Microwave Rewarming of Limb Frostbite Injuries (Simulation of Modes)

Abstract

Cold limb injury remains a serious and widespread condition both in countries with a cold climate and in regions located close to the equator, but having high-altitude territories. There is no medical equipment for the treatment of this condition. One of the ways to solve this problem is the use of microwave radiation at an early stage, which penetrates deep into the cooled volume and, accordingly, can accelerate the activation of internal vessels. The technical implementation of this approach involves the selection of the appropriate frequency and power of radiation, as well as the creation of a microwave chamber in which it is possible to ensure a sufficiently uniform heating of the entire volume of the frostbitten limb. The results of modeling the distributions of electromagnetic and thermal fields in the volume of the heated limb at microwave frequencies allowed for medical applications are presented.

1. Introduction

A large part of the world population lives in areas with subzero winter temperatures, where frostbites of extremities are quite common. Such injuries occur in warmer climates as well—in high-mountain regions, high-altitude stations and ski resorts. Frostbite of hands or feet develops unnoticeably and without pain, but the complications can be extremely severe and often result in amputations or disability [1, 2, 3, 4].

Surprisingly, to date, no equipment exists to treat this condition.

The aforesaid negative outcomes tend to develop with deep, volume frostbites when due to low temperatures, blood flow and lymph circulation are impaired or entirely stop in the limb volume. In these cases, any attempts to rewarm outer areas (the most common scenario in frostbites) result in a rapid dilatation of topmost vessels, which try to “push” their contents. At the same time, main deep-seated vessels remain ischemic due to the cold and prevent the blood/lymph flow, which invariably causes thrombosis, ruptures, and necrosis. This explains why fingers and toes are particularly affected. They rewarm quickly but amputations are practically inevitable if other vessels of the extremities (palms, forearms, feet, lower legs) are not activated.

One of the possible approaches to this problem is the use of deeply penetrating, microwave radiation, which helps rewarm the inner volume of an extremity and activate innermost blood vessels more quickly.

In medicine, electromagnetic fields (EMFs) have wide applications, including deep rewarming. One of the uses is physical therapy [5, 6, 7, 8]. Physical therapy machines are comprised of a microwave generator and a set of antennas, which are applicators that focus microwave radiation on the specific area of the body. The maximum generator power is 200 W [9] up to 400 W [10] and both permanent and pulsed modes are possible. During the procedure, the patient wears safety goggles and the technician must leave the room. Such machines are ineffective for rewarming of frostbitten limbs because they do not rewarm the entire volume of the limb simultaneously and uniformly.

Another EMF application in medicine is induction of hyperthermia in malignant tumors [11, 12, 13]. For this purpose, more powerful electromagnetic machines, also with narrowly targeted antennas are used. Thus, this equipment is not applicable for the condition in question either.

In this paper, we describe the method of limb rewarming in a closed metal chamber, which provides thawing of the affected limb simultaneously from all sides [14]. The patient and the technician can be completely protected from the negative exposure. Moreover, to achieve the desirable effect, considerably less powerful microwave radiation is sufficient.

I. Gorelik demonstrated the efficacy of this technique in rabbits [15].

In Figure 1, scintigrams of rabbit limbs following frostbite and a recovery procedure with microwaves are shown.

Figure 1.

Scintigrams of rabbit limb vessels following frostbite and microwave rewarming: 4 hours after frostbite (a), 1 hour after microwave exposure (b).

Clearly, more research is in order to apply this technique to treatment in humans.

We will not explore here the medical aspects of this technique, assuming that all positive and negative sides of microwave rewarming were investigated at the time of designing of these physical therapy and hyperthermia machines. However, it is important to note that to ensure the activity of blood and lymphatic vessels, the entire volume of a frostbitten limb must be rewarmed to over 15°C [4] as this is the absolute threshold when the vessels do not simply “open” but create the necessary flow of fluids.

