal process is proposed in in vitro LFS. The temperature distribution and temperature rising curves can also be acquired by this simulation method, and the experimental results prove its validity in in vitro LFS. Finally, several potential influence factors of temperature increase and permeation, including the duty ratio and amplitude of the driving voltage and the liquid height in the donor, can be used to restrain the temperature rising with little sacrifice of permeation ability in in vitro LFS. The results demonstrate that the FEM calculated method in this study can also be

t T u V0p x y z

time, variable temperature, variable velocity field, Eqs. (10) and (12) zero-to-peak voltage, variable x direction of Cartier coordinate system shown in Fig. 7 (a), variable y direction of Cartier coordinate system shown in Fig. 7 (a), variable z direction of Cartier coordinate system shown in Fig. 7 (a), variable

Greek letters a absorption coefficient, Eqs. (1) and (9) b gas volume void fraction, Eq. (7) c specific heat ratio of the gas inside the bubbles, 1.4 l the dynamic viscosity of the liquid (Pas), 1.01  103 (40 °C water) ll the viscosity of the liquid (Pas), 6.51  102 (40 °C water) lT the turbulent viscosity of the liquid, (Pas) variable q material density, material parameter qc complex density of liquid, Eq. (1) rl surface tension of the liquid (N/m), 69.56  103 (40 °C water) rSD standard deviation of bubbles distribution (m), 2  103 [27] U complex dimensionless parameters, Eqs. (6) v a coefficient in Eq. (6), =D/xR2 x angular frequency of the ultrasonic transducer, = 2pf x0 resonance frequency of bubbles, Eq. (4)

effective for the optimized structural designs of ultrasonic transducers and drug delivery systems to solve overheating problems in LFS. 2. Material and methods 2.1. Skins Healthy rat skins were prepared by China Pharmaceutical University and were harvested within one hour after sacrificing the animals. The subcutaneous fat was removed and the hair was shaved with scissors. Then, the skins were sectioned into small strips before storing at 80 °C until use. 2.2. Chemicals Phosphate buffer saline (PBS; 0.01 M phosphate, pH = 7.4) was obtained from Novland BioPhama Co., Ltd. (Shanghai, China); Calcein (a fluorescent indicator dye in LFS, molecular weight: 622.55) and sodium lauryl sulfate (SLS) (a surfactant used to synergistically enhance the effects of sonophoresis) were purchased from Hefei Bomei Bio-technology Co., Ltd. (Hefei, China). 2.3. Ultrasonic transducer An ultrasonic transducer (21 kHz) was obtained from Hainertec (Suzhou) Co., Ltd. (Suzhou, China). Fig. 1 shows the transducer structure used in the simulated and experimental analyses. It has a Langevin type and size in the transduction section. Four pieces of piezoelectric ceramic rings (PZT-8) with opposite polarization

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Fig. 1. Ultrasonic transducer: (a) structural sketch; (b) setup.

directions were sandwiched by the back and front masses (titanium alloy) to form the transduction area. An aluminum alloy frame was assembled to hold the entire transduction section. The top of the front mass was used as the acoustic exposure section, which was named the transducer head in this paper (also called an ultrasonic horn in other papers). When voltage was applied to the piezoelectric ceramics and the frame was fixed, the transducer head emitted ultrasonic waves into the liquid media.

2.4. Measurement methods A PSV-500 scanning vibrometer from Polytec Co., Ltd. (Waldbronn, German) was used to measure the normal acceleration amplitude on the top surface of the transducer head in the water. Its measurement sketch and experimental setting are shown in Fig. 2. Fig. 2(a) shows that one PSV-500 scanning head is used to emit and receive laser signals, and a mirror to reflect the laser light beam in order to measure the vibration of the transducer head in the water. Fig. 2(b) shows that the real experimental setting and collection data points on the surface of the transducer head. Thus, the non-contact measurement technique of PSV-500 can direct one laser to one grid point and measure the vibration along its incident direction. Due to the difficulty in direct measuring of its actual vibration amplitude upon the skin, the amplitude in the water (approximately equal to the liquid volume in in vitro LFS) was approximately assumed as the main initial condition in acoustic field calculation. A Franz diffusion cells system for in vitro LFS, shown in Fig. 3, was used to measure the permeation of Calcein and rising values of the system temperature as time increases. A rat skin was sectioned and mounted in vertical Franz diffusion cells TT-8(D) (15mm inner diameter), which were obtained from Tianjin Rightway Technology Co., Ltd. (Tianjin, China). A donor, a skin sample, and a receptor typically constitute one Franz cell, as shown in Area A of Fig. 3. A constant temperature system keeps the circulating

