Modeling Haptic Data Transfer Processes through a Thermal

Interface using an Equivalent Electric Circuit Approach

Yosef Y. Shani and Simon Lineykin

Mechanical Engineering and Mechatronics, Ariel University, Ramat HaGolan Street 65, Ariel, Israel

Keywords: Data Transfer, Haptic Thermal Interface, Termo-Electric Cooler, Equivalent Circuit Modeling.

Abstract: Many activities and scenarios today require human-computer interactions (HCI), and since traditional

communication channels such as vision and hearing are often overloaded or irrelevant, there is an increasing

interest in haptic interfaces, specifically thermal. Designing and optimizing an effective tactile interface

requires an easy-to-use simulation tool to reduce the time for empirical experiments. An original modeling

tool was developed in this study to support cutting edge research on human response to thermal stimuli. The

human skin tissue model is developed as an equivalent electrical circuit for simultaneous simulation with a

thermal display scheme and its control circuitry. The simulator enables monitoring heat flows and temperature

variations at any location of the system without intervening in the process itself and inside the skin tissue, for

instance, at the depth of the thermoreceptors. The other generic advantage of performing tests with a simulator

is the ability to adjust the parameters according to the variety of skin types, test conditions, or thermo-display

characteristics, and to simulate the response to different generated stimuli. This report presents the

methodology and structure of the model along with an initial empiric validation and suggests directions for

further research and future implementation.

1 INTRODUCTION

The human thermal sensory modality offers a novel

dimension for transferring information, provided the

presented thermal cues are designed in accordance

with the sensory system properties. Like other senses,

the thermal sense is based on the effect a stimulus has

on the sensory system, and its sensitivity to the

change that occurred. Therefore, the effect of

different properties of thermal stimuli on the sensory

system has been studied, and thermal thresholds have

been determined. The results show that humans are

remarkably sensitive to changes in skin temperature,

especially for cooling (Stevens, 1998). For instance,

we can resolve a difference of 0.02–0.07°C in the

amplitudes of two cooling pulses or 0.03–0.09°C for

warming pulses (Smith, 1977), (Kenshalo, 1976). and

detect thermal stimuli when skin temperature rises by

0.2°C or descends by 0.11°C (at rates above

0.1°C/sec) (Stevens, 1998), (Ho, 2018). These

fundamental properties of the thermal sensory

system, and others, provide a framework for defining

https://orcid.org/0000-0002-4251-0725

the optimal characteristics of any thermal stimuli

presented to the skin.

Much of the research regarding thermal displays

has been focused on their use to simulate the thermal

properties of objects in VR scenarios or to facilitate

material identification and discrimination based on its

typical thermal signature (Jones, 2008). Recent

studies have started investigating the feasibility of

conveying information via thermal sensation, i.e.,

using a thermal display to present encoded abstract

information, to be sensed and decoded by touch. First

steps have been made towards designing suitable

thermal cues (Wilson, 2012, 2013), (Singhal, 2015,

2018). The thermal cues must be knowledgeably

designed in order to guaranty perceptual distinction

with high reliability. There are many challenges in

using thermal cues for this purpose, due to the human

factor on one hand and technology or experimental

factors on the other. Some of the major challenges are

the limited and small number of sensations evoked by

changes in skin temperature, the multiplicity of

parameters that influence the human thermal

sensitivity, spatial summation causing poor location

Shani, Y. and Lineykin, S.

Modeling Haptic Data Transfer Processes through a Thermal Interface using an Equivalent Electric Circuit Approach.

DOI: 10.5220/0010262101270135

In Proceedings of the 14th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2021) - Volume 3: BIOINFORMATICS, pages 127-135

ISBN: 978-989-758-490-9

127

capability, thermal adaptation, and thermal dynamics

of the tissue affecting the human response and hence

the sensation, creating the stimuli and monitoring the

response. To date, the concept of using a thermal

display as a means of transferring data has been

established, but the basis for designing the actual cues

requires further study regarding the human response

to dynamic thermal stimuli.

A haptic thermal interface is a device that excites

tactile sensations by relevant thermal stimulation

(Nam, 2005). A thermoelectric cooler/heater is very

suitable to serve as a thermal interface. It responds

fast to variations in the electric driving current and

allows the wave-shape forming of thermal haptic

signals. It also allows various methods of the drive,

including different types of feedback control, such as

controlling the temperature of the transmitting

surface, the amount of sinking/sourcing heat, and

more.