For an effective and safe application of the proposed technique in humans, it is important to examine it as carefully as possible, using mathematical and numerical modeling as well as physical modeling on limb-equivalent dielectric phantoms. The modeling made it possible to better describe field distribution within the volume of an affected limb and experiments in the phantoms resulted in recommended values of the microwave power fed to the chamber as well as the duration of rewarming procedures.

Clearly, the reader is interested in practical applications of the technique. Normally, rigorous healthcare regulations require meticulous preclinical and clinical research of new treatment methods. Because for the actual application of the technique, a certified SMVI-200 physiotherapeutic device was used and the microwave radiation was far less powerful than the maximum allowed for this device, the TSU Committee of Bioethics allowed the team of developers to enroll informed volunteers in the studies. The final part of the chapter gives an overview of the findings.

2. Microwave rewarming in the chamber. Principle, features, physical problems

A multi-wave metal chamber was proposed as the basis of the recovery technique when the electromagnetic microwave field is fed to an affected limb from all sides simultaneously. A schematic diagram of this device is shown in Figure 2.

Figure 2.

Schematic diagram of the microwave rewarming device: 1 – Microwave chamber, 2 – Safety sleeve, 3 – Microwave generator, 4 – Source antenna [14].

The limb is placed inside a chamber (1) through the opening in one of the chamber walls. The opening is equipped with a radioprotective sleeve (2). The excitation is performed by a generator (3) from the outside of the chamber via the built-in antenna (4).

Figure 3 shows one of the possible designs of this device, where a generating unit of a SMVI-200 medical physiotherapeutic device [16] is used as a microwave generator. This generating unit produces microwave frequency of 2.45 GHz. Notably, even though the highest power of this device is 200 W, to achieve the desired effect, 30–40 W of power output is sufficient.

Figure 3.

A design of the rewarming limb device with a microwave chamber and a generating unit of SMVI-200 medical physiotherapeutic device [16].

If we assume that microwave rewarming is sufficiently explored from the medical viewpoint, the application of this design to treat humans, though seemingly simple, should be justified clearly in terms of technology.

The key task is to determine the distribution of electromagnetic and thermal fields in the chamber and in the volume of the affected limb and estimate the extent of nonuniformity of the fields and their behavior in fingers and toes. Palms, fingers, and toes require special attention because they can be considered critical zones because on the one hand, they are most susceptible to frostbite, and on the other, they can be rewarmed with microwave radiation far faster than the remaining limb volume, which may negatively affect treatment outcomes.

The choice of the microwave frequency is highly important. Biological tissues that form limbs (skin and fat, muscles, bones) are considerably different in terms of dielectric permittivity and electrical conductivity, which vary at different frequencies. Thus, the rewarming depth and rapidness depend on the frequency.

It is also important to study the behavior of the rate of reflection of microwaves off the chamber and related with it voltage standing wave ratio (VSWR), which determines what amount of the power fed by the generator reaches the chamber and gets absorbed inside the limb and what amount is reflected back and not used for rewarming.

3. Field modeling in a dielectric phantom

A human limb (an arm or a leg) is a multi-component object of a complex and continuously varying shape, which is quite difficult to describe with a mathematical model. Even a greater difficulty is to create a physical phantom that accurately imitates a limb with all its variety of tissues. For this reason, both mathematical models and physical phantoms are inevitably simpler yet still suitable for predicting rewarming dynamics of a real object.

The mathematical problem of describing electromagnetic and thermal fields in the limb placed inside a microwave chamber can be presented as a simultaneous solution of Maxwell equations describing the electromagnetic fields,

$$\left\{\begin{array}{l}\mathit{rot}\overrightarrow{\mathit{H}}=-i\mathit{\omega }\mathit{\epsilon }{\mathit{\epsilon }}_0\overrightarrow{\mathit{E}}+\mathit{\sigma }\overrightarrow{\mathit{E}}\\ \mathit{rot}\overrightarrow{\mathit{E}}=i\mathit{\omega }\mathit{\mu }{\mathit{\mu }}_0\overrightarrow{\mathit{H}}\end{array}\right.,$$E1

