sensors Article
Development of Body-Tissue Temperature-Control Transducer Audrone Dumciene 1, * 1 2
*
and Saule Sipaviciene 2
Department of Health, Physical and Social Education, Lithuanian Sports University, Sporto St. 6, LT-44221 Kaunas, Lithuania Department of Applied Biology and Rehabilitation, Lithuanian Sports University, Sporto St. 6, LT-44221 Kaunas, Lithuania;
[email protected] Correspondence:
[email protected]; Tel.: +370-698-277-66
Received: 9 November 2018; Accepted: 17 December 2018; Published: 20 December 2018
Abstract: The aim of this study was to develop a transducer for non-invasive temperature measurement in deeper tissue layers during tissue cooling. Simulation of the temperature field distribution in human tissues and the transducer were done, and the influence of transducer structure and material properties were studied. Using simulation results, the experimental transducer was designed for temperature measurement in deeper tissue layers during cooling. The temperature measurements with the needle thermometer and the transducer were well correlated at both before tissue cooling r = 0.723 and after cooling r = 0.945, and the temperature difference was no more than ±0.2 ◦ C. Keywords: body temperature; sensors; transducer
1. Introduction Several concepts are used in human-body temperature measurements—core body temperature, body temperature, muscle temperature, body skin temperature, etc. The functioning of body-temperature measuring devices is based on various physics principles (nonelectric, thermoelectric, resistance, impedance, semiconductors, fiberoptic, ultrasonic, etc.). There is no rigorous classification of body-temperature measurement methods and gear due to the invasiveness. Gear can be divided into invasive, if an invasion in the human body is necessary to over-extend the skin; less-invasive, if natural body openings are used for temperature measurement; and non-invasive, if body temperature is measured on intact skin surface [1,2]. Core-body temperature can be most accurately measured with a gear known as the Swan–Ganz catheter, which is invasively introduced into the pulmonary artery, or by an esophageal catheter inserted into the esophagus [3]. The core-body temperature of healthy people is in the range of 37 ◦ C ± 0.6 ◦ C, which can be changed with the circadian rhythm. This temperature is assumed to be relatively standard, and it is called the “gold standard.” Invasive temperature measurements in deeper layers of tissue are performed using needle thermometers (thermocouple) [4–6]. For precise less-invasive body-temperature measurements, tympanic ear, oral, and rectal thermometers are more commonly used [7–9]. Some studies have shown that the normal body temperature, measured by less-invasive body-temperature methods, can be in the range of 36.2 ◦ C to 37.5 ◦ C [10]. The advantages and disadvantages of invasive and less-invasive methods have been discussed [1], stating that invasive (pulmonary artery, esophagus, and nasopharynx) methods are only clinically relevant and associated with certain risks, while less-invasive (urinary bladder and rectum) methods are less accurate [1].