Monitoring skin response to thermal stimuli,

throughout the experiments, is necessary for

understanding the sources of inefficient

identification, and consequently allows stimuli fine-

tuning seeking an unambiguous distinction. This

issue was illustrated at MIT (Singhal, 2018),

(Singhal, 2015), as the skin temperature measured at

skin-thermal display interface, while exposed to

various types of thermal inputs, indicated that

different waveforms such as square waves, sinusoids,

and triangular waves resulted in very similar changes

in skin temperature, and therefore were unlikely to be

perceptually distinguishable. Furthermore,

comparing the easiest stimulus to identify (with 100%

correct responses across participants), that involved a

linear decrease in skin temperature, with the pattern

with the lowest percentage of correct responses (64%)

that involved a linear increase in temperature from

cold to warm, lead the authors to suggest conclusions

that can be used as guidelines for designing thermal

cues. However, measuring skin temperature at the

skin-thermal display interface, is a known challenge.

The main difficulties being that the very act of

measuring influences the result as it enhances local

pressure on the skin and interferes with the heat

transfer process, as well as the fact that the layer of

the skin relevant for warmth and cold sensation is

inherently inaccessible. (Ho, 2017) apparently

neglected these influences for her research practical

purposes and placed the thermistor at the skin-display

interface. Another reported example is (Singhal,

2018) that chose to place a thermistor at the periphery

of the contact area of the skin and the display, out of

the actual interface area. Both approaches achieving

their research goals.

The complicity and the time consumption of these

experiments lead us to develop a unique emulator

capable of predicting thermal response to various

stimuli. The main advantages of this model are that it

enables effortless extensive resetting and retesting, as

well as 'monitoring' temperature at any chosen point

throughout the display - skin array, free of

interference in the heat transfer process. Hence, it

shall support further research allowing a better

understanding of the human thermal sensory

processing and enhancing thermal feedback

applicability.

A universal model of averaged skin tissue that

allows co-simulation with different thermal interfaces

can serve as a useful tool for choosing the optimal

thermal interface. This method makes it possible to

make predictions about parameters in the formation

and perception of a tactile signal such as the attack,

amplitude, delay, etc. before experimenting with

participants.

This paper presents the modeling methodology,

the structure of the developed skin-tissue & thermal-

display model and an initial empiric validation.

Finally, directions for further research and future

implementation are suggested.

2 SCIENTIFIC BACKGROUND

AND METHODOLOGY

A simplified mathematical model of the skin close to

the contact zone was developed, in the form of an

equivalent electrical circuit. The advantage of this

kind of model is that it can be used to simulate

stimulus-response process in conjunction with the

electric current driver model using electrical circuits

simulation software. In addition, we have developed

and built a laboratory system for generating thermal

exciting signals (stimuli). The following is a

description of the laboratory system, the proposed

skin model, and examples of simulating the stimulus-

response process in dynamics.

The heat transfer within tissues and the heat

transfer in solids can be modeled using an equivalent

electrical circuit, as shown in the (Holman, 2002). An

equivalent electrical circuit is convenient for joint

simulation of thermal processes in tissues and in a

thermoelectric module, as well as electrical processes

in drivers and control networks. The system of

thermo-electrical analogies, where voltage is

analogous to temperature and current is analogous to

a heat flow, is summarized in the Table 1.

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This system of analogies helps to represent a

thermal system with distributed parameters as an

equivalent electrical circuit with lumped parameters

consisting of resistors (equivalent to thermal

Table 1: Thermo-electrical analogies.

Thermal

quantities

Units Analogues

Electrical

Quantities

Units

Heat, q W Current, I A

Temperature, T °C Voltage, V V

Thermal

resistance, Θ

°C/W Resistance, R

Heat capacity, C J/°C Capacity, C F

Common

temperature

0°C Common ground,

gnd

resistance) and capacitors (equivalent to thermal

masses). The initial and boundary conditions of the

equivalent circuit are specified as voltage sources

(equivalent to a temperature source) and current

sources (equivalent to heat sources). The LTSpice

program was used in the current study as the

environment for simulations. Any other software for

electric circuits simulation can be used for this goal

as well.