water at 37 °C, and the drug liquid (Calcein solution in this paper) height in the donor is maintained at 21 mm. To achieve safe non-invasive drug delivery, heat should be controlled to a certain extent. Therefore, thermocouple wires and intelligent temperature controllers (XMTD-618) were used to measure the liquid temperature with a resolution of 1 °C, which were obtained from Yuyao Gongyi Meter Co., Ltd. (Zhejiang province, China). An infrared camera (FLIR i7, FLIR Systems, Inc., USA) with a resolution of 0.1 °C was used to measure the temperature on the surface of the donor. In the experiments, two thermocouple wires and intelligent temperature controllers recorded the temperature data in the donor and receptor: one wire was under the transducer head and the other in the liquid draw-off position, as shown in Right view of Area A of Fig. 3. In the first 90 min, the temperature data were recorded every 15 min. In this paper, 1 mmol/L Calcein and 1.0% (w/v) SLS were used in PBS in the donor and PBS alone in the receptor before permeation. When the ultrasonic transducer worked at a resonance frequency of 21 kHz (a minor frequency adjustment was occasionally required to guarantee that the transducer was at resonance all the time), the ultrasonic head emitted an ultrasonic wave into the Calcein solution and rat skin. Then, the SC was broken to increase Calcein permeation. The permeated Calcein was stored in PBS in the receptor, and samples were taken with a dropper every 15 min to obtain the permeation value of Calcein by an ultraviolet visible spectrophotometer (UV-1800) obtained from Shanghai Mapada Instruments Co., Ltd. (Shanghai, China). The Calcein concentration in the receptor represents the effectiveness of lowfrequency sonophoresis. In this paper, all of the experimental and simulated data in LFS are obtained at the resonance frequency unless otherwise stated, and all experimental data points were the average values of 2
5 skin samples.

3. Theory and FEM model In LFS, a high-intensity acoustic field in the donor produces an appropriate number of acoustic bubbles. The bubbles can be classified into two categories, stable and inertial cavitation: in stable cavitation, the acoustic pressure and streams may increase the permeability of a drug outside the skin; in inertial cavitation, plenty of shock waves occur and micro-jets physically penetrate the SC, contributing to the drug permeation through the skin. Furthermore, some portions of the skin are compressed and the others are stretched due to acoustic streams. Until now, the above synthetic effects have been known to be the main methods of destroying SC to increase permeation, as shown in Fig. 4. Nevertheless, the acoustic cavitation and acoustic absorption produce a sufficient amount of heat. In this paper, a FEM simulation method based on COMSOL is used to calculate the acoustic field distribution and the temperature rise in in vitro LFS. Here, the simulation is conducted with the following main assumptions: 1) The acoustic absorption calculation is in a plane-wave limit; 2) The acoustic field is assumed to be an attenuation of linear elastic waves in the lossy media, including the skin and liquids in the donor and receptor; 3) The acoustic streaming calculation is based on Turbulent Flow (k-e) Model; 4) The heat transfer coefficients includes the coefficients of conduction and convection (ignoring heat radiation); 5) The influence of the liquid draw-off pipe to the acoustic field and temperature are ignored because the temperature rise is almost zero in the receptor (detailed results are presented in Section 4 and Fig. 8(a)).