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In the absence of a commonly agreed classification of body-temperature measurement methods, some researchers assign methods and gears to non-invasive if the natural body openings are used for temperature measurement [11–16]. Non-invasive measurements of human body temperature utilize various digital medical thermometers, in which thermistors are commonly used as temperature sensors. Known as “zero-heat-flow” (ZHF) temperature gauges, they come with the following options—a heat source to create a heat-flow equilibrium between the human body and an artificial heat source [3,17,18], two sensors that do not require a heat source [19–21], and four temperature transducers [22], which have been used in various studies [23]. Magnetic Resonance Imaging (MRI) [24] and the multi-frequency impedance method [25] are used to monitor the distribution of temperature fields in tissue. The most common tools used for measuring skin temperature are contactless infrared and conductive devices [26,27]. There are commercial non-invasive body temperature ZHF sensors, with a declared accuracy of 25 ◦ C to 43 ◦ C ± 0.2 ◦ C [28]. A comprehensive comparative study of invasive (a urinary bladder temperature probe), semi-invasive (in the esophagus during vascular surgery and in the nasopharynx and the pulmonary artery during cardiac surgery), and non-invasive measurements of temperature using zero-heat-flux sensor type SpotOn skin probe on the forehead and skin temperature probe on the forehead was conducted [1]. The results of this study showed a good agreement (95% limit of agreement) between zero-heat-flux sensor body measurements and invasive measurements. But there was a bad coincidence when the body temperature was below 32 ◦ C. The forehead skin temperature was “2 to 30 ◦ C lower than the deep body temperature” [1] (p. 976). Thus, according to Reference [1], the SpotOn skin probe is suitable for body temperature and core temperature measurements alongside invasive methods until the body temperature is higher than 32 ◦ C. Body-temperature measurements by non-invasive methods, the author’s so-called skin-temperature measurement methods, are extensively analyzed in a review article [29]. It states that, in their opinion, there is no universally acceptable method of measurement to measure the temperature of the skin. The measurement results can be influenced by many factors such as sensor properties, clamping, and attaching to a particular body, environmental conditions, and other factors. It is likely that the thermal balance between the body’s area covered with a sensor and its environment results in heat-transfer conditions different from that in the adjacent uncovered skin zones, and the measured temperature should usually differ from the temperature of the adjacent areas of the skin. For measuring temperature in deeper tissue layers, needle thermometers are usually used, which are inserted 2–4 cm in depth [6,30–37]. They must be sterilized before use and disinfected after use. This measurement procedure is not pleasant to the subject. The above-discussed methods and gears were used to measure body, body core, and skin temperature, but we did not find any research that proves that these methods and gears could be used to determine the temperature at a certain tissue level. This is required for the research on the effects of cooling on muscle properties [31,32], or of cooling for treatment [4,6,32–37]. The temperature in deeper tissue layers was measured by microwave radiometry in which the tissues were heated by high-intensity-focused ultrasound, and using temperature imaging algorithm, the temperature distribution was calculated in real time [38], and microwave radiometry was used for the brain temperature measurement [39]. The mathematical model that describes the relationships of the core temperature with the individual physical activity, heart rate, skin temperature, ambient temperature, and relative humidity was proposed in a previous study [40]. An algorithm was developed for calculating the core temperature from the measurements data mentioned above. In Reference [41], a model to calculate core body temperature from heart rate observation data was proposed, but it needed continuous heart rate monitoring. Mathematical models [42] enabling assessment of core-body temperature using individual characteristics, physical activity, clothing biophysics, and environmental conditions were created. A model was proposed in study [43] for core-body temperature prediction using the skin temperature over the carotid artery measurement