and a Pennes bio-heat equation describing the process of heating a limb (or an imitating phantom) with the electromagnetic field [17]:

$$\begin{array}{c}\mathit{\rho C}\frac{\mathit{dT}}{\mathit{dt}}=\mathit{k}\nabla \mathit{T}\left(\overrightarrow{\mathit{r}},\mathit{t}\right)-{\mathit{\omega }}_{\mathit{B}}{\mathit{C}}_{\mathit{B}}{\mathit{\rho }}_{\mathit{B}}\left(\mathit{T}-{\mathit{T}}_{\mathit{B}}\right)+{\mathit{q}}_{\mathit{M}}\left(\overrightarrow{\mathit{r}},\mathit{t}\right)+{\mathit{q}}_{\mathit{MW}}\left(\overrightarrow{\mathit{r}},\mathit{t}\right).\end{array}$$E2

This equation consists of the following terms: $-{\omega }_B{C}_B{\rho }_B\left(T-T_B\right)$ is a summand arising from the heat transfer by the blood flow, $q_{м}\left(\overrightarrow{r},t\right)$ is energy produced in the tissue as a result of metabolism [W/m³], $q_{\mathit{MW}}\left(\overrightarrow{r},t\right)$ is energy absorbed in the tissue due to microwave electromagnetic fields [W/m³].

The paper [18] demonstrates that for a simplified model, for example, a single-layer cylinder, the analytical solution of the three-dimensional bio-heat equation is possible with a Green’s function. In our case when the object (a limb) has multiple layers, it is reasonable to use a one-dimensional model only [19, 20, 21], which helps describe the process of microwave rewarming in layers.

We will study a phantom representing a one-dimensional model consisting of five plane-parallel uniform layers with biophysical properties of human tissues (Figure 4). The model is idealized and enables the modification of physical properties, layer thickness and layer number. It is assumed that a plane wave is incident on the phantom surface, any loss occurs only within the volume of the warmed layer, and all the delivered power is absorbed only within the volume of the phantom.

Figure 4.

A schematic diagram of the single-layer problem in question: A five-layer model of the phantom consisting of the skin, muscles, bones, muscles, skin.

Furthermore, we will contemplate the solution of the heat-transfer Eq. (2) without accounting for the energy of metabolism and heat transfer by the blood. This approach is justified because during hypothermia, the blood flow in tissues virtually stops and the metabolism is also minimal. Without the aforementioned terms, the Pennes equation turns into the heat-transfer equation for a solid object inside which there are heat sources, i.e. in our case, absorbed power of the EMF:

$$\begin{array}{c}\mathit{\rho C}\frac{\partial T}{\partial t}=\mathrm{\lambda }∆T\left(\overrightarrow{r},t\right)+q_{\mathit{MW}}\left(\overrightarrow{r},t\right)\end{array}.$$E3

The EMF volume power for a one-dimensional problem can be written as:

$$\begin{array}{c}{\mathit{q}}_{\mathit{MW}}\left(\mathit{r}\right)=\frac{1}{2}\mathit{\sigma }\ast \mathit{E}{\left(\mathit{r}\right)}^2.\end{array}$$E4

Electric field intensity Е included in the volume power expression can be determined by solving the Eq. (1). For a simplified one-dimensional model, the field can be described as the following expression:

$$\begin{array}{c}\mathit{E}\left(\mathit{z}\right)={\mathit{E}}_0{\mathit{e}}^{-\frac{\mathit{z}}{\mathit{d}}}+{\mathit{E}}_0{\mathit{e}}^{\frac{\mathit{z}-\mathit{Z}}{\mathit{d}}},\end{array}$$E5

where Z is the thickness of the rewarmed layer, and d – the thickness of the penetration depth. Because, the distribution occurs in the multi-layer environment, the value of penetration depth and distribution of the field intensity are calculated individually for each layer.