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Fig. 2. Measurement system of normal acceleration amplitude on the top surface of the transducer head in the liquid: (a) schematic design; (b) experimental setting.

and the initial condition satisfies: n  q1 rpt ¼ an where x = 2pf is

3.1. Acoustic field coupling in a gas-liquid medium (first step)

c

In LFS, the vibration of the transducer head forms an acoustic field, and COMSOL presents a Pressure Acoustics Module to obtain the total acoustic pressure pt. In this paper, the acoustic cavitation effect should be considered. Cavitation bubbles appear when the acoustic power of the ultrasonic transducer exceeds the cavitation threshold value. This gas-liquid medium changes the acoustic field distribution and acoustic pressure amplitude in the liquid. Here, a linear absorption coefficient a of sound propagation is used to represent the above acoustic field variation due to cavitation bubbles. Therefore, by introducing complex density qc and complex acoustic speed cc to explain the damping of ultrasonic effect, the Helmholtz equation for the propagation of sound waves can be revised as [25]:

r

1

qc

2

ðrpt Þ 

keq pt

qc

¼0

8 pt ¼ p þ pb > > > > > k ¼ x=c  ia > < a 2 2 q where c ¼ qc =c c > > > c ¼ x =k c a > > > : 2 2 keq ¼ ðx=cc Þ2 ¼ ðx=c  iaÞ

ð1Þ

the angular frequency, pt is the total acoustic pressure as a function of angular frequency x at three-dimensional coordinates (x, y, z), pb is the undisturbed pressure in the liquid, a is the absorption coefficient, q is the liquid density, c is the acoustic speed, n is the normal vector (unit vector) and an is the inward normal acceleration on the top surface of the transducer head. The equivalent wavenumber keq in the gas-liquid medium is equal to the equivalent wavenumber ka in the acoustic field while considering sound attenuation. In in vitro LFS, many bubbles existed in the donor due to ultrasonic cavitation, but fewer bubbles present in the receptor because the acoustic intensity in the receptor is much less than that in the donor. This is due to the large absorption coefficient of skin at a low-frequency driving voltage. According to the Cafisch equations theory proposed by Commander and Prosperity [26], the equivalent wavenumber keq in the gas-liquid medium in an acoustic field should be: 2

keq ¼

x2 c

þ 4px2

Z 0

1

Rf ðRÞ

x20  x2 þ 2ibx

dR

ð2Þ

where R is the equilibrium radium of cavitation bubbles and f(R) is its certain radial distribution and volume fraction, which can be assumed to be a Gaussian distribution. x0 is the resonance

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Fig. 3. Measurement system of permeation and temperature rising in in vitro LFS;

frequency of the bubbles, i is the imaginary unit and b is the damping factor. They are defined as [26]:

( f ðRÞ ¼

x20 ¼ b¼

2

C coe eðRR0 Þ

=r2SD

0

pb

2l1

qR

2

otherwise



qR2 þ

R 1 < R < R2

ReU  pb 2qR

2

2r1 Rpb

ð3Þ



ImU þ

ð4Þ

x2 R 2c

ð5Þ

where Ccoe is a parameter chosen to match the gas volume void fraction b, R0 is the radius for the Gaussian radii distribution with a maximum value, rSD is a standard deviation of approximately 2  103 m, R is in a range of bubble radii from R1 = 5  106 m to R2 = 3  103 m, rl is the surface tension of the liquid, ll is the viscosity of the liquid and the undisturbed pressure in the bubble (equal to in the liquid) pb = p1 + 2rl/R, and p1 is the equilibrium pressure in the liquid. The complex dimensionless parameter U is defined as [26]:

Fig. 4. Sketch of the in vitro LFS working principle in a high-intensity acoustic field.

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U¼

3c

1  3ðc  1Þiv½ð1=vÞ

1=2

cothð1=vÞ

1=2

 1

ð6Þ

where c is the specific heat ratio of the gas inside the bubbles and v = D/xR2, with D as the thermal diffusivity of the gas. The relationship between the function f(R) and the gas volume void fraction b is [26–27]:

bðr; tÞ ¼

4 p 3

Z 0

1

R3instant ðr; R; tÞf ðr; RÞdR

  2 Re keq ¼ Re

 x

2 

 ia c  Z ¼ Re ðx=cÞ2 þ 4px2

0

1

Rf ðRÞ dR x20  x2 þ 2ibx

 ð8Þ

In terms of Eq. (8), the absorption coefficient a can be represented as:

