Relationship between skin temperature and blood flow during exposure to radio frequency energy: implications for device development

Abstract

Background

The ST response to high frequency EM heating may give an indication of rate of BF in underlying tissue. This novel method, which we have termed REFLO (Rapid Electromagnetic Flow) has potential for applications such as detection of PAD. The method utilizes the relationship between blood flow rate and tissue temperature increase during exposure to radio frequency (RF) energy. We are developing an REFLO device to screen for peripheral artery disease (PAD). PAD is characterized by impaired blood flow to the legs, as reflected in the skin microcirculation. The REFLO system incorporates a radio frequency transmitter and a compact transducer housing a micropatch antenna and an infrared (IR) temperature sensor. At high RF frequencies (> 6 GHz) tissue heating is confined to the skin, such that an indication of blood flow may be inferred from the temperature response to controlled heating. The objective of this study is to determine the extent to which the magnitude and depth of heating as well as device sensitivity are functions of (i) RF frequency and (ii) thickness of the dermal tissue layer.

Results

Results show that it is feasible to measure blood flow rate with REFLO technology. Surface temperature increases were found to be more dependent upon the magnitude of power absorption than location of absorption within the skin. While surface temperature response does depend upon radio wave frequency and thickness of the dermis layer, such dependencies are mild. Sensitivity to blood flow rate was found to be proportional to the magnitude of absorbed power.

Conclusion

Results show that it is feasible to discriminate between blood flow rates using REFLO technology at frequencies within the 10–94 GHz range. All frequencies analyzed produced similar levels of sensitivity to blood flow rate despite significant differences in penetration depth. These results are being used in the development of a preclinical prototype for quick and easy detection of asymptomatic PAD in humans.

Background

Peripheral Artery Disease (PAD) is a common vascular condition associated with a high risk for serious cardiovascular events (heart attack, stroke) [1]. An estimated 8–12 million persons in the U.S. are affected by PAD [2]. Prevalence is increasing due to an aging population and lifestyle factors (obesity, diabetes). If caught early enough, effects of PAD can be slowed and even reversed with medication and lifestyle changes (diet, exercise). However, many individuals with PAD are either asymptomatic or are never screened for the disease. As a result, PAD often goes undiagnosed until a sudden life threatening cardiovascular event occurs.

Individuals with PAD experience atherosclerotic narrowing or blockage in the conduit arteries in the lower extremities, with a concomitant reduction in microcirculatory flow in the skin. This lack of blood flow makes it impossible for surrounding tissue to meet minimum metabolic demands and receive adequate nutrition [3]. Because vascular leg diseases such as PAD have historically been perceived as nonfatal, they have been understudied and underrecognized in comparison to myocardial infarction and stroke [4].

The preferred method of diagnosing PAD is the Ankle-Brachial Index (ABI), which is the ratio of the systolic pressure in the ankle to the systolic pressure in the arm. ABI measurement requires six separate systolic pressure measurements (bilateral measurements at the brachial, posterior tibial and dorsalis pedis arteries) in a supine patient. Measurements at the ankle require use of doppler ultrasound for auscultation. The procedure is time and staff intensive, requires specialized training, and may not be reimbursable [5]. ABI measurements are not reliable in patients with arterial calcification, which is common in older or diabetic patients. A simple, fast and easy method for measuring skin blood flow rate (BFR) could be extremely useful in screening for asymptomatic PAD and allow for earlier diagnosis and intervention.

The ST response to high frequency EM heating may give an indication of BFR in underlying tissue. This novel method, which we call REFLO (Rapid Electromagnetic Flow) has potential for applications such as detection of PAD. The method utilizes the relationship between BFR, defined as volumetric flow rate per volume tissue (mL/s/mL), and tissue surface temperature (ST) increase during exposure to low power (< 1W) radio frequency (RF) energy.

At frequencies above 6 GHz, RF energy absorption occurs almost entirely within the skin [6] without significantly affecting deeper tissues or organs [7]. The rate and magnitude of ST increases during low power, high frequency RF heating are functions of volumetric blood flow in the underlying tissue [8]. Thermographic experiments have shown that blood flow restricted human skin heats at a faster rate and cools at a slower rate than non-occluded tissue [9]. These results suggest that the presence of blood flow enhances the ability of human tissue to transfer heat.