2.1 Modeling the Skin Tissue

The surface of human skin is not smooth. The varying

degrees of moisture, oiliness, elasticity, hairline, and

other parameters make even measurement of the skin

surface temperature, nontrivial. Heat distribution

under the skin surface is not measurable in vivo.

There are many types of models for thermal

processes in tissues. We have chosen the equivalent

electrical circuit model type to simulate it together

with the model of the thermal signal generator. The

basic concept of the presented model is a division of

the tissue into submillimeter layers, so that lumped

parameters can be used to simulate each layer. Since

the overall depth of interest is small, the heat transfer

can be considered one-dimensional (Cui, 1990).

Each layer has a thermal resistance (𝛩, °𝐶 ∙ 𝑊



)

and a thermal capacity (𝐶, 𝐽 ∙ °𝐶



). The values of

those

parameters can be calculated based on the data

in Table 2 and using the following expressions:











∙









(1)











∙









(2)

𝐶



𝑚



∙𝑐



𝜌∙𝐴



∙ℎ



(3)

𝐶



𝑚



∙𝑐



𝜌∙𝐴



∙ℎ



(4)

where 𝐴



is the contact area, k and c are thermal

properties tabulated in, subscripts “e” and “d” refer to

epidermis and dermis respectively, h is the thickness

of the corresponding layer.

When building the model, we assume the

temperature of the subcutaneous tissue remains

unchanged throughout the experiment (𝑡𝑠𝑡 ≈ 37°𝐶),

due to its low thermal conductivity and since the

effect on the skin is performed for a short period of

time. Figure 1 shows a schematic visualization of a

skin structure using data from (Ratovoson, 2010), (Xu,

2008), and an equivalent circuit model of the

fragment of skin close to contact zone. The outer

layer of the skin (stratum corneum) is shown at the

top of the scheme. The dermis layer of tissue is

significantly thicker than the epidermis layer. The

temperature of the inner part of the dermis can be

assumed as constant stimuli independent (Cui, 1990).

The coloured semi-transparent frames show the

approximate location of the various receptors

responsible for tactile sensations within the skin

tissue. The tissue is divided into elements that can be

represented as lumped parameters. The mesh

resolution was chosen empirically so that increasing

the grid resolution does not lead to significant

differences in the simulation results. Thus, the

epidermis is presented as one element, and the dermis

as five identical elements. Each element has its

thermal resistance and thermal capacity

corresponding to the values of Table 2 and

expressions (1)-(4). In normal conditions, the skin is

cooled by ambient air. The ambient air temperature is

depicted as an equivalent voltage source in Figure 1

(b). The thermal resistance of the convective heat

exchange between the skin and the air is shown as an

equivalent resistor. As a result, the temperature on the

skin surface is about (≈32°C), which is lower than the

temperature of subcutaneous tissue. The voltage at

point 𝑡



is equivalent to the temperature at the depth

of the thermal receptors in kelvin.

Table 2: Skin mechanical and thermal properties (Ratovoson, 2010).

Layer Thickness, h

(m)

Specific heat, C

(J.kg

-1

)

Thermal conductivity, k

(W.m

-1

-1)

Specific mass, 

(Kg.m

-3

)

idermis 0.081

3590 0.24 1200

Dermis 2m 3300 0.45 1060

Modeling Haptic Data Transfer Processes through a Thermal Interface using an Equivalent Electric Circuit Approach

129

(a)

(b)

Figure 1: Schematic visualization of the skin structure - (a)

Scheme of the fragment of skin based on (Ratovoson,

2010), (Xu, 2008) and (b) Equivalent circuit model of the

skin at thermal contact zone based on data from

(Gowrishankar, 2004), (Xu, 2008).

2.2 Modeling the Thermal Interface

The laboratory setup is shown schematically in Figure

2(a). The thermostatic hot plate is the substructure of

the thermoelectric driver. The temperature of the hot

plate is mounted at a constant value of about 40C

using the PID temperature controller. The current-

driven solid-state thermoelectric cooler (TEC) is

attached with its hot side to the hot plate. Thus, the

cold side of the TEC, which is in contact with the skin

of the experiment participant, tends to be cooled as

the driving current increases. In such a way, the

maximum possible temperature of the contact surface

is less than 40C, and the lowest possible temperature

value is set to about 5°𝐶. This is a safe range for test

subject at short-time thermal cues. The TEC is

thermally insulated laterally using aerogel, and at the

cold side using Teflon sheet, except for the contact

window, as shown in the

Figure 2

(a).