ð7Þ

where Rinstant(r, R, t) denotes the instantaneous bubble radius at time t and position r with an equilibrium radius R. In the experiments, the volume of the diffusion cell is small (<20 mL) enough to assume an average constant b instead of b(r, t) to calculate parameter Ccoe. According to the same real part of wavenumber keq in Eqs. (1) and (2), there are:

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  ffi Z R2 Rf ðRÞ 2 a ¼ Re 4px dR 2 2 R1 x0  x þ 2ibx

ð9Þ

Therefore, Eqs. (3)–(7) can be substituted into Eq. (9) with the initial and boundary conditions, and the absorption coefficient a in LFS can be calculated. Then, the total acoustic pressure pt can be calculated in terms of Eq. (1). The boundary conditions mainly

Fig. 5. Boundary conditions in the FEM model: (a) Pressure Acoustic Module; (b) Turbulent Flow (k-e) Module; (c) Heat Transfer Module.

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include that the liquid boundary contact with air is assumed to be a sound-soft boundary and the liquid boundary contact with the glass wall is a sound-hard boundary, as can be seen in Fig. 5(a). 3.2. Acoustic streaming (second step) When an ultrasound beam passes through a volume of liquid and the skin, some of the energy of the primary acoustic field is absorbed locally by the mediums and turned into heat. In in vitro LFS, the main heat source from ultrasound energy is the liquid in the donor, and acoustic streaming in the liquid will accelerate its heat transfer to thermal equilibrium. Therefore, the computation of acoustic streaming is also implemented by COMSOL Multiphysics in order to calculate the temperature rise. The vibration velocity and sound pressure of the ultrasonic field (in Section 3.1) are used to calculate the velocity field of acoustic streaming, which is required in the next Heat Transfer module of the software. The steady acoustic streaming satisfies the following equation: 

2 3

2 3

@T þ qC p u  rT ¼ rðkrTÞ þ Q @t

ð12Þ

where T is the temperature, t is the time, q is the material density, Cp is the heat capacity, k is the thermal conductivity, u is the velocity field and Q is the heat source in which different heat sources can be added separately. For the heat source Q in the vitro experiment, the following parts are formed: the acoustic cavitation (the sound absorption in the liquid) and acoustic absorption of the skin. Given the acoustic pressure field the acoustic intensity field is readily derived. The heat source Qa for thermal simulation, given in the plane-wave limit, is then calculated [29] as:

Q a ¼ 2a½p2t =ð2qcÞ

ð10Þ

where Qa is the heat source from the acoustic absorption in the liquid and skin. p2t =ð2qcÞ is the root-mean-square value of the acoustic intensity in the plane-wave limit. Then, the thermal calculation can be obtained from Eq. (12) according to initial and boundary conditions. The boundary conditions mainly covers all the surfaces of the ultrasonic transducer, and the Franz diffusion cell contact with air is assumed to be the heat external natural convection, as shown in Fig. 5(c).

where q is the liquid density, u is the velocity field of acoustic streaming, pF is the total pressure in the flow, l is the dynamic viscosity of the liquid, lT is the turbulent viscosity of the liquid, kTKE is the turbulent kinetic energy, and F is the volume force of acoustic streaming. F in 2D Turbulent Flow (k-e) Model can be represented by Fj which is calculated by [28]

@ðqui uj Þ @xi

qC p



qðu  rÞu ¼ r  pF I þ ðl þ lT Þðru þ ðruÞT Þ  ðl þ lT ÞðruÞI  qkTKE I þ F

Fj ¼ 

ultrasonic transducer and liquid in the donor and receptor. Furthermore, the heat source from the mechanical loss and dielectric loss of ultrasonic transducer can be ignored, because it is much smaller than that in the liquid. The transient thermal equilibrium equation can be represented as [25]:

ð11Þ

where ui (subscript i & j denote the flow direction) is the vibration velocities in the sound wave, and the bar signifies the mean value over one period. In this case, ui can be calculated from the Pressure Acoustics Module (see Section 3.1).