A prototype REFLO transducer is undergoing preliminary testing on human subject volunteers (Fig. 1) under an IRB (Institutional Review Board) approved protocol. The transducer consists of a small patch antenna and an infrared (IR) non-contacting temperature sensor (Melexis 90,614) configured in a plastic chassis or housing. The antenna is driven by an RF transmitter (not shown), while the resulting skin ST is recorded on a laptop computer [10]. When properly calibrated, measurement of the temperature rise (or rate of temperature rise) during RF exposure could enable determination of volumetric skin blood flow from the temperature data.

Fig. 1

A prototype REFLO transducer is shown during testing

As the depth of RF energy penetration and absorption is a function of wavelength [8], the transmitter frequency is a critical design variable. Blood flow in the skin is concentrated in the dermal plexus of the dermis. We hypothesize that increased energy deposition within the dermis, as a fraction of the total energy absorption, will increase the response sensitivity to BFR.

The stratum corneum (SC) and epidermis (ED) are thin non-perfused layers located above the dermis. The hypodermis (HD), or subcutaneous layer is a mildly perfused tissue layer located below the dermis. Focused energy absorption within any of the tissue layers outside of the dermis (SC, ED or HD) may compromise measurement sensitivity.

There is significant intra- and inter-subject variability in dermis thickness. Dermis thickness can vary by several mm between locations on the body ($\approx$ 0.5–2.2 mm) [11, 12], and is largely a function of sex and age [11]. The range of dermis thicknesses of the lower extremities, more specifically the lateral head of the gastrocnemius muscle, is much smaller [11]. By restricting attention to this region, we may be able to refine the dermis thickness range under investigation. If gross temperature rise is used as an indicator, and the thermal response of skin to RF heating is found to be a function of age and sex, it may be necessary to independently account for variations in dermal thickness by offering different device calibrations. It may also be possible to use a different indicator, such as rate of heating to avoid dermis thickness dependency.

We hypothesize that both dermis thickness and BFR will have substantial effects on ST increase during RF exposure. We further hypothesize that in order to maximize the sensitivity of ST increases to BFR, it is necessary to deposit energy within the perfused area of interest, the dermis.

The objective of this study is to determine optimal operating frequency of the blood flow sensor by evaluating the sensitivity of skin temperature increase to BFR and dermis thickness during RF exposure to various frequencies. The extent to which frequency and skin anatomy may affect dermal temperature response is not well established. RF heating in the skin is a function of many variables and can be difficult to model or predict. A detailed understanding of how device parameters, skin morphology and physiologic factors affect localized temperature response is essential for device design and optimization.

Methods

Modeling tissue heating in response to RF exposure is a two-step process entailing (i) determination of the specific absorption rate (SAR) using a discretized model of the tissue(s) of interest and (ii) incorporating the local SAR values into a thermal model that relates RF absorption and other relevant factors to predict local tissue temperatures over time.

RF Absorption and SAR

Potential operating frequencies were selected based on frequency dependent penetration depths of RF energy in human skin. Penetration depth $\delta$ is defined as the depth at which the electric field magnitude has decayed to ${e}^{-1}$ of the surface value. Equivalently, it can be defined as the depth at which the power density (magnitude of the Poynting vector) has decayed to ${e}^{-2}$ times the surface value [13]. For a lossy dielectric such as skin, the penetration depth decreases with increasing RF frequency over the range of 6–100 GHz [6].

Existing literature reports that within the 6–100 GHz range, RF waves have penetration depths between 0.4 and 8 mm in human skin [6] . This range of depths encompasses the dermis in all skin profiles. Frequencies within the 10–35 GHz range were selected because they are known to provide substantial heating within the highly perfused dermis [6]. 94 GHz was also selected because there are existing published results at this frequency [14].

The skin was modeled as a planar, four-layer structure consisting of the stratum corneum (SC), epidermis (ED), dermis (D) and hypodermis (HD). Tissue layer depths were chosen to represent the nominal thicknesses of non-glabrous skin: SC = 0.015 mm, ED = 0.1 mm, D = 1.5 mm, HD = 5mm [11, 12]. Because the penetration depth of waves in the 10–94 GHz range is reported to be less than 4 mm in existing literature [6], a HD depth of 5 mm was deemed sufficient and no additional tissue layers were required.

