Skin Temperature Increase Mediated By Wearable, Long Duration, Low-Intensity Therapeutic Ultrasound

Abstract

One of the safety concerns with the delivery of therapeutic ultrasound is overheating of the transducer-skin interface due to poor or improper coupling. The objective of this research was to define a model that could be used to calculate the heating in the skin as a result of a novel, wearable long-duration ultrasound device. This model was used to determine that the maximum heating in the skin remained below the minimum threshold necessary to cause thermal injury over multiple hours of use. In addition to this model data, a human clinical study used wire thermocouples on the skin surface to measure heating characteristics during treatment with the sustained ultrasound system. Parametric analysis of the model determined that the maximum temperature increase is at the surface of the skin ranged from 40–41.8° C when perfusion was taken into account. The clinical data agreed well with the model predictions. The average steady state temperature observed across all 44 subjects was 40°C. The maximum temperature observed was less than 44° C, which is clinically safe for over 5 hours of human skin contact. The resultant clinical temperature data paired well with the model data suggesting the model can be used for future transducer and ultrasound system design simulation. As a result, the device was validated for thermal safety for typical users and use conditions.

INTRODUCTION

Therapeutic ultrasound delivers acoustic energy to biological tissues, which is typically absorbed and then converted into heat. For the usual application of therapeutic ultrasound, the movement of the transducer during treatment dissipates the heat over a broad area, preventing the accumulation of thermal energy. Recently, a wearable, long duration ultrasound device was developed for the treatment of musculoskeletal pain and accelerating recovery ^1–3. This device is worn in one location for the entire duration of treatment, providing sustained acoustic medicine to the treatment location. To investigate the safety of this new configuration for ultrasound devices, an understanding of the resultant heating of tissue was required. The maximal steady state temperature was estimated using a heat transfer model. Following estimation of the maximum temperature, experimental data were obtained for average skin temperature observed over a four hour treatment. This study describes the heating characteristics of a stationary therapeutic ultrasound device theoretically and experimentally.

METHODS

The theoretical modeling of the heat transfer was done using the bioheat equation. The experimental monitoring of skin temperature was done using an IRB-approved trial where thin wire thermocouples were attached the skin of human subjects during treatment with the wearable, long duration ultrasound device.

Bioheat Transfer Model

Balance Equation

The bioheat equation is the time-dependent balance equation that governs heat transfer in biological tissue (Equation 1) ⁴. The energy absorbed by the tissue is represented on the left side of the equation, with the time-dependent term. The right hand side of the equation represents the energy transferred into the tissue and out of the tissue by heat conduction, perfusion, and outside thermal sources, respectively. This model was concerned with determining the maximum temperature in the tissue, observed at steady state. This simplification led to the steady state bioheat equation, which was used for the model (Equation 2).

$$\rho \ast c\frac{dT}{dt}=\nabla k\nabla T+{\rho }_b\ast c_b\ast \omega \ast \left(T_b-T\right)+q$$ (1)

$$0=\nabla k\nabla T+{\rho }_b\ast c_b\ast \omega \ast \left(T_b-T\right)+q$$ (2)

Tissue Model

The tissue model was based upon the typical application of the device to an area with at least 3 cm of tissue between the skin and the bone. In this case, the layers of tissue considered were the skin (2.5 mm thick) and then muscle tissue down to the 3 cm depth. The model was defined to be a cylinder due to the circular shape of the ultrasound transducer, which was the energy source (Figure 1). Heat conduction was considered to occur axially and radially, transferring heat deeper into the tissue and into the surrounding tissue. Heat convection occurred primarily through transfer of energy to the circulatory system. Finally, the added heat to the body was considered to occur from two sources. The device is one energy source as it heats during treatment, and the acoustic energy emitted by the device is absorbed in the tissue and converted to heat. The thermal conductivity, acoustic attenuation, perfusion rate, specific heat, and tissue density information was researched to solve the model (Table 1)^{5, 6}. Based upon the acoustic attenuation data, the muscle layer was split into two regions. The upper region consisted of the muscle region up to the depth where 99% of the acoustic energy became attenuated. The lower region consisted of the remainder of the muscle, acting as a bulk. The length of the radial conduction was not known, so it was varied from 2.25 cm to 3.25 cm (a 1–2 cm increase from the transducer itself).