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equation proposed in non-invasive Reference [33], which includesmeasurement variables like using time, ZHF skin temperature, skinfold, data. New design for core temperature method was proposed room temperature, and[44]. bodyIntramuscular core temperature. Temperature measured the given tissue depth and used in Reference temperature can bewas predicted at aatdepth of 2 cm using the using diffuse optical method variables and a relevant equipment [45]. A method of equation proposed in spectroscopic Reference [33],imaging which includes like time, skin temperature, skinfold, temperature estimation that was on the thermal dependence of the acoustic speedtissue in a heated room temperature, and body corebased temperature. Temperature was measured at the given depth medium was used in Reference [46].imaging Novel photoacoustics was proposed [45]. and used in study using diffuse optical spectroscopic method and asensor relevant equipment A method of [47] for non-invasive monitoring blood temperature estimation that was of based ontemperature. the thermal dependence of the acoustic speed in a heated The was methods References [38,45,46] hold possibility for temperature medium used inimplemented Reference [46]. in Novel photoacoustics sensor was aproposed and used in study [47] measurement in tissue deeper in local areas unlike the methods used in References [40– for non-invasive monitoring of layers blood and temperature. 44,47]The for methods measuring core body temperature, the equipment on thefor diffuse optical implemented in Referencesbut[38,45,46] hold a based possibility temperature spectroscopic imaging method or the thermal the acousticused speed in a heated[40–44,47] medium measurement in tissue deeper layers and in localdependence areas unlikeof the methods in References is to use in additional cases, example, when treating with an iceoptical pack after injury or forcomplicated measuring core body temperature, butfor the equipment based on the diffuse spectroscopic trauma. imaging method or the thermal dependence of the acoustic speed in a heated medium is complicated It in was shown incases, Reference [31] thatwhen skin surface during cooling time change to use additional for example, treatingtemperature with an ice pack after injuryversus or trauma. almost linearly. It was found in Reference [6] that when the surfaceduring (skin) temperature varied It was shown in Reference [31] that skin surface temperature cooling versus timelinearly change in time linearly. during cooling, temperature of muscles 2 cm the depth also varied linearly withvaried time. linearly So, if it almost It was found in Reference [6] thatatwhen surface (skin) temperature was possible to cooling, measuretemperature the temperature of the tissue surface fromtime. the thermal in time during of muscles at 2 cm deptharea, also thermo-isolated varied linearly with So, if it effects of the environment, the tissueof temperature at a depth 3 cm can be calculated the was possible to measure thethen temperature the tissue surface area,ofthermo-isolated from theusing thermal following equation [48]: then the tissue temperature at a depth of 3 cm can be calculated using the effects of the environment, following equation [48]: T = 0.5026 × Tss + 18.399 (1) T = 0.5026 × Tss + 18.399 (1) where Tss—temperature on the skin surface measured by the transducer. where Tss —temperature on the skin surface measured by the transducer. Therefore, the purpose of this study was to find out the possibility and develop an instrument Therefore, the purpose of this study was to find out the possibility and develop an instrument for measuring temperature in deeper layers of tissue, without the use of needle thermometers, but by for measuring temperature in deeper layers of tissue, without the use of needle thermometers, but by measuring temperature on intact skin surface during cooling. measuring temperature on intact skin surface during cooling. 2. 2. Materials Materials and and Methods Methods Here, Here, we we discuss discuss aa new new multisensory multisensory transducer transducer design, design, of of which which the the structure structure is is shown shown in in Figure 1. This is because the thermal channel and isolation cover dimension and the influence Figure 1. This is because the thermal channel and isolation cover dimension and the influence of of the the channel channel material material have have not not been been clarified. clarified.
Figure 1. 1. Transducer Transducer structure: structure: 1, 1, 2, 2, 3, 3, 4, 4, and and 5—temperature 5—temperature sensors sensors (Thermistor (Thermistor 55 can can be be used used to to Figure inspect the thermo-isolation cover); 6—thermal channel; 7—thermal channel; 8—thermo-insulation inspect the thermo-isolation cover); 6—thermal channel; 7—thermal channel; 8—thermo-insulation cover; 9—skin; 9—skin; 10—fat; 10—fat; and and 11—muscle. 11—muscle. cover;
The thermal equivalent circuit of the transducer shown in Figure 1 without considering the The thermal equivalent circuit of the transducer shown in Figure 1 without considering the influence of the thermistors can be formed, as shown in Figure 2. influence of the thermistors can be formed, as shown in Figure 2.
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Figure —deep tissue tissue layer layer temperature; temperature; Figure 2. 2. Equivalent Equivalent resistance resistance circuit circuit of of two two heat-flow heat-flow channels. channels. T Ttt—deep T —sensor 1 temperature; T —sensor 2 temperature; T —sensor 3 temperature; T —sensor 44 T11—sensor 1 temperature; T22—sensor 2 temperature; T33—sensor 3 temperature; T44—sensor temperature; thermalresistance; resistance; R1 —thermal resistance of one thermal channel; t —tissuethermal R1—thermal resistance of one thermal channel; and Rand 2— temperature; RRt—tissue R —thermal resistance of another thermal channel. 2 thermal resistance of another thermal channel.