ð13Þ

3.4. FEM calculation Our calculation of temperature rise in LFS is implemented by the FEM software COMSOL Multiphysics. The calculation process mainly consists of three steps:

3.3. Heat transfer (final step) In in vitro LFS, the heat transfer in the Franz diffusion cell can be divided into solid heat transfer and fluid heat transfer. The former includes the skin, entire ultrasonic transducer and structural frame of one Franz diffusion cell; the latter includes the interior air in the

1) First, the measured acceleration on the surface of the transducer head, an important initial parameter, is used to solve the acoustic field based on the Pressure Acoustics Module of the software; 2) Second, the acoustic pressure and vibration velocity of the acoustic field are utilized to calculate the volume force of

Table 1 Main material parameters values in the FEM model. Ultrasonic transducer (as shown in Fig. 1) Items

Material

Heat capacity at constant pressure (J/(kgK))

Density (kg/m3)

Thermal conductivity (W/(mK))

Part Part Part Part

Aluminium alloy Titanium alloy PZT-8 High-strength alloy steel

893 539.6 420 475

2730 4430.2 7650 7850

155 7.1 2.1 44.5

Franz cell system (as shown in Fig. 3) Part 1 Titanium alloy Part 2 & 7 (external) Glass Part 2 & 7 (internal) Liquid (similar to water) Part 5 Teflon Part 6 Skin Part 8 Magnetic stirring bar was ignored in our FEM model

542.6 730 4180.5 928.4 3391

4429 2210 1000 2131.5 1109

7.1 1.4 0.6 0.27 0.37

Items

Material

Speed of sound (m/s)

Dynamic viscosity (Pas)

Part 2 & 7 (internal) Part 6

Liquid (similar to water) Skin

1450 1600

0.001 Null

1 2&5 3 4

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H.-M. Peng et al. / Ultrasonics Sonochemistry 35 (2017) 458–470 Table 2 Main initial conditions in the FEM model. Pressure Acoustics Module Items

Initial normal acceleration amplitude (m/s2)

The measured normal acceleration on the top surface of the transducer head (an)

1.05  105 m/s2 (at V0p = 30 V); 1.69  105 m/s2 (at V0p = 40 V); 2.14  105 m/s2 (at V0p = 50 V)

Turbulent flow (k-e) module Items

Volume force of acoustic streaming (N)

The liquid in the donor

F can be calculated from Eq. (11).

Heat transfer module Items

Heat sources (W/m3)

Skin and liquid both in the donor and the receptor

Qa can be can be calculated from Eq. (13)

Items

Initial temperature (°C)

Items

Boundary temperature (°C)

Ultrasonic transducer (except transducer head) Transducer head, liquid and glass in the donor Skin, liquid and glass in the receptor

26 30.5 37

Water outside the receptor Environment temperature in the air

37 26

Items

Velocity of acoustic streaming (m/s)

Heat transfer in fluids (in the donor) Heat transfer in fluids (in the receptor)

u can be calculated from Eq. (10) u can be deduced from the magnetic stirring at 400 rpm

the fluid which can generate the acoustic streaming and enhance the heat convection in the donor, based on the Turbulent Flow (k-e) Module of the software; 3) Finally, the above acoustic pressure and velocity field of acoustic streaming are used to calculate the temperature rise in in vitro LFS. The acoustic field in in vitro LFS can be calculated according to Section 3.1 in terms of Eqs. (1)–(9) and the Cafisch theory [26]. The SLS added in the donor in the experiments, which is a surfactant widely used in shampoo and bubble bath could dramatically enhance the gas volume void fraction by effective production of bubbles. There was 1.0% (w/v) SLS used in PBS in the donor and PBS alone in the receptor. Referring to the equation b = 4pR3N/ (3V) (see Eq. (24) in document [27]) where R is the present radius of the bubbles and N/V is their density, the gas volume void fraction in the water, b, can be approximately computed to be 105 in the receptor as [26,27], and assuming to be 103 as the approximate average value in the donor at 21 kHz [27] which is 100 times larger than that in the receptor. Therefore, the absorption coefficient a can be numerically calculated to be 29.4 Np/m and