Inter and intra-subject variations in skin composition and thickness are common. Tissue thickness, primarily dermis thickness, can alter the thermal outcomes during RF exposure. To determine the full spectrum of possible thermal outcomes, a range of dermis thicknesses were considered (0.5–2.2 mm). In addition to the nominal dermis thickness (D_nom), two heterogeneous tissue models, representing the upper (D_max) and lower (D_min) ranges of dermis thicknesses were considered (Fig. 2). HD depths and thicknesses were adjusted to maintain an overall model depth of 6.615 mm.

Fig. 2

Heterogeneous (D_min, D_nom, D_max) human skin models and corresponding dermis thicknesses (mm). The hypodermis (HD) layer was adjusted to maintain an overall model depth = 6.615 mm. SC = 0.015 mm and ED = 0.1 mm in all models [11, 12]

Tissue specific dielectric values were assigned to each tissue layer. Dielectric properties determine the magnitude of the resulting field when the tissue is exposed to RF waves and are frequency dependent. The complex dielectric value, or permittivity value for each layer of skin was calculated using a four pole Cole–Cole Eq. [15] alongside known electrical constants. Electrical constants for each tissue layer were obtained from literature [16,17,18].

The SAR values were calculated throughout the tissue domain via the finite-difference time-domain (FDTD) method using commercially available software [19]. Simulations were run for 10, 15, 25, 35 and 94 GHz. Exposures were far-field, continuous wave with forward power densities (FPD) = 50, 125 and 250 mW/cm². Simulations were allowed to run until a convergence of -50 dB was met.

The prototype device’s antenna configuration is such that it is positioned within the Fraunhofer distance (approximately 1.0 cm at 35 GHz), with respect to the skin surface. While reactive effects in the near field will alter the power density at the surface, the penetration depth and subsurface temperatures, relative to the incident power, are similar for near-field and far-field exposures [20]. Hence, it may be necessary to scale the results to account for reactive effects in the near field. Normalized temperatures versus depth should be similar for near-field and far-field exposures, however.

Thermal models

The SAR values were used as input to a custom thermal solver. The thermal solver was based on the modified Pennes bioheat Eq. [21]:

$${\rho }_{i}{c}_{i}\frac{\partial T}{\partial t}={{k}_{eff}}_{i}\frac{{\partial }^{2}T}{\partial {x}^{2}}-{\omega }_{i}{c}_{b}\left[T\left(x,t\right)-{T}_{a}\right]+q\left(x\right)+SAR(x)$$

(1)

The subscripted i is an index referring to the tissue type in a heterogeneous model (i takes on values from 1 to 4). The $\rho c$ term is the volumetric heat capacity of tissue, $\omega$ the mass BFR per unit tissue volume, ${c}_{b}$ is the specific heat of blood, ${T}_{a}$ is the temperature of blood entering the heated region = 35 $^\circ{\rm C}$, $q\left(x\right)$ is metabolic heat production and $SAR(x)$ is the RF heating term. The Pennes equation was modified by replacing the constant conductivity term k, with effective conductivity ${k}_{eff}=0.45(1+975 \omega )$ to account for increased levels of conductivity in perfused tissue layers [22]: The semi-empirical term accounts for the linear relationship between blood flow and thermal conductivity. Thermo-physical values for each tissue layer (SC, ED, D and HD) and blood are given in Table 1.

Table 1 Thermo-physical tissue and blood parameters [22, 23]. β = 975 (mL/s/mL)⁻¹  [22]

The bioheat equation was discretized using the central difference method and the Crank–Nicholson method. A convective surface boundary condition was used to account for environmental heat loss:

$$\frac{h}{k}\left[T\left(0,t\right)-{T}_{env}\right]-{\frac{\partial T}{\partial x}|}_{x=0}=0$$

(2)

where h is the convection heat transfer coefficient at the model surface, ${T}_{env}$ is the environmental temperature (23 °C) and k is the thermal conductivity of the SC. A h value of 5 W/m²K was chosen to represent free convection on a resting body [24]. A range of h values characteristic of typical indoor ambient conditions were simulated to determine the effect of varying environmental conditions during RF heating. Varying the convection heat transfer coefficient from 5 to 20 W/m²K had minimal effect on the thermal response of skin. Tissue temperature at model depth was set to deep arterial temperature (37 °C). A matched boundary and interface technique was applied to ensure continuity at tissue interfaces [25].