FIGURE 1.

Schematic of the heat transfer model. The blue cylinder represents the transducer. Blue arrows represent the direction of heat transfer.

TABLE 1.

The parameters used to solve the heat transfer model^{5, 6}. The frequency, electrical input, acoustic output, and heat loss of the device were measured by the manufacturer.

Term	Value	Units
kskin	0.37	W/(m*K)
lskin	0.0025	m
kmuscle	0.2	W/(m*K)
lmuscle	0.0006	m
αwater	0.0022	dB/(MHz*cm)
αskin	0.7	dB/(MHz*cm)
αmuscle	1	dB/(MHz*cm)
Frequency	3	MHz
Electrical Input	0.8646	W
Acoustic Output	0.65	W
Heat Loss Factor	0.8	-
ρskin	1.09	g/mL
ρblood	1.06	g/mL
ρmuscle	1	g/mL
Cp,skin	3.39	J/(g*K)
Cp,blood	3.62	J/(g*K)
Cp,muscle	3.42	J/(g*K)
ωskin	0.2	mL/(min*g)
ωmuscle	0.0027	mL/(min*g)

Temperature Measurement

Healthy subjects were recruited to take part in an IRB-approved study measuring the skin temperature during the use of the device. Subjects were classified as normal weight or overweight by BMI. Subjects wore the device on the arm or the leg, with two transducers applied to the limb. For the arm, transducers were applied to the elbow and forearm. For the leg, transducers were applied to the knee and calf. When the device was applied, the lead of a wire thermocouple was taped to the skin directly under the center of the transducer. This thermocouple monitored the skin temperature throughout a four hour treatment with the stationary ultrasound device. The subjects were asked to remain still during the measurement, preventing excessive movement from disturbing thermocouple placement.

RESULTS

Model

The model described in the methods section was solved numerically. The steady state temperature distribution for the tissue exposed to a circular source of ultrasound energy was determined. The maximal temperature calculated was 41.8°C, at the skin surface when the total length of radial heat transfer was 2.25 cm, or 1 cm from the outside edge of the transducer (Figure 3). This represented the maximal theoretical skin temperature. The theoretical steady state temperature distribution sharply decreased over the first centimetre of depth, and then plateaued out, with temperature increases persisting to a depth of 3 cm.

FIGURE 3.

Temperature distribution predicted by the heat transfer model, depending on the outer radius of heat transfer.

Temperature Measurement

The temperature measurement study was successfully completed by 44 subjects, equally divided into normal weight and overweight by BMI. The temperatures observed in both sets of subjects had a similar distribution, at all four locations. In all four locations, the temperature at the skin increased to 40°C within 0.5 hours of treatment initiation, and remained constant for the duration of the treatment (Figure 4). The thermal dose delivered to the skin had a CEM43°C of 3.75, which is generally considered safe ⁷.

FIGURE 4.

Average skin temperature observed during a 4 hour ultrasound treatment at four locations. (a) The elbow. (b) The forearm. (c) The knee. (d) The calf.

CONCLUSION

This study determined the theoretical steady state temperature distribution for a stationary ultrasound device, depending on the radius of heat conduction, and then measured the observed skin temperature. The skin temperature was 40°C, and the overall thermal dose was within acceptable limits. Based on the theoretical calculations, the actual radius of conduction is 2 cm larger than the radius of the transducer. When that parameter is modeled, the skin temperature that is predicted corresponds with the observed skin temperature. This study demonstrates that, while regular transducer motion is effective at distributing thermal energy, it is not essential for transducer safety. This study demonstrates that long duration, low intensity therapeutic ultrasound, or sustained acoustic medicine, is a viable and safe alternative modality for delivering the biophysical benefits of ultrasound therapy. The characterization of the physiological benefits of this new modality will be the next wave in acoustic medicine.

FIGURE 2.

Experimental design and treatment locations for the human clinical study. (a) table showing division of subjects. (b) example of device on the arm. (c) example of device on the leg.