2.9 Np/m in the donor and receptor, respectively. Furthermore, the absorption coefficient a2 was approximately assumed to be 4 Np/m (soft tissue is closer to 10 Np/m at 1 MHz) when the skin thickness was measured as d = 5.62  104 m. In this FEM model, the primary material parameters are shown in Table 1, for most of which the COMSOL material database can provide. The initial and boundary conditions of our FEM model are mainly included in the Tables 1 and 2 and Fig. 5, whose values are the same as those of the experiments. In addition, as shown in Fig. 3 the magnetic stirring bar (Part 8) was ignored because its structure scarcely influenced the thermal process, but its rotation speed was considered as a fluid velocity in the heat transfer module. 4. Results and discussion First, the normal vibration acceleration amplitude on the top surface of the transducer head in the liquid was measured by a PSV-500 scanning vibrometer, and more details can be seen in Section 2.4. The test results were an = 1.05  105 m/s2, 1.69  105 m/s2 and 2.14  105 m/s2 at f = 21 kHz and V0p = 30 V

Fig. 6. Measured normal acceleration amplitudes on the top surface of the transducer head in the liquid at f = 21 kHz and V0p = 30 V, 40 V and 50 V, respectively.

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(input electric power 2 W), 40 V (input electric power 5.5 W) and 50 V (input electric power 8 W), respectively, as can be shown in Fig. 6. They were assumed as the initial values for the FEM calculations in in vitro LFS, which can be substituted into Eq. (1) to solve the acoustic pressure. Then, acoustic pressure, the velocity of acoustic streaming and temperature rise in a Franz diffusion cell can be calculated based on Eqs. (1)–(13), according to the initial and boundary conditions listed in Tables 1 and 2 and Fig. 5. Here, as a calculation example, the calculated results at V0p = 40 V and 21 kHz presented in Fig. 7.

Fig. 7(a) shows that in the entire acoustic pressure distribution in in vitro LFS the maximum value is 3.37  105 Pa, which appears close to the transducer head in the donor. Fig. 7(b) and (c) describe the acoustic pressure distribution on both the SC and dermis of the skin, and the maximum value is 8.21  104 Pa and 5.10  104 Pa, respectively. The maximum values appear on the SC under the center of the transducer head and the maximum acoustic pressure difference is 3.11  104 Pa, which may enforce the drug permeation of the skin. Fig. 7(d and e) show the computed velocity distributions of acoustic streaming (in axial symmetry) in the x and

Fig. 7. FEM calculated results at V0p = 40 V: (a) acoustic pressure distribution in the Franz diffusion cell; (b) acoustic pressure distribution at the upper surface of the skin in the donor; (c) acoustic pressure distribution at the lower surface of the skin in the receptor; (d) the velocity along x/y direction (namely radial direction) of acoustic streaming in the donor; (e) the velocity along z direction of acoustic streaming in the donor; (f) temperature distribution in the Franz diffusion cell in the first 90 min of continuous operation; (g) temperature distribution at the upper surface of the skin under the ultrasonic transducer in the first 90 min of continuous operation.

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Fig. 8. Maximum temperature rising curves in the liquid, on the outside surface of the donor chamber and Calcein concentration change in the receptor with and without ultrasound in the first 90 min: (a) maximum temperature rising curves in the first 90 min of continuous operation (simulated and experimental results); (b) the concentration rising histogram of Calcein and the optical images of rat skin epidermis after in vitro LFS.

z directions, whose maximal values between the transducer head and skin are 0.2 m/s and 0.18 m/s, respectively. The above results are substituted into the thermal equivalent equation Eqs. (12) and (13); thus, the temperature distribution after 90 min of continuous operation can be calculated, and its results are shown in Fig. 7 (f). It shows that the maximum temperature reaches 52.4 °C in the donor, but the temperature in the receptor is always 37 °C due to the constant temperature water bath (37 °C). Fig. 7(g) shows that the temperature distribution is approximately uniform on the SC of the skin in the permeability zone, also reaching 52.4 °C. Thereby, it demonstrates that the rise in temperature in the donor is the major reason for skin overheating problem, and the temperature control method in the donor should be considered. In terms of the above FEM method, the characteristics of temperature rise in in vitro LFS are computed and measured at 40 V and 21 kHz (continuous operation mode), as can be seen in Fig. 8 (a). Fig. 8(b) shows its Calcein permeation curves versus time and photographs of skin samples after in vitro LFS. The temperature rising curves in the first 90 min of continuous operation can be acquired, and the curves illustrate that the first 15 min of continu-