Initial skin temperature profiles were determined for all models and BFRs by initializing the model at skin blood temperature (35 °C) and running the model without RF heating until steady-state conditions were achieved.

Values of resting, normothermic human skin BFR reported in literature show a great deal of variability. BFRs are given in terms of volume of blood per volume tissue per unit time (mL/s/mL or s⁻¹). Reported values range from 0.0002 to 0.05 s⁻¹ [26]. Rowell [27] estimates a whole-body average value of 100–300 ml/min, per unit of surface area. For a nominal skin thickness of 0.2 cm, this is equivalent to a volumetric BFR per unit tissue volume of 0.8–2.4 × 10^–3 s⁻¹. Williams [28] recommends values in the range 3.3 × 10^–4 to 2.2 × 10^–3 s⁻¹. Gordon [29] estimates values equivalent to 1.4 × 10^–3 and 1.2 × 10^–3 for the skin of the arms and legs, respectively.

D and HD BFRs of 0.0014 s⁻¹ and 0.0003 s⁻¹ were selected as base BFRs for the D_nom model [12]. Mass BFR within each layer was conserved between models by altering the volumetric BFR (Table 2).

Table 2 BFR (s⁻¹) for heterogeneous model tissue layers. Note that BFR is given in terms of volumetric flow rate per volume tissue (mL/s/mL or s⁻¹)

To determine the level of measurable BFR differentiation during exposure to each frequency, BFRs ranging from 0 to 10 times the base model BFRs were simulated ($\text{0,0.1,0.5,1},\text{2,10} \times \omega )$. ST increases and temperature throughout model depth during a 300 s heating period were evaluated. It should be noted that peripheral blood flow is not constant, in part due to autonomic drive and variations in peripheral resistance (vasodilation). BFR variations caused by vasodilation are known to occur in human skin after experiencing STs above 40 °C for more than 60 s [30]. Any measurement technique based on the results presented in this work should therefore have a measurement time sufficiently short to avoid significant vasodilation or incorporate mechanisms to minimize vasodilation i.e., surface anesthetic [31].

We verified our model by applying it to the conditions of Alekseev’s [32] computational simulations at 42.25 GHz using the D_nom model. The difference in absorptivity between Alekseev’s computational results and simulations carried out in this study is less than 0.07. Figure 3 shows that resulting ST increases are consistent with Alekseev’s model.

Fig. 3

ST increases after a 50 s heating period by 42.25 GHz source (PD = 208 mW/cm²) in comparison with Alekseev’s [32] computational broad beam results. Alekseev BFR = 0.0006 s⁻¹. Computational results from this study given for 0.5,1,2 $\times\omega$ where $\omega =0.00055$ s.⁻¹

Results

RF absorption

Steady state normalized SAR (nSAR¹) as a function of depth is shown in Fig. 4 for the three tissue models, at each of the five frequencies considered. Peak SAR values occurred in the ED or D at all frequencies for the three tissue models (Fig. 4). At depths greater than 3 mm nSAR values are negligible and are not shown.

Fig. 4

Normalized SAR (nSAR) (m²/kg) vs depth for D_min, D_nom and D_max models at all frequencies. Dermis denoted by shaded gray area. nSAR values at depths greater than 3 mm are negligible and are therefore not shown

Total skin absorptivity and the energy penetration depth were calculated from the SAR results. The values for the D_nom model at each frequency of interest are provided in Table 3 and compared with corresponding values for skin obtained from the literature [7, 33,34,35].

Table 3 Penetration depth ($\delta$) and absorptivity ($\alpha$) for the D_nom model in comparison with published results

The portion of the total absorbed energy that is absorbed in each layer is shown for each tissue model and for each frequency of interest in Table 4.

Table 4 Absorptivity ($\alpha$) and percentage of total absorbed power dissipated within each layer (SC, ED, D and HD) for heterogeneous models at all frequencies

Penetration depths for all frequencies in each of the three models are shown in Fig. 5. The dermis region of the three tissue models is shaded, showing the location of penetration depth with respect to dermis tissue.