First, the initial condition defining the temperature of an entire phantom is set:

$$t=0:T\left(z,0\right)=T_0,0\le z\le Z.$$E6

In the phantom, at interfaces between the biological layers, the interface boundary condition equation is used and expressed as follows [22, 23]:

$$\left\{\begin{array}{c}-{\mathrm{\lambda }}_1\frac{\partial T_1\left(z_0,t\right)}{\partial z}=-{\mathrm{\lambda }}_2\frac{\partial T_2\left(z_0,t\right)}{\partial z}\\ T_1\left(z_0,t\right)=T_2\left(z_0,t\right)\end{array}\right..$$E7

Two problems are interesting to explore. The first is to consider gravity-type airflow between the environment and the warmed object. To solve it, the convection boundary condition is used [22, 23]:

$$\begin{array}{c}z=0:-\mathrm{\lambda }\frac{\partial T\left(0,t\right)}{\partial z}=\mathit{\kappa }\left(T_{\mathit{air}}-T\left(0,t\right)\right),t>0;\end{array}$$E8

$$\begin{array}{c}z=Z:-\mathrm{\lambda }\frac{\partial T\left(Z,t\right)}{\partial z}=\mathit{\kappa }\left(T\left(Z,t\right)-T_{\mathit{air}}\right),t>0.\end{array}$$E9

The second problem is related to a situation when the rewarmed object is surrounded by the medium sustained at a constant temperature, for example, by air blowing around at a specific temperature. To solve it, the specified boundary condition is used [22, 23]:

$$\begin{array}{c}\mathit{z}=0:\mathit{T}\left(0,\mathit{t}\right)={\mathit{T}}_{\mathit{air}},\mathit{t}>0;\end{array}$$E10

$$\begin{array}{c}\mathit{z}=\mathit{Z}:\mathit{T}\left(\mathit{Z},\mathit{t}\right)={\mathit{T}}_{\mathit{air}},\mathit{t}>0.\end{array}$$E11

In the expressions above, $\kappa$ is the heat-transfer ratio that describes heat flow from one medium to the other. For natural convection air, it ranges from 1 to 25 W/m²°C [22]. For the purpose of further calculation experiments, the value of $\kappa$ = 25 W/m²°C is chosen.

The heat-transfer equation was numerically solved with the sweep method, which is often used to solve heat-transfer equations [24, 25]. It is one of the methods of a sequential elimination of unknowns. For the sweep method Eq. (3), partial differentials need to be approximated with corresponding finite differences, which results in the system of linear algebraic equations. To solve the heat-transfer problem in a multi-layered one-dimensional phantom imitating human tissues, Mathcad 15 package was used [26] for this method.

Parameters of biological tissues that were applied to model the phantom are presented in Table 1 [27]. The initial temperature of the cool phantom was 10°C, the surrounding air was 25°C.

	EMW frequency, MHz	Density ρ, kg/m^3	Heat capacity С, J/kg ̊C	Thermal conductivity λ, W/kg°C	Dielectric permittivity ε	Conductivity S/m	Penetration depth δ, cm
Skin tissue	433	1100	3150	0.25	51.3	0.72	2.9
	915				47.8	0.92	1.7
	2450				44.6	1.72	0.78
Muscle tissue	433	1050	3500	0.49	63.6	0.98	2.4
	915				60.7	1.19	1.5
	2450				55.8	2.33	0.67
Bone tissue	433	1990	2238	0.36	13.3	0.116	7.1
	915				12.5	0.18	3.9
	2450				11.7	0.41	1.6

Table 1.

Biophysical properties of human tissues.

The spatial parameters in the examples below are as follows: the overall phantom is 80 mm thick, the skin layer is 4 mm, the muscle layer is 28 mm, and the bone layer is 16 mm.

Figure 5 shows temperature distribution across the phantom when the phantom is rewarmed (a) without the electromagnetic field only owing to the thermal exchange with stationary air, and (b) by forced air of +25°C. The latter was proposed in the paper [28] to cool the skin layer during microwave rewarming to minimize the risk of overheating critical zones.