The temperature on the boundary between the skin surface and the transducer pad can be The temperature on the boundary between the skin surface and the transducer pad can be calculated using the following modified equation [48]: calculated using the following modified equation [48]: T1 ·⋅λλ((TT3 − T ) − T ( T1 T −2 )T2 ) 1 3 − T44) −T3 (3T1 − Tt T ==T t λλ( T − T ) − ( T − T 3 (T3 − T44 ) − (T1 1− T2 )2 )
(2)(2)
where T1 , T2 , T3 , and T4 —temperatures at points shown in Figure 2; and λ—ratio of thermal channel where T1, T2, T3, and T4—temperatures at points shown in Figure 2; and λ—ratio of thermal channel thermal resistance R1 /R2 . thermal R1/R2be . higher than four [48]. So, the ratio of thermal resistors R1 and R2 of the Thisresistance ratio λ must This ratio λ must be higher four [48]. So, the ratio of thermal resistors R1 and R2 of the thermal channels in this study wasthan equal to five. thermal channels in this study was equal to five. To determine the optimum parameters of the transducer, a simulation of the distribution of To determine the parameters the transducer, a simulation of the distribution of temperature fields in theoptimum human tissue and theoftransducer structure was performed. temperature fields in the human tissue and the transducer structure was performed. The human body, using nutrients, generates bioheat. Due to the flow of blood and the heat-transfer Theheat human body, using nutrients, generates bioheat. Due to the the environment. flow of bloodThe and the heatprocess, is transferred to the entire body until it is balanced with description transfer process, heat is transferred to the entire body until it is balanced with the environment. of heat propagation in living organisms is most often done with the Pennes’ [49] equation orThe its description of heat propagation in living organisms is most often with the Pennes’ [49]boundary equation modifications, which assess specific conditions [50–52]. Using the done Pennes’ equation and the or its modifications, which assess specific conditions [50–52]. Using the Pennes’ equation and the conditions established for the variants under consideration, one can simulate the heat-propagation boundary conditions established for the variants under consideration, one can simulate the heatprocess in the human body and calculate the distribution of temperature fields. propagation process in the human body and calculate the distribution of temperature fields. Thus, the bioheat-transfer process in the human body can be described by the following Thus,[49]: the bioheat-transfer process in the human body can be described by the following equation equation [49]: δT δts ρC + ∇ · (−k∇ T ) = ρb Cb ωb ( Tb − T ) + Qm + Qex (3) δt δT +∇(dimensionless); ⋅(−k ∇T ) = ρb Cb ωρ—tissue Qm + Qex(kg/m3 ); C—specific (3) ts ρ C b (Tb − T ) + where δts —a time-scaling δcoefficient density heat
δt
of tissue (J/(kg·K)); k—tissue’s thermal conductivity tensor (W/(m·K)); ρb —blood density (kg/m3 ); 3); C—specific heat of 3 where δts—a time-scaling coefficient (dimensionless); ρ—tissue density (kg/m C b —specific heat temperature (K); Qm —heat source from metabolism (W/m ); Qex —spatial heat sourse 3 ·s)); T —arterial blood temperature 3 in body of blood k—tissue’s (W/m3 ); ω bthermal —blood-perfusion rate (m3 /(m tissue (J/(kg·K)); conductivity tensor (W/(m·K)); b— b ρb—blood density (kg/m ); C(K); T—dependence variable temperature (K). 3 specific heat temperature (K); Qm—heat source from metabolism (W/m ); Qex—spatial heat sourse in We investigated a case where the person is in a state of rest and at a relatively stable ambient body of blood (W/m3); ωb—blood-perfusion rate (m3/(m3·s)); Tb—arterial blood temperature (K); T— temperature. In this case, we can write: dependence variable temperature (K). We investigated a case ∇ where ab state rest and · (−kthe ∇ T )person = ρb Cbisωin − T ) of +Q Qexat . a relatively stable ambient (4) m+ b (T temperature. In this case, we can write: If the person is in a state of rest, we can accept that Qex = 0, and transform Equation (4) as ∇ ⋅ ( − k ∇ T ) = ρ b C b ω b ( Tb − T ) + Q m + Q ex (4) . ∇ · (−k∇ T ) = ρb Cb ωb ( Tb − T ) + Qm . (5) If the person is in a state of rest, we can accept that Qex = 0, and transform Equation (4) as Therefore, Equation (4) can be toTsimulate ∇ ⋅used (− k ∇ ) = ρ b C btemperature ω b (Tb − T ) +fields Qm in the tissue. We are interested (5) . in the distribution of temperature fields in the tissue and in the transducer body.