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ous operation can cause the temperature to reach a thermal equilibrium status. Furthermore, the rising temperature in in vitro LFS is mainly concentrated in the liquid of the donor and skin, and the external temperature on the surface of the donor is smaller than the internal value. This is because of the effect of acoustic streaming on convective heat exchange. However, the temperature in the receptor remains the same because of the other heat convection from the magnetic stirring at 400 rpm. In Fig. 8(a), the calculated temperature rises are similar to the experimental results, so this acoustic-flow-thermal FEM method can effectively predict thermal problems in in vitro LFS. In Fig. 8(b), the average concentration of Calcein in the receptor under ultrasound, which reaches 4.2 lmol/L in the first 90 min, is larger than 0.8 lmol/L under ultrasound-free condition. The optical images of skin samples show that the surface of the SC is rougher than the other, which illustrates that the skin was stretched due to acoustic streaming, whose principle can be seen in Fig. 4. Consequently, these illustrate that ultrasonic effect can not only enhance the drug permeation but also generate a certain rise in temperature under a highintensity input. Aiming at safe clinical applications of LFS, potential influence factors should be used to decrease the temperature rise but improve the permeation as much as possible. There are many potential influence factors of the increasing temperature, e.g., the transducer structure, liquid container, driving voltage, drug liquid, and liquid volume. In the experiments, the voltage signals and liquid volume are selected to analyze the thermal characteristics, and Calcein permeation is chosen as further proof of the effectiveness of LFS, by comparing the simulated and experimental results. Fig. 9 shows the maximum temperature and Calcein permeation with different driving voltages in in vitro LFS. Fig. 9 (a) illustrates that the driving voltage amplitude can adjust the maximum temperature in the liquid and decreasing the voltage can restrain the temperature. Meanwhile, the simulated temperature rising curves at 30 V, 40 V and 50 V are approximately identical to the experimental results. Moreover, the calculated results at V0p = 50 V are close to the upper bound of experimental results, which may be the reason for the slight change of acoustic intensity due to a layer of bubbles forms on the vibration surface of the transducer head. In Fig. 9(b), the 50 V driving voltage produces the largest permeation of 13.4 lmol/L, but the rat skin images after in vitro LFS show damage regions (black sections in the pictures) on both the epidermis and dermis due to a larger temperature rise. Therefore, driving voltage should be synthetically considered for suitable permeation and temperature increases with less damage. Fig. 10 shows the maximum temperature curves and concentration increase of Calcein at a 50% duty driving voltage ratio along with a continuous operation at V0p = 40 V in the first 90 min. In Fig. 10(a), a 50% duty ratio can more effectively decrease the temperature rise than a continuous operation, from 54.0 °C to 43.0 °C in the experiments and 53.7 °C to 43.7 °C in the simulation, which is closer to a security temperature of 42 °C for the skin. In this case, Fig. 10(b) shows that the Calcein permeation in continuous operation is 4.2 lmol/L after 90 min, larger than 1.6 lmol/L at the 50% duty ratio, sacrificing about 62% of the permeation. Therefore, adjusting the driving voltage duty ratio is a feasible method for controlling the rise in temperature in LFS with some sacrifice of permeation. In addition to adjusting the driving voltage, liquid height in the donor is another influence factor that was investigated in Fig. 11. Fig. 11(a) describes the maximum temperature with different liquid height at V0p = 40 V in the first 90 min. The calculated maximum temperature is approximately the same as that in the experiment, where little temperature change at different heights is observed in the experimental results. Fig. 11(b) illustrates that a small scale of liquid volume alternation cannot change the tem-