Fig. 5

Penetration depth of all frequencies in D_min, D_nom, D_max models in relation to dermis depth. Dermis region is denoted by the grey shaded region

Surface temperature increases

SAR values from REMCOM simulations were used as input to the thermal model to examine the role of blood flow on skin ST. The following ST results were found using the discretized skin models, relating RF absorption to local tissue temperatures over time.

ST increases over a 300 s heating period for all frequencies are shown in Fig. 6. Results compare temperature increases of the three models with a range of BFRs ($\text{0,0.1,0.5,1},\text{2,10} \times \omega$). Temperature increases for all models decrease with increasing $\omega$. Models with high BFRs ($10 \times \omega$) were less significantly affected by frequency.

Fig. 6

ST increases of D_nom with 0,0.1,0.5,1,2,10 × $\omega$ over a 300 s heating period at all frequencies, FPD = 125 mW/cm²

For each frequency considered, the magnitude of the temperature change decreased as the skin BFR increased. The extent of this effect (temperature rise decreases with increasing blood flow) is not consistent across frequencies, however. This could reflect differences in the magnitude of the effect of blood flow, presumably due to frequency-dependent differences in the depth of energy deposition. Alternatively, it could be due to frequency-dependent differences in RF absorptivity, or a combination of the two factors.

Temperature results were adjusted to account for differences in RF absorptivity by scaling the SAR values by the inverse of the total skin absorptivity at each frequency, so as to achieve a total absorbed power of 75 mW/cm² at each frequency considered. In practice, this is equivalent to increasing transmitter power to adjust for lower power absorption in the skin at frequencies below 94 GHz.

Figure 7 compares (a) ST responses to all frequencies with FPDs = 125 mW/cm², and (b) thermal responses to frequencies with normalized absorption = 75 mW/cm². Figure 8 shows the same ST increases for all models (absorption = 75 mW/cm²).

Fig. 7

D_nom ST increases at each BFR after 300 s exposure to (a) all frequencies with FPD = 125 mW/cm² (varying $\alpha$) and (b) all frequencies with FPDs altered to maintain a constant power absorption of 75 mW/cm.² ($\alpha$ = 0.6)

Fig. 8

ST increases after 300 s heating period for all frequencies at each BFR in all models. FPDs altered to maintain a constant power absorption of 75 mW/cm² ($\alpha$ = 0.6) at each frequency and model

Figure 9 shows a linear relationship between PD and ST increases at 10 GHz. The same linear trend was observed at 15, 25, 35 and 94 GHz in all models.

Fig. 9

D_nom ST increases after a 300 s heating period by 10 GHz at FPDs of 50, 100 and 200 mW/cm²

The difference in ST increases between adjacent flow levels for each model and frequency are given in Fig. 10. FPDs were again altered at each frequency to maintain constant power absorption of 75mW/cm² during a 300 s heating period.

Fig. 10

Difference in ST increases between adjacent BFRs for each model and frequency. FPDs altered to maintain a constant power absorption of 75 mW/cm²

Figure 11 shows nSAR of all models during exposure to 94 GHz, alongside variation in ST response of all models after exposure to 94 Hz for a 300 s heating period.

Fig. 11

a Normalized SAR (nSAR) (m²/kg) vs depth for D_min, D_nom and D_max at 94 GHz. b ST increases for all models during a 300 s exposure period to a 94 GHz source at 125mW/cm² FPD

Sensitivity analysis

Figure 12 shows ST sensitivity of each model to BFR after 300 s exposure to each frequency. The FPD of each frequency was normalized ensuring total absorption = 75 mW/cm². Sensitivity was estimated by comparing the difference in ST increases between adjacent BFRs divided by the difference in BFRs. Sensitivities between each BFR are given.

Fig. 12

Sensitivity to BFR for all models after a 300 s heating period at each frequency. PD varied at each frequency to achieve a total absorption of 75 mW/cm². Sensitivity is quantified in terms of the difference in ST response between adjacent flow rates divided by the difference in flow rate

Discussion

The use of REFLO technology for measurement of skin blood flow presumes a consistent and predictable thermal response to low-power RF irradiation of the skin. Measurements sensitive to dermis thickness may confound determination of flow rates and make it difficult to compare inter- and intra-subject results.