Figure 5.

Distributions of temperature fields in a one-dimensional phantom with microwave-free rewarming in stationary air (a) and by forced air (b) of 25°C.

With microwave rewarming, the distributions change, that being considerably dependent on electromagnetic field frequencies. Corresponding thermal field distributions are shown in Figure 6.

Figure 6.

Thermal field distribution in the phantom volume rewarmed in the microwave field of different frequencies (433 МНz, 915 МНz, 2.45 GHz), without forced air (a) and with forced air (b), t_max = 30 min.

The role of microwave rewarming and the dependency of the end result with the frequency value is clearer in Figure 7, where temperature distributions after 30-minute rewarming in the absence of the electromagnetic field and with fields of different frequencies are shown.

Figure 7.

Temperature distributions after 30-minute rewarming with (a) stationary and (b) forced air without the microwave field and with fields of different frequencies.

Critical zones, such as fingers, toes, palms, that is, a less thick phantom, demonstrate a drastically different picture. Figure 8 shows field distributions in a 5-layer phantom with a total thickness of 2 cm after 30-minute rewarming.

Figure 8.

Temperature distributions in a multi-layered 2-cm thick phantom after 30-minute rewarming with (a) stationary and (b) forced air with microwave fields of different frequencies.

Rapid rewarming is observed throughout the entire depth of the phantom and without forced moving air, there is a high risk of overheating, particularly, with the low-frequency microwave exposure.

4. Modeling of the chamber with a dielectric phantom inside in CST studio

As noted above, because a human limb does not lend itself easily to a mathematical description, initially, the modeling was performed by imitating it with a dielectric phantom of a more basic shape with similar dielectric permittivity and thermal conductivity. For example, the paper [29] explores field distributions in a cylindrical dielectric phantom inside a microwave chamber (Figure 9).

Figure 9.

A rectangular conductive chamber and a partially inserted cylindrical dielectric phantom in the protective shield—A mathematical model of a microwave chamber with a limb phantom.

It was assumed that microwaves would be excited by a spike antenna located in the upper-right corner of the chamber side wall that is closer to the reader. Figure 10 shows an example of the distribution of electric field amplitudes in the middle section of the chamber and phantom, a two-layer cylinder whose dielectric permittivity of the inner volume resembles the one of the muscle tissue and the outer layer is similar to the human skin and fat tissue.

Figure 10.

Distribution of the electric field in the plane corresponding to the chamber’s central section (a) along the 0X axis and (b) along the central 0Z axis [29].

Figure 10a clearly demonstrates that electromagnetic field in the chamber penetrates the phantom volume but its amplitude rapidly decreases. High amplitude on the right in Figure 10b is due to the placement of the radiator on this side of the chamber.

As noted, the VSWR, the ratio of reflection off the chamber with the phantom, contributes to the effect. Figure 11 shows estimated VSWR dependence on the frequency in the case of a single-layer (muscle tissue) and two-layer (muscle and skin/fat tissues) phantom in the chamber. The skin and fat tissue plays the role of an “aligning” layer and decreases the VSWR value to some extent (Figure 11).

Figure 11.

The frequency dependence of the voltage standing wave ratio, the dotted line corresponds to a single-layer phantom, the solid line to a two-layer phantom [29].

It is clear that around 2.45 GHz, the standing wave ratio for a two-layer cylinder is approximately 2–2.5.

5. Physical modeling (dielectric phantoms)

Practically at the same time as we were trying to describe this process with mathematical models, attempts were being made to perform physical modeling of the frostbite rewarming process in dielectric phantoms imitating a human limb. Initially, it was a thin wall polymer cylinder filled with normal saline [29]. Afterwards, arm [30, 31] and leg [32] phantoms were created (Figure 12).

Figure 12.

Phantom shells used in the experiments.

Normal saline, ground pork meat, HEC gel [33] were used as a phantom filling materials. Dielectric permittivity and conductivity of the last-named were selected to be similar to ones of the muscle tissue.