Therefore, Equation (4) can be used to simulate temperature fields in the tissue. We are interested in the distribution of temperature fields in the tissue and in the transducer body.
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Since the volume of the transducer is small compared with the parts of the human body in which the temperature will be measured, the accuracy is reduced using Equation (5) for the propagation of Since the volume of the transducer is small compared with the parts of the human body in which heat in the transducer body. the temperature will be measured, the accuracy is reduced using Equation (5) for the propagation of conditions: heatBoundary in the transducer body.− n ⋅ ( − k∇ T ) = q 0 + h (Text − T ) —heat flux (external boundary of the tissue →
Boundary conditions: ( Text − T )—heat (external boundary of the on flux the entire interior boundary and the transducer model);− n ⋅·( k(− ∇kT∇−T k) 2= ∇ Tq2 0) =+0h—continuity →1 1 tissue and the transducer model); n · (k1 ∇ T1 − k2 ∇ T2 ) = 0—continuity on the entire interior boundary →n ⋅ ( − k∇T ) = 0 —using the symmetry of the between tissue layers and the transducer body model; − between tissue layers and the transducer body model; − n · (−k∇ T ) = 0—using the symmetry of the object —external (bulk) temperature. objectunder understudy, study,the thesymmetry symmetry condition condition is is given, given, where where TText ext —external (bulk) temperature. The Thehuman humantissue tissuemodel modelproperties properties[53] [53]used usedin inthe thesimulation simulationare aregiven givenin inTable Table 1. 1. Table Table1.1.Human Humantissue tissuelayer layerproperties. properties. Layer Layer
3 )3) (kg/m ρρ(kg/m
Muscle Muscle Fat Fat Skin Skin Blood Blood
1090 1090 850 850 1100 1100 1050 1050
kk(W/m*K) (W/m*K) 0.5 0.5 0.16 0.16 0.21 0.21 0.32 0.32
3) 3 ωb (1/s) Cp (J/kg*K) (m) (W/m Cp (J/kg*K) Thickness Thickness (m) Qm Q ωb (1/s)Tb (K) Tb (K) m (W/m ) 3766 0.12 5 0.0001 3766 0.12 5 0.0001 310.15 310.15 2510 0.0025 4/5e−6310.15 310.15 2510 0.0025 0 0 4/5e−6 3250 0.002 7.2e−8 310.15 310.15 3250 0.002 4 4 7.2e−8 1313 0.03 0.5 310.15 1313 0.03 0.5 310.15
TheCOMSOL COMSOL Multiphysics Multiphysics 3.5. software temperature fields in the The software package packagewas wasused usedtotosimulate simulate temperature fields in ◦ C. tissue andand transducer body at an environment temperature of 20 the tissue transducer body at an environment temperature of 20 °C. PrecisionCantherm Canthermthermistor thermistor(Cantherm, (Cantherm,Monteal, Monteal,Canada), Canada),type typeMF51E103F3380, MF51E103F3380,with withaatime time Precision constantofof≤3.2 ≤3.2s swas wasused usedasastemperature temperaturesensor sensorthat thatisisintended intendedfor formedical medicalequipment. equipment.For Forthe the constant thermistor, a calibration procedure was conducted, and the Steinhart–Hart equation was used for the thermistor, a calibration procedure was conducted, and the Steinhart–Hart equation was used for the resistancetemperature temperatureR(T) R(T)characteristic characteristicapproximation. approximation.The Theequation equationcan canbe bewritten writtenas asfollows: follows: resistance