Penetration depth

Energy penetration depth $(\delta )$ and RF absorptivity ($\alpha$) are both functions of incident RF frequency (Fig. 4, Table 3). Table 3 shows that absorptivity values and penetration depths found in the current research are in agreement with existing data [7, 33,34,35,36]. Trends are similar for all three tissue models.

The RF penetration depth is affected by thickness of the dermal tissue layer at frequencies below 35 GHz. Results (Fig. 5) at f = 15 GHz indicated a penetration depth for the thin dermis model ($\delta =5.2$ mm), which is almost twice that obtained for the other two skin models (2.5 and 2.9 mm). Penetration depths for other frequencies examined (f = 10, 25, 35, and 94 GHz) are similar in all three tissue models. The reason for the anomalous behavior at 15 GHz, and whether it is confined to a narrow frequency band are subjects of current investigation.

With the exception of the results at 15 GHz, the skin heating patterns appear to be fairly insensitive to the thickness of the dermal layer, both intra-subject and inter-subject (Fig. 4). In that case, tissue temperatures for a given RF frequency and incident power level would reflect the depth and magnitude of the blood flow, as well as any variations in thermal properties that may exist between the tissue models. This would suggest that optimal operating frequency could be selected based on considerations of sensitivity to blood flow, as well as practical considerations of hardware costs and safety.

Effects of frequency on ST increases

ST increases resulting from RF heating are dependent upon BFR in underlying dermal vasculature. Decreased dermis BFRs generated larger temperature increases. BFR was able to affect ST increase by up to 10 °C (Fig. 6). Figure 7a shows that given equal FPD, there is a non-linear relationship between frequency and ST increase. This relationship can be explained in part by the fact that absorptivity increased with frequency, as shown by values in Table 3. This is consistent with the results shown in Figs. 6 and 7a, where maximum temperature increases occurred at 94 GHz. The sensitivity to BFR, as quantified by differences in ST increases between adjacent BFRs levels also increases with frequency given equal forward power.

To determine whether the depth of energy absorption, or the total power absorption was responsible for the varying levels of BFR sensitivity, transmitted power was normalized at each frequency by altering source FPD to ensure equal absorption. Figure 8 shows that the magnitude of ST increase is less dependent upon frequency than FPD regardless of dermis thickness. All frequencies heated the model surface to approximately the same degree at each BFR. This shows that the thermal response of skin is not strongly influenced by frequency of incident radiation within the 10–94 GHz frequency range. Sensitivity can instead be scaled by altering FPD.

Effects of dermis thickness

ST increase was found to be dependent upon dermis thickness. As dermis tissue has the highest BFR, it is not surprising that the thickness of this layer has an effect on temperature response. There are two potential causes of temperature dependence on dermal thickness: differences in volumetric BFR, and the location of blood flow. The region of blood flow increases with dermis thickness, increasing the region of high permittivity tissue, thereby altering the absorption profile. Assuming mass BFR is conserved within the dermis across models, altering the thickness of the perfused region alters the volumetric BFR. Figure 11 shows that although SAR profiles for 94 GHz exposure are nearly identical in all three models, thermal responses vary, suggesting that temperature response is more dependent upon location of blood flow than absorption profiles.

Our hypothesis that the location of energy deposition would affect device sensitivity is not supported by the results. Heating within the perfused region of interest (the dermis) did not increase sensitivity to dermal BFRs. Figure 12 shows that given equal absorption at all frequencies, the sensitivity to BFR is not significantly affected by frequency and thereby the location of power absorption. Table 4 shows that at 94 GHz, approximately half of total absorbed power was deposited within the nonperfused ED in all models, while at 15 GHz less than 12% of absorbed power dissipated within the ED. Despite the significant disparities in location of energy deposition, all frequencies produced the similar levels of sensitivity to BFR. Between 10 and 94 GHz, sensitivity only slightly increased with frequency.

Variations in ST increase between models were also unaffected by frequencies between 10–94 GHz. Figure 10 shows that dermis thickness affects ST increase by nearly the same amounts at all frequencies.