To study the distribution of temperature in the phantom volume, an experimental unit was set up, with the key components being a vertical microwave chamber (Figure 13) and the mechanism above that controlled a dip temperature sensor.

Figure 13.

The experimental unit to measure longitudinal temperature distributions in the volume of dielectric phantoms (a) and LT-300 dip temperature sensor (b) [30].

The phantom under investigation was placed into the chamber vertically and initial temperature distribution along the phantom’s central axis was measured with the dip temperature sensor. Then the sensor was removed, the chamber (safety sleeve) was closed, and microwave rewarming was initiated. Following a procedure of microwave rewarming, the sleeve was opened and the dip sensor measured temperature distribution along the phantom axis again. Figure 14 shows measurement results for temperature distribution in the volume of a cylindric phantom (Figure 12a) filled with ground pork meat. For this filler, the measured real part of dielectric permittivity was 50, imaginary part–16.9, being close to the parameters of blood-filled human muscle tissue [18].

Figure 14.

Temperature distribution along the longitudinal axis of the phantom warmed up in the microwave chamber: 1 – Without microwave rewarming in the phantom center; 2,3,4 – In the phantom center after 6-minute microwave rewarming; 5 – Along the phantom wall after 6-minute microwave rewarming.

Importantly, the distribution observed showed no considerable non-uniformities of the temperature such as “standing wave” along the central longitudinal axis and along the phantom layer near the wall. The initial non-uniform temperature distribution along the longitudinal axis (curve 1) due to non-uniform cooling of the phantom was smoothened out as the rewarming progressed. A considerable rise in the temperature was observed on the right in the zone immediately near the radiator (located in the plane that corresponds to 55 cm, according to the scale in Figure 10). Rapid warming observed on the left side of the figure corresponding to the open upper part of the phantom is due to the rapid thermal exchange of the filler with air.

From Figure 14, it is clear that after 6-minute rewarming at the generator’s power of about 40 W, the temperature rise in the volume is approximately 2°C. More rapid rewarming of the filler along the phantom wall matches model expectations shown in Figure 6.

To reduce the intensity of the electromagnetic field near the chamber’s side wall where fingers/toes are located, it was proposed to use a linear antenna a little shifted to the input aperture [30]. Figure 15 shows a sequential process of rewarming a cylindrical phantom for such radiator location. The initial non-uniformity of the temperature along the axis of the cooled phantom is also substantial but it is smoothed out as it is warmed up. The temperature in the right zone where toes/fingers will be located does not rise as rapidly.

Figure 15.

Temperature distribution in the volume of a cylindrical phantom in a chamber with a linear radiator: 1 – Before microwave rewarming, 2–4 – After 3 rewarming sessions, each 6 minutes long, 40 W.

In Figure 16, measurement results are given for temperature distribution in the volume of a leg phantom (along the longitudinal axis up to the heel, excluding the foot and toes). Figure 17 shows temperature distribution along an arm phantom, excluding fingers.

Figure 16.

Temperature measurement results along the gastrocnemius muscle along the longitudinal axis of the leg phantom: 1 – Before microwave rewarming, 2–5 – After 4 rewarming sessions, each 6 minutes long, 40 W.

Figure 17.

Temperature measurement results in the volume of the arm phantom: 1 – Before microwave rewarming, 2–5 – After 4 rewarming sessions, each 6 minutes long, 40 W.

Both figures demonstrate a considerably steeper increase in the temperature in the areas of phantom narrowing (around the ankle and wrist).

The change in the temperature distribution in fingers/toes was investigated using a papier-mâché phantom (Figure 12c), This phantom was also filled with ground pork meat. The phantom was first cooled, with temperature distribution measurements performed at all test points (Figure 18), followed by three rewarming procedures, each 6 minutes long, with generator power 40 W. Temperature measurements were performed in the phantom volume with a temperature sensor LT-300 through openings in each of the marked points. Thermal field distribution was evaluated both in the upper arm and the hand, palm (dorsal side) and fingers (Figure 19).