The stimuli generator has been tested in the

laboratory. It works properly according to design. The

primary experiments were carried out with the

participation of the researchers. There were just

preliminary qualitative measurements without

statistical elaboration. The preliminary results are

presented below in the corresponding section and do

not differ dramatically from the data indicated in the

literature.

In a steady-state or quasi-steady-state case, the

temperature of the contact surface of the TEC is

proportional to the amount of heat pumped from the

(a)

(b)

Figure 2: An experimental setup (a) includes the

thermoelectric cooler (TEC), thermostatic plate, thermal

insulation and a current driver. The circuit for simulation

depicted in (b). Solid line represents electrical domain and

the dotted line is used for thermal domain. V and I represent

voltage and current correspondently, T is the temperature in

°C,  is the thermal resistance of convective heat transfer.

The subscripts ref, hp, h, amb, sa, contact and c refer to

reference, hot plate, hot surface, ambient, skin-to-air,

contact, and cold surface respectively. The model of TEC

is taken from (Lineykin, 2007), the model of skin is shown

in Figure 1.

surface by the TEC. The amount of heat sourced or

sunk from/to the surface at constant temperature is

proportional to the current flowing through the TEC,

so it can be easily controlled. At the same time, during

transients, a significant part of the heat goes to

heating the cooler itself, which has some heat

capacity. In order to study the thermal transients and

in order to create temperature excitation signals of the

desired shape, we used a model of a thermoelectric

cooler, developed in early research and published in

(Lineykin, 2007). This model can be easily simulated

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using a circuit simulator such as LTSpice together

with electrical driver circuitry.

Equivalent circuit model of the TEC has two

electrical terminals (“+” and “-“) and two terminals in

thermal domain (“Th” and “Tc”), as shown in

Figure

(b). The system of thermo-electrical analogies,

where voltage is analogous to temperature and current

is analogous to a heat flow, is summarized in the

Table 1.

Figure 2

(b) depicts the simulation circuit of the

laboratory setup. The electrical part of the circuit is a

voltage-controlled current source (Trans-admittance

amplifier). Resistors R

, R

, and R

are selected in

such a way to provide the trans-admittance gain of 0.1

(A/V). In the figure, the thermal interface system is

loaded by human skin model in thermal domain. The

contact thermal resistance is shown as Θ



. The

principle of skin modeling is explained above.

As an example, let us simulate the effect on the

skin of a thermal signal having a relatively standard

pattern with a trapeze-shaped cooling wave, as shown

in Figure 3. This shape refers to the desired curve

describing temperature change of the skin surface vs.

time, in response to a corresponding thermal

excitation signal. We have designed the shape of the

necessary electrical exciting signal, that when applied

to the TEC will produce the corresponding thermal

signal that is predicted to cause the desired skin

temperature change at the contact zone. The result of

the simulation of the process of excitation and

reaction is shown in Figure 3.

Figure 3: Example of simulating the temperature of skin

exposed to a cold pulse thermal excitation. The upper

waveform represents the TEC current vs. time. The lower

curves show the temperature (1 Vcorresponds to 1°C) vs.

time. The green curve shows the skin surface temperature

at the contact zone. The red curve shows the temperature of

the thermo-display (TEC) under the skin.

3 EXPERIMENTAL VALIDATION

To validate the emulating model, and prove its

reliability and precision, we shall refer to previously

explored pattern-based thermal icons. For the sake of

simplicity and clarity, we chose to focus on one of six

basic patterns reported by (Singhal, 2018): a cooling

step, i.e, an 8 seconds sequence initiating at steady

normal skin temperature, a sudden reduction of 6°C

@ 3°C/sec rate of change (ROC), followed by

temperature maintenance, and return to baseline

@3°C/sec ROC.

3.1 Method

The characteristics of the specific thermoelectric

Peltier element used by the authors of (Singhal,

2018), were entered into the emulator, and a similar

thermal pattern was reproduced. The output simulated

thermal cutaneous response, was then observed in

comparison to the reported empirical data. To

complete the validation process the electrical input

required to produce the simulated designated thermal

cue, was retrieved and applied to an experimental

thermal display setup in our laboratory. The resulting

skin and display temperatures were observed in

comparison to the corresponding simulated data.

3.2 Results

The heading of a section title must be 13-point bold

in all-capitals, aligned to the left with a linespace

exactly at 15-point, hanging indent of 0,7-centimeter

and with an additional spacing of 24-point before (not

applicable to the first title section of the paper) and

12-point after.

3.2.1 Comparison to Reported Data

The thermal display used in prof. Jones' laboratory

(Singhal, 2018, 2015) was composed of a

thermoelectric cooler model TE-127-1.0-2.5, TE

Technology, Inc. 30mm in length and width, attached

to a heat sink. Three monitoring thermistors were

mounted on the system; thermistor #1 on the surface

of the thermal display (used for feedback control)

indicating the thermal patterned display temperature

change, thermistor #2 on the skin at the edge of the

contact area with the display indicating the skin

response to the thermal stimulus, and #3 on the skin

distanced from the contact area indicating the

baseline skin temperature. Similarly, the simulated

temperature was sampled at two locations in the

model; by the TEC and at the TEC-skin contact point.

Figure 4

visually shows the correlation between the

simulated skin response thermal and the reported

empiric skin response to a chosen stimulus.

Modeling Haptic Data Transfer Processes through a Thermal Interface using an Equivalent Electric Circuit Approach

131

Figure 4: Comparison between simulated and reported

signals - (a) Temperatures simulated at skin-display

interface (green, solid) and at the display (blue, dashed),

(b) Temperature measured by thermistor#2 on skin at the

edge of the display (green, solid) and by thermistor #1 on

the display (blue, dashed), in response to a cooling step

stimulus.

3.2.2 Empirical Evaluation

The electric stimulus, i, e. the electric signal that

produced the designated thermal pattern, was

retrieved from the emulator and applied to an

experimental thermal display setup in our laboratory.

The outcoming thermal stimulus was presented to the

thenar eminence, as the examinee placed a hand on it

and waited for a 2 minute thermal adaptation period.

The temperature was measured at three points using

three thermistors. Thermistor # 1 was placed directly

on the display with a layer of aerogel thermally

isolating it from the skin, indicating the thermal

display temperature change, thermistor #2 was placed

directly on the display with no isolating material

making direct contact with the display and with the

skin, and indicating skin temperature at interface

zone, and thermistor #3 was isolated from the display

and in contact with the skin, as shown in

Figure 5

. The

temperatures obtained were recorded and compared

with the corresponding simulation data, see

Figure 6

Figure 5: Scheme of experimental thermo-display and

monitoring thermistors' layout.

The goal of the experimental measurements at this

stage was to prove the proper operation of the thermal

display and the correlation between laboratory

measurement and simulation results. The experiment

did not involve a group of participants. The

researchers themselves were the test subjects. In this

study, one of many examples is demonstrated that

illustrates the correlation between simulation results

and laboratory measurements.

4 DISCUSSION

The example of a cooling step brought herein,

together with similar results from the evaluation

process conducted for other patterns as well, clearly

indicates that the presented simulating model stood

up to the expectations.

The emulator predicts cutaneous response to a

given evoking thermal stimulus, and enables

sampling the temperature at any desired location

without intervening in the heat transfer process. It

also enables deriving corresponding electrical

stimulus or predicting thermal response to a given

electrical stimulus. Finally, it allows for adjustments

to be made throughout testing, in any parameter of the

thermodisplay-skin system, in a simple and

convenient manner.

Observing the simulated thermal response vs. the

reference reported empiric one (Figure 4) shows that

the correlation between them is not perfect. Whereas

for the reported experiment results, the curve

indicating the display temperature change is a well-

shaped symmetrical step as predetermined, and the

curve indicating the skin temperature is somewhat a

distorted step, for the simulated output, it is vice

versa. The reason the reported data is such is due to

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the experiment description defining the display

temperature as the controlling parameter. Another

iteration with the emulator would have produced a

better correlation, but we specifically chose to strive

for the skin temperature curve to be the well-shaped

step, because that is the more relevant parameter for

thermal sensation. The thermal cue is actually not the

displayed temperature change, but rather the change

sensed by the skin.

Figure 6: Comparison between measured and simulated

signals:

(a) Temperatures measured by thermistor #2 at the

skin-display interface (green, solid), by thermistor #1 on the

display with isolation from the skin (blue, dashed) and by

thermistor #3 on the skin with isolation from the display

(brown, doted) all in response to the cooling step stimulus,

(b) Temperatures simulated at skin-display interface (green,

solid), at the display (blue, dashed) and inside the dermis

layer (brown, doted).

The locations of the monitoring thermistors reveal

a difference between the reference reported

experiments and the experiment described herein.

The thermistor monitoring the display temperature

(marked #1) was mounted the same way, i.e. at the

contact zone with isolation from the skin. The

reported thermistor #2 was used to measure the skin

temperature, and was attached to the skin at the edge

of the contact zone. Whereas we chose to place the

second thermistor adjacent to the first one at the

contact zone, only without any isolating material, as

it was meant to monitor the temperature at skin-

display interface. The different approach was mainly

for practical reasons, and may have a slight

quantitative influence on the magnitude of the

temperature change, but should not have any

qualitative impact on the shape of the curve. The

different technical approaches demonstrate part of the

challenges involved in conducting haptic thermal

sensing experiments, many of which may be avoided

by the presented emulator.

The thermal sense is based on the effect a stimulus

has on the sensory system and its sensitivity to the

change that occurred. It is important to emphasize that

the actual effect on the skin is the resultant of the heat

transfer process that occurs between the thermal

display and the skin following a thermal stimulus.

The heat flow depends not only on the stimulus but

also upon the thermal characteristics of the elements

involved in the interaction, namely the display, the

skin, and the thermal resistance of the contact at the

interface between them. The contact resistance is

derived from many parameters other than the

material's thermal resistance, e.g, the contact area,

quality of contact due to surface roughness, pressure

etc. All these parameters are simulated by the

presented model with electrical elements and can

easily be controlled and adjusted, representing

various people, skin conditions, locations on the

body, etc. as well as contact conditions.

When investigating the haptic thermal sense in the

context of data transferring capabilities, the main

issue is the recognizability of the thermal cues.

Although temperature monitoring on the surface of

the skin throughout the heat transfer process, provides

essential data for understanding the process, however,

the ability to distinguish between cues and recognize

them, derives from the temperature changes that the

thermoreceptors are exposed to, combined of course

with the psychophysical aspects that ultimately

determine the thermal sensation. Actually, at the

biochemical level the receptors really respond to the

temporal absolute temperature (by firing action

potentials at frequencies in accordance to the

temperature), however, since the thermo-sensation is

the outcome of the combined warmth and cool

thermoreceptor's transmissions together with the

adaptation phenomena (at temperatures of 30-36°C)

and other neural and cognitive analysis, at the

functional level the sensory system responds to

changes in cutaneous temperature. The temperature

change that occurs inside the dermis layer at the

Modeling Haptic Data Transfer Processes through a Thermal Interface using an Equivalent Electric Circuit Approach

133

depths of the cold and warmth thermoreceptors, is

determined by the rate of heat flow initiated by

stimulus at the skin-display interface. Under normal

steady-state conditions of body core temperature

(approx. 37°C) and skin surface temperature (approx.

32°C), a natural heat flow constantly occurs due to the

temperature gradient, resulting in, and balanced by,

body heat emitting off the skin. Once skin surface is

evoked by the thermal cue, heat flow changes

accordingly. A cooling pulse increases the

temperature drop, hence the rate of heat flow pumped

out of the body through the skin. A warm pulse only

decreases the total heat flow but the local and

temporal response involves a change of direction. To

conclude this remark, the absolute temperature on the

skin surface does not reveal the thermal sensation,

whereas the temperature change at the

thermoreceptors does indicate the sensation. The

presented emulator will allow exploring the

possibility that the heat flow, simulated by electrical

current, can predict the sensation perhaps even with

greater reliability than temperature change.

As mentioned in the description of the

experiment, a third thermistor (marked #3) was

placed at the skin-display contact zone but with

thermal isolation from the display (see Figure 5). This

was in an attempt to capture the skin response without

the display temperature distorting the measurement.

However, in practice, this caused not only the

thermistor to be isolated from the display, but also a

significant area of the skin was isolated from it,

thereby distancing it from the heat flow between the

display and the skin. This distance dramatically

flattened the temperature curve, due to cutaneous

thermal resistance, as shown in Figure 6(a). It is

interesting to notice the resembling behavior to the

simulated temperature curve sampled inside the

dermis layer, indicating the cutaneous response

sensed by the thermoreceptors, as shown in Figure

6(b). In other words, this preliminary finding

insinuates that a distance on the surface of the skin

may perhaps represent the inaccessible depth, for

practical experimental purposes. Another application

could be using the simulated temperature change

sensed by the thermoreceptors, to design thermal

cues. This obviously requires empirically

characterizing criteria for recognizable thermal

changes. In a more general view, this finding is just

an example of the potential contribution the emulator

may have to advance further research.

It shall be noted that the amplitude of the

temperature change by the thermoreceptors, is

approximately 1°C @ rate of change (ROC) of

approximately 0.2°C/sec. This value is substantially

greater than the human threshold, as detailed above

(see introduction), supporting the fact that the thermal

cue was well noticed by experiment participants.

Known design limitation: The temporal

processing of the human thermal sense, has a great

impact on the ability to design thermal displays, but

at this stage is not simulated or in any way reflected

by the presented model. This is especially significant

when cues include both warm and cool stimuli, as

explained hereinafter. The response time to thermal

stimuli was found to differ between cold and warm

stimuli, with a more rapid response to the cold stimuli

(0.3-0.5 sec for ROC greater than 0.1°C/sec) than

warm stimuli (0.5-0.9 sec) (Ho, 2018), (Nam, 2005).

This finding is consistent with the biological structure

and biochemical function of the thermal sensory

system, with warmth thermoreceptors located deeper

in the dermis in comparison to cool thermoreceptors

(0.3 vs. 0.15 mm) hence, heat transfer initiated at the

interface on skin surface is detectable with delay, and

the different types of nerve fibers innervated by the

receptors cause a conduction velocity difference in an

order of magnitude (0.5-2 vs. 3-30 m/sec). Ho et al.

(Ho, 2017) investigated the physical-perceptual

correspondence of dynamic thermal stimuli. They

showed that for warm stimulation, as expected,

subjective sensation always comes after the

corresponding physical event (change in skin

temperature), in respect to onset and to peak. Whereas

for cold stimulation, although the subjective onset

always follows the physical onset (with smaller delay

than the response to warm onset), the sensation of

cooling peak is accelerated to an extent that it can

even precede the physical temperature peak

temperature. They concluded that the sense of cold is

more transient than the sense of warmth, therefore

responds more readily to transient changes (dT/dt). If

necessary, this issue will be addressed in the future.

5 CONCLUSIONS

The presented equivalent circuit-based simulator was

developed in light of scientific knowledge available

to date that is based on decades of research in the

different relevant disciplines. The model simulates

heat transfer processes in thermodisplay-skin

interactions, and provides a generic capability that

can potentially be used to advance R&D in this

unique and promising field of interest. The simulator

has been validated via several tests and experiments.

The main advantages the simulator offers, are the

following: The ability to monitor temperature

changes during heat transfer processes, at any chosen

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location without influencing the very process and

hence the result, including subcutaneous layers. The

ability to conduct extensive tests by readjusting the

parameters according to the variety of skin types, test

conditions, or thermo-display characteristics, and

various stimuli, thereby dramatically reducing the

need for actual experiments. In addition, the ability to

conveniently determine the electrical stimulus

required to produce a designated thermal cue, or

alternatively to predict the cutaneous thermal

response to a given stimulus.

Implementation in Future Work: The general

objective of the research is to develop methods to

effectively use the human thermal sense, as a data

transfer medium – an alternative or complementary

channel for various scenarios in which conventional

channels, vision, hearing, and tactile sensing are not

applicable or not sufficient (e.g. enhance a

communication capability for the deafblind (Korn,

2018), transfer messages in noisy/silent

environments). Future study will focus on

diversifying the variety of thermal cues suitable to

convey information, with two specific goals:

 Create a broad set of recognizable thermal

icons – the research will include evaluating a

variety of pattern-based structured thermal

icons designed in light of the latest reported

findings.

 Evaluate new approaches for advanced

thermal icons - overcoming inherent human

limitations due to special summation and other

sensual phenomena.

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