11/T /T = ++B3B(ln R )3 3 T T =BB00++BB1 1lnlnRR 3 (ln TR T )
(6) (6)
where whereT—temperature T—temperaturein inK; K; BB00, ,BB11, ,and andBB33—equation —equationcoefficients; coefficients;and andRRTT—thermistor —thermistorresistance resistanceatat the temperature T. the temperature T. CoefficientsBB0,0 ,BB1,1 ,and andBB wereestimated estimatedfrom fromthermistor thermistorcalibration calibrationresults, results,since sincethe theR(T) R(T) Coefficients 3 3were characteristics from the manufacturer are not for individual thermistors, but averaged thermistor type characteristics from the manufacturer are not for individual thermistors, but averaged thermistor MF51. The The accuracy of calibrated thermistors afterafter applying the linearization of the type MF51. accuracy of calibrated thermistors applying the linearization of Steinhart—Hart the Steinhart— ◦ equation was was in the of ±0.02 C. °C. Hart equation inrange the range of ±0.02 Thestructure structureof ofthe thephysical physicalmodel modelused usedfor fortransducer transducerexamination examinationisisshown shownin inFigure Figure 3. 3. The M 4 3 2 1
PC
TM DC
Figure 3. Structure diagram of the experiment. 1—cooler; 2—Peltier element; 3—polyethylene Figure 3. Structure diagram of the experiment. 1—cooler; 2—Peltier element; 3—polyethylene plate plate (phantom); 4—transducer; M—temperature meter; TM—temperature meter with thermo-probe; (phantom); 4—transducer; M—temperature meter; TM—temperature meter with thermo-probe; PC—laptop; and DC—programmable DC source. PC—laptop; and DC—programmable DC source.
Temperature was measured at six points using the FLUKE thermometer type Black Stack 1560 and Temperature was measured at six points using the FLUKE thermometer type Black Stack 1560 Thermistor readout module type 2564 (readout four decimal digits after point). Reference temperature and Thermistor readout module type 2564 (readout four decimal digits after point). Reference at the top of the polyethylene plate (phantom) was maintained within the range of 30 ± 0.1 ◦ C. temperature at the top of the polyethylene plate (phantom) was maintained within the range of 30 ± The temperature of transducer sensors 1, 2, 3, 4, and 5 was measured using, as noted above, 0.1 °C. a FLUKE thermometer. The temperature of transducer sensors 1, 2, 3, 4, and 5 was measured using, as noted above, a The dimension of the thermal channel and the thermos-isolation cover is shown in Figure 4. FLUKE thermometer. The dimension of the thermal channel and the thermos-isolation cover is shown in Figure 4.
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L1
L4
L5
L2
L6
L3
D
d
L7
Figure Figure 4. 4. Main Main dimension dimension of of transducer transducer elements. elements.