Figure 18.

A view of the arm phantom with indicated temperature measurement points.

Figure 19.

Temperature distribution throughout an arm phantom: Pinky finger (a), ring finger (b), middle finger (c), index finger (d), thumb (e), forearm (points 21, 20, 19), wrist (point 18) and palm (points 17, 16) (f).

First, notably, due to a smaller volume, more uniform initial cooling was achieved. The initial temperature rise in the finger area in the absence of electromagnetic field rewarming is elaborated in Part 1 of the paper as caused by thermal exchange with the environment at room temperature.

Under microwave exposure, we observe more rapid rewarming of the narrowing forearm zone (points 20, 19, 18), which was well consistent with the calculation results for the model presented above in Part 2. The temperature then rises in the critical palm zone (points 17, 16) and proximal and middle finger phalanges (points 3, 2, 6, 5, 9, 8, 12, 11, 15, 14) and decreases in distal phalanges (points 1, 4, 7, 10, 13). The decrease is caused by two factors: smaller electromagnetic intensity in this chamber area due to the location of the radiator more closely to the opening (see Figure 15 for distribution in the cylindric phantom) and more rapid thermal exchange between the fingers and air, as noted above.

6. Some findings of experiments with volunteers

Approval of the Tomsk State University Committee of Bioethics was obtained to involve informed volunteers in this study, considering widespread, years long practice of microwave applications in physical therapy and hyperthermia and positive effects of frostbite microwave treatment of animal limbs [15] and demonstration of the method in phantoms. The volunteers invited to participate in the study were emergency patients admitted to Tomsk Medical Sanitary Unit No. 2 and Tomsk Municipal Hospital No. 3.

The treatment technique included thermal insulation of the cold-injured area prior to microwave rewarming, followed by 1–3 30-minute rewarming procedures in the microwave chamber. For this purpose, a generating unit of a SMVI-200 medical physiotherapeutic device was used with generator power of 30–60 W. Routine drug treatment for such injuries was administered.

In 2019–2022, a total of 14 patients underwent treatment with this technique [34, 35]. For the majority of patients, the technique indeed helped prevent amputation altogether or considerably lessen the scale of it. The compelling demonstration of the technique’s efficacy is the case of a patient [35] who, after being outside in the cold for many hours, was indicated to have both hands (Figure 20a) and both feet (Figure 20b) amputated.

Figure 20.

Cold-injured limbs: (a) hands and fingers, (b) feet and toes [35].

Following the microwave treatment, the patient was discharged only with the toe distal phalanges amputated (Figure 21).

Figure 21.

Outcomes of microwave rewarming treatment: Amputation scale is minimized, both hands and feet are salvaged, only toe distal phalanges are amputated [35].

7. Conclusion

As a result of mathematical modeling of the microwave rewarming in a chamber and experiments in dielectric phantoms, appropriate modes were identified to ensure safe and effective deep rewarming of a frostbitten limb. The efficacy of the technique was demonstrated in informed volunteers. The treatment consisted in the microwave frequency of 2.45 GHz permitted for medical use and power that is less than the one used in physiotherapy procedures. The most efficient procedure was the combination of microwave rewarming and a surgical procedure (fasciotomy, onychectomy), as well as haemorheologic drugs and vasodilators. It is of outmost importance to use this approach in the early reactive period and have no skin rewarming of the affected limb at all prior to microwave rewarming. It is also recommended to perform thermal insulation limb before microwave rewarming.

Clearly, both the chamber and the microwave generator should be optimized, which requires solution of a number of other electrodynamic, thermophysical, and engineering problems. However, the available results already demonstrate a novel, useful, and noteworthy application of microwave radiation in medicine.

Acknowledgments

The work is supported by the Tomsk State University Development Program (Priority-2030).

Conflict of interest

The authors declare no conflict of interest.

Notes/thanks/other declarations

The authors thank Professor Gavrilin E.V., and Antipov V.B. for significant contribution, active participation and support of this work.