IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-24, NO. 4, JULY 1977

309

Engineering Models of the Human Thermoregulatory System-A Review CHING-LAT HWANG

AND

Abstract-The literature on engineering models of the human thermoregulatory system is reviewed and classified. The present review is a sequel to "A Review on Mathematical Models of the Human Thermal System." Emphasis in this review is the incorporation of physiological thermoregulation into engineering models. The objective is to present major mathematical models of human thermoregulatory systems which can be used in simulation and design for practicing engineers.

1. INTRODUCTION

MJAN'S physiological functions and his capacity to function in a wide range of environmental conditions have been of interest to scientists and engineers for a long time. It is no wonder that the human thermoregulatory system, being a part of the whole mystery, has been the subject of many studies and, inevitably, many controversies as well. The controversies result, in part, because of the complexity of the human body and its functions, and the simplifications necessary to quantify them for formulating a successful mathematical model. The need or reason for developing such quantitative models comes from the necessity to simulate certain regulatory behaviors and their results to better understand the actual body actions or response. The primary reasons for the complexity of the human thermoregulatory system are the number of variables involved and the feedback in the many control loops. The large number of quantitative models reflects the various approaches to study and understand this complex system. The bulk of the work in the field of physiology of thermoregulation has been reviewed elsewhere. A series of excellent reviews by Hardy [16], Downey, Phil, and Darling [101, Bligh [4], Hammel [151, Wissler [381 and Wyndham [39] lists more than 1,000 papers and presents comprehensive and critical assessments of the status of work in that field. Physiological and behavioral temperature regulation also has been presented extensively in books and monographs by Hardy [18], Hardy, Gagge, and Stolwijk [19], Nangun [23], Bligh and Moore [6], and Bligh [5]. Mathematical models of the human thermal and/or thermoregulatory system have been reviewed by Fan, Hsu, and Hwang [11], Shitzer [27], Hardy [17], and Mitchell, Atkins, and Wyndham [22]. The present review is a sequel to "A Review on Mathematical Models of the Human Thermal System" [11]. Emphasis in this review is the incorporation of physiological thermoregulation into mathematical models. The objective is to present major mathematical models of human thermoManuscript received January 26, 1976; revised August 9, 1976. This study was supported by NSF Grant ENG-7303676. The authors are with the Department of Industrial Engineering, Kansas State University, Manhattan, KS 66506.

STEPHAN A. KONZ

regulation systems which can be used in simulation and design for practicing engineers. This review is intended to present an engineer's view of the literature on human thermoregulation. The mathematical models included in this review, after a short summary on a basic servosystem and thermoregulation, are: 1) One-Cylinder Models: a) Gagge model-two node (core and shell) model; b) Wyndham-Atkins model-multilayer model; c) Kawashima-Yamamoto model-three part model: 2) Multisegment Model: a) Stolwijk model. 3) Model with External Thermoregulation System-Webb model. 2. A BASIC SERVOSYSTEM AND THERMOREGULATION Most control engineers are familar with the basic concept of closed-loop control systems (feedback control systems or servosystems). The elements of a basic servosystem can be schematically represented by the closed-loop block diagram as shown in Fig. 1 [21]. Elements of the block diagram are an error-sensing device (error detector), control elements, controlled system, and feedback elements. The human thermoregulatory system can be conformed to the block diagram. A simplified- negative-feedback human thermoregulatory system is in Fig. 2 [281. The body heat capacitance can be subjected to a disturbance from environmental heat or cold or metabolic heat. The disturbance causes a change in the controlled variable (a body temperature or combination of temperatures). The controlled variable is measured by a transducer (thermal receptors) which generates related neural or hormonal information. This information, the feedback, is compared with reference information. The difference between the feedback and the reference, termed the error, is a measure of the effect of the disturbance on the controlled variable. The error activates a control center which provides a control action in such a way as to oppose the effect of the disturbance. In thermoregulation the control actions are means of modifying heat loss, heat production, or heat conservation by sweating, shivering, or vasomotor activity. Block diagrams such as Fig. 2 cope only with short-term exposures to heat, cold, or exercise. Diagrams coping with longer term adaptive changes require at least one extra loop (indicated by dashed lines) as shown in Fig. 3 [291. Figure 4 [20] assigns a logical role of thermal receptors to both the central and the peripheral sensors. The central sensors control the action of the feedback loops, whereas

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, JULY 1977

310

Fig. 1. Basic negative feedback control system with a reference signal [211.