Dimensions L11,, LL22,,LL33, ,LL4,4L , L5,5L, L , D, and shownininFigure Figure4 4are areused usedasasvariables variablesby bysimulating simulating Dimensions 6L , 7D, and dd shown 6 7L the distribution of temperature fields in a transducer. the distribution of temperature A hard-plastic polyurethane foam for thermo-isolation and epoxy with cooper A hard-plasticcover coverand and polyurethane foam for thermo-isolation and epoxy with powder cooper were used forused the transducer design. design. powder were for the transducer Ethical approval approval for for an an experiment experiment with with human human subjects subjects was was granted granted by by the the Kaunas Kaunas regional regional Ethical biomedical-researchethics ethicscommittee, committee, measurements in accordance the biomedical-research andand measurements were were taken taken in accordance with the with Helsinki Helsinki Declaration. Declaration. The experiment experiment with the human Before temperature temperature The human subject subject included included one one volunteer. volunteer. Before measurements were were taken, taken, the the test test subject subject was was lying lying supine supine on on aa laboratory laboratory bed bed for for 15 15 min min for for measurements ◦ C. The deep muscle temperature was measured relaxation in a room with a temperature of 20 ± 1 relaxation in a ± 1 °C. The deep muscle temperature was measured using needle needle thermometer thermometer (Ellab (Ellab A/S, A/S,type typeDM DM852, 852,Hillerød, Hillerød,Denmark). Denmark).The Theskin skinof of left left thigh thigh was was using prepared before and disinfecting before andand afterafter needle insertion with prepared before each eachmeasurement measurementbybyshaving shaving and disinfecting before needle insertion a padasaturated with isopropyl alcoholalcohol (Shanghai Channelmed Import &Import Export&Co., Ltd., Co., Shanghai, with pad saturated with isopropyl (Shanghai Channelmed Export Ltd., China). Needle thermometer was inserted perpendicular to the skin covering ofcovering the muscle quadriceps Shanghai, China). Needle thermometer was inserted perpendicular to the skin of the muscle femoris at afemoris depth of cm including ofone-half the skinfold inskinfold the middle-third on the sideon of the the quadriceps at ~3 a depth of ~3 cmone-half including of the in the middle-third femur. skinfold was measured the Holtain (Sibercaliper Hegner GMP,Hegner Zurich,GMP, Switzerland). side of The the femur. The skinfold wasby measured by caliper the Holtain (Siber Zurich, After measuring, themeasuring, needle thermometer extracted, and skin was disinfected and disinfected sealed with Switzerland). After the needlewas thermometer was the extracted, and the skin was a waterproof anti-bacterial patch on the spot. and sealed with a waterproof anti-bacterial patch on the spot. Transducer was was hermetically hermetically attached attached using using adhesive adhesive tape tape 11 cm cm away away from from the the needle needle Transducer thermometer and and left left during during immersion immersion in in cold cold bath. bath. The The needle needle thermometer thermometer was was sterilized sterilized after after thermometer each use. use.The The measurements were conducted before repeated immediately leg cooling. each measurements were conducted before andand repeated immediately afterafter leg cooling. Test ◦ C) Test subject’s leg was immersed formin 15 min (with 10 min break) in cold water subject’s leg was twicetwice immersed for 15 (with a 10amin break) in cold water bathbath (15 (15 ± 1± °C)1 for for cooling measurement was repeated five timeswith withtwo-week two-weekbreaks. breaks.The Thepatient patient was was cooling [54].[54]. TheThe measurement was repeated five times advised on on the the thermometer thermometer needle needle insertion insertion site site supervision supervision and and to to inform inform researchers researchers about about any any advised signs of of infection. infection. signs 3. Results Results 3. The distribution distribution of of the the temperature temperature fields fields in in the the tissue–transducer tissue–transducer models models (Figure (Figure 1), 1), at at different different The ◦ C, is given in Figure 5 variables L , L , L , L , L , and L , when the environment temperature was +20 variables L11, L22, L33, L44, L55, and L66, when the environment temperature was +20 °C, is given in Figure 5(a,(a,b,b,and andc cfor fordifferent differentvariable variablevalues). values).
(a)
(b)
(c)
Figure 5. Distribution of temperature fields in the tissue and the transducer. (a) Transducer structure version when (L1 + L2) < (L5 + L6); (b) Transducer structure version when (L1 + L2)
signs of infection. 3. Results The distribution of the temperature fields in the tissue–transducer models (Figure 1), at different L3, L4, L5, and L6, when the environment temperature was +20 °C, is given in Figure 7 of 12 5 (a, b, and c for different variable values).
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(b)
(c)
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Figure Distribution of temperature fieldsfields in theintissue and theand transducer. (a) Transducer structure Figure5. 5. Distribution of temperature the tissue the transducer. (a) Transducer 1 2 5 6 3 version (LTransducer + L ) < (L + L ); (b) Transducer structure version when (L + L ) (L