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Fig. 9. Maximum temperature rising curves in the liquid and Calcein concentration change in the receptor at V0p = 30 V, 40 V and 50 V, respectively: (a) maximum temperature rising curves in the first 90 min; (b) the concentration rising histogram of Calcein and the optical images of rat skins after in vitro LFS.

perature rise, but would enhance the drug permeation in in vitro LFS. This may be the reason that the increment of static pressure in the liquid may enhance the effect of LFS. Besides the previous thermal analyses of in vitro LFS, there would be some differences in in vivo LFS considering the effect of blood flow. There would be a little larger temperature rising in vivo LFS, because the heat conduction coefficients of human skin, fat and muscle are 0.37, 0.25 and 0.49 W/(mK), respectively, which are smaller than 1.4 W/(mK) of the receptor’s glass. In this case, the previous method of duty ratio adjustment can be utilized to in vivo LFS, and the varying tendency can be calculated by setting relative biological parameters based on our FEM simulation method. 5. Conclusions In this paper, to avoid overheating damage to the skin or healthy tissues in LFS, an acoustic-flow-thermal FEM calculation method based on COMSOL is proposed to achieve thermal analyses in in vitro LFS. The driving voltage and liquid height are

independently investigated to acquire the influence factors of the rise in temperature and Calcein permeation. The calculated and experimental results demonstrate that in vitro LFS with certain input power intensity may induce overheating problem on the skin, for example, the temperature rise reached 50 °C at V0p of 40 V and 21 kHz during the first 15 min continuous working; our FEM method can effectively simulate and predict the temperature rise in in vitro LFS; the duty ratio and amplitude of the driving voltage are sensitive to the rise in temperature, but a small scale of liquid volume increase can enhance the drug permeation without obvious temperature change. An optimized selection for the LFS process may be used to guarantee suitable permeation with a safe temperature rise and LFS selection can be calculated and designed by the proposed FEM method. Thereby, the proposed FEM calculated method can be also used to design the structure of a drug delivery system and shape of an ultrasonic transducer for safe clinical applications with high-intensity ultrasound, and would especially be applied to

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Fig. 10. Maximum temperature rising curves in the liquid and Calcein concentration change in the receptor with 50% and 100% (continuous operation) duty ratios at V0p = 40 V: (a) maximum temperature rising curves in the first 90 min; (b) the concentration rising histogram of Calcein.

LFS thermal analyses in healthy human body whose experiments might be against traditional moral or ethics. Acknowledgements This work is supported by the following funding organizations in China: the National Natural Science Foundation of China (Grant No. 51405224), the Natural Science Foundation of Jiangsu Province (Grant No. BK20140818), the Fundamental Research Funds for the Central Universities (Grant No. NJ20160003). References [1] B.G. Amsden, M.F.A. Goosen, Transdermal delivery of peptide and protein drugs: an overview, AIChE J. 8 (1995) 1972–1997. [2] D. Park, H. Park, J. Seo, S. Lee, Sonophoresis in transdermal drug deliverys, Ultrasonics 1 (2014) 56–65. [3] M. Aldwaikat, M. Alarjah, Investigating the sonophoresis effect on the permeation of diclofenac sodium using 3D skin equivalent, Ultrason. Sonochem. 22 (2015) 580–587. [4] S. Mitragotri, J. Kost, Low-frequency sonophoresis: a review, Adv. Drug delivery Rev. 5 (2004) 589–601. [5] B.E. Polat, D. Hart, R. Langer, D. Blankschtein, Ultrasound-mediated transdermal drug delivery: mechanisms, scope, and emerging trends, J. Control. Release 3 (2011) 330–348. [6] S. Mitragotri, D. Blankschrein, R. Langer, Ultrasound-mediated transdermal protein delivery, Science 5225 (1995) 850. [7] S. Mitragotri, D. Blankschrein, R. Langer, Transdermal drug delivery using lowfrequency sonophoresis, Pharm. Res. 3 (1996) 411–420.

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Fig. 11. Maximum temperature rising curves in the liquid and Calcein concentration change in the receptor with different liquid heights at V0p = 40 V: (a) maximum temperature rising curves in the first 90 min; (b) the concentration rising histogram of Calcein.

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