Because device functionality does not appear to be dependent upon frequency from a sensitivity standpoint within the 10–94 GHz range, operating frequency could potentially be selected based on factors like cost and availability. It should be noted that Fig. 12 shows BFR sensitivity is highest at low BFRs. This suggests that an REFLO device might be best utilized for resolving cases of low blood flow.

Safety considerations

Non-glabrous human skin can withstand a temperature as high as 44–45 ℃ indefinitely without pain or burning [37, 38]. Above threshold temperature, the severity of damage done to the skin is a function of exposure time [38]. Figure 6 shows that after a 300 s heating period by a 94 GHz source (FPD = 125 mW/cm²), STs either approached or surpassed 44 ℃ at low BFRs depending upon initial ST. By manipulating the device’s FPD and exposure time, safe temperatures can be maintained at all analyzed frequencies. Optimal FPD will ensure temperatures are high enough for sufficient BFR differentiation, while not exceeding safe temperatures for all skin types.

Because exposure to frequencies over 10 GHz causes highly localized heating, the development of subsurface hot spots is a potential concern. Subsurface hot spots can result in pain or injury (burns) even when the average ST increase is modest. Although results from this study show that maximum temperature increase occurs at the skin surface for all frequencies and FPDs, it has been shown that atypical environmental conditions can allow for the formation of hot spot [6].

Additional design considerations

The proposed device’s operating frequency is an important design consideration not only from a functional standpoint, but also from a cost perspective. Because sensitivity does not appear to be frequency dependent, the cost of transmitting hardware may dictate selection of appropriate operating frequency. Hardware costs for amplifiers in particular tend to be quite high for frequencies above 35 GHz. All other components: transducers, small antennae and temperature sensors, are inexpensive and readily available. Hence the optimization of the operating frequency may be important to the success of the technology.

Conclusion

A simple, one-dimensional model of RF absorption in skin is presented. Results show that it is possible to discriminate between BFR based on gross ST increase using REFLO technology at frequencies within the range 10–94 GHz. Our hypothesis that penetration depths corresponding to the dermal vascular plexus will provide increased levels of sensitivity is not supported by results. Heating primarily within the perfused region of interest (D) does not increase sensitivity to dermal BFRs.

The generalized finding from this study is that there is a trade-off between robustness to changes in dermal thickness and maintaining a high level of sensitivity to BFR provided equal power absorption at frequencies within the 10–94 GHz range. At 10 GHz the thermal response of human skin is insensitive to both tissue thickness and BFR in comparison to higher frequencies analyzed in this paper. 94 GHz on the other hand is much more sensitive to both BFR and dermal thickness in comparison to 10 and 15 GHz. Because optimum frequency will depend upon the blood flow range of interest and the variation in dermal thickness for the given population and anatomical measurement site, a more concrete numerical or visual conclusion regarding optimal frequency for this specific device cannot be made at this time as these variables are yet to be determined,

A definitive figure or equation of merit would also depend upon the exact algorithm used to infer blood flow from temperature data. The exact algorithm that will be used to determine measurements could be based on several potential factors including maximum temperature reached within a given time period, heating time constants, rate of heating, and rate of cooling. Once the appropriate variables have been determined, the method of measurement optimization can be determined.

Sensitivity to BFR is proportional to the magnitude of temperature increase and can be scaled with device FPD. Sensitivity levels are highest at low BFRs, implying a device could potentially discriminate between borderline insufficient microcirculation.

The ST response at all frequencies considered show a dependence on dermis depth, strengthening with increasing frequency within the range analyzed. This poses a functional challenge for a clinical device, in that it might be necessary to adjust calibration to account for dermal thickness. It may be possible to develop measurement protocols to mitigate ST sensitivity to dermis depth.

Computational results from this study are conditional. Absorption profiles were obtained using far field simulations and do not take near-field interactions into consideration. Additionally, RF simulations were carried out at a single frequency and do not consider transmitter bandwidth. Broadband and bimodal sources will be investigated in an upcoming study.

We are currently experimenting with a prototype transducer using volunteer subjects under an IRB approved protocol. We will compare our computational results against the subsequent experimental data. The results will be used to determine computational model accuracy and further develop the diagnostic device and measurement protocol.