REGULATOR

REGULATED SYSTEM

Fig. 2. Simplified block diagram of human thermoregulation [28]. ENVIRONMENTAL CHANGE

ADAPTIVE

__I CHANGE

i I

IELEMENTS ICOMMAND I Vset |SET L

I |

| ~~~~~~~~~~ADX

REFERENCE

REFERENCET

SIGNAL

OR

POINT




In

u.U.W

Fig. 4. Human thermoregulation for normal short-term control

COTOLIG-

w n

a

F-

~0o jF-

L)

Z

N-

PATN

[201.

CONTROLLED

SYSTEM

I

. . _EITC

I

THET

Fig. 5. A schema for the controlling and controlled systems for the regulation of internal body temperature. ARAS = ascending reticular activating [ 15 1.

312

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, JULY 1977

the peripheral sensors, by virtue of their direct contact with the environment, serve an anticipatory (early warning) function. Furthermore, it is logical for the amount of compensation initiated by the feedforward loop to be proportional to the rate at which environmental temperature is changing. Accordingly, the motivating potential for feedforward controllers (designated as "II" in Fig. 4, a signal flow diagram) has been stated in terms of the magnitude of the time derivative of skin temperature. The total signal strength would be a summation of some combination of the individual derivatives and the areas of skin exposed. The role of the central temperature-sensitive structures in human thermoregulation has been intensively studied by many investigators. Hammel [151 presents a comprehensive review of this work. A schema for the controlling and controlled systems for the regulation of internal body temperature is illustrated by Hammel in Fig. 5. There is controversy among physiologists about the role of the temperature receptors in the hypothalamus, in the skin and subcutaneous areas, and the other less well-defined regions of the body, in the regulation of the rates of sweating and of heat conductance to the skin when man is exposed to heat. At the one extreme, Benzinger et al. [3] claim that these temperature regulatory mechanisms are controlled solely by the temperature of the receptors in the hypothalamus (as indicated by the temperature in the ear hole). At the other extreme are Randall et al. [25], Van Beaumont and Bullard [32] and Bullard et al. [7], who see a sole role for the temperature of the skin in temperature regulation in man. An intermediate position is taken by Hardy and Wyndham. Hardy [161 considers that temperature receptors in both the hypothalamus and the skin and other regions of the body participate in thermoregulation, but that the exact proportions for the effects of peripheral and central receptors could not be evaluated at that time [7]. Wyndham [40] showed that the temperatures of both peripheral and central receptors play a role in temperature regulation in man but that the role of the temperature of the central receptors is more important. Stolwijk and Hardy [29] support Wyndham's conclusion that the temperature receptors in the hypothalamus are about four times as important as the receptors in the skin to an increase in temperature in their effect upon the rates of sweating and of heat conductance.

the knowledge of the physiological heat regulation as it applies to comfort, temperature sensation, and health. The model considers the role of the temperature receptors in the hypothalamus to be accomplished primarily by the mean skin temperature and a central core temperature; the latter may be the rectal or the esophageal temperature. In Gagge's simplified model, the human body is considered to be a single cylinder with two concentric layers; see Fig. 6. The inner layer is the central core and the outer layer is the skin shell. Heat exchange between the human thermal system and the environment continuously takes place at the skin surface. Heat production continuously occurs inside the body by various biochemical actions or by exercise. Heat generated inside the body is transferred by convection to the skin surface through blood flow and by conduction in the radial direction. From the skin, heat is transferred to the environment by convection, conduction, radiation, and evaporation of sweat. Heat in excess of that which can be dissipated is stored in the tissue, resulting in a rise of body temperature. There are seven independent environmental variables in the model: 1) metabolic rate, 2) work accomplished, 3) the combined heat transfer coefficient for radiation and convection, 4) the conductive heat transfer coefficient, 5) the insulation of clothing used, 6) the dry bulb temperature of the ambient air, and 7) the vapor pressure of the ambient air as measured by relative humidity, wet bulb temperature, or dew point temperature. The principal physiological factors predicted by the model are mean skin temperature, core temperature, total evaporative heat loss, and skin blood flow. 1) The Controlled System:. The classic heat balance equation can be written as [1 ]

3. ONE-CYLINDER MODELS Mathematical models based on a simplified one-cylinder configuration of the human body will be reviewed in this section. They are Gagge's two-node (core and shell) model, Wyndham and Atkins' multilayer model, and Kawashima and Yamamoto's three-part model.

In a thermal equilibrium condition, S (or net rate of heat storage) is zero. Metabolic rate M is proportional to the rate of oxygen (02) consumption, which may be measured directly. W = 0 for most tasks. For bicycle pedalling it is about 20%; that is, 80% of M stays in the body as heat and 20% of M becomes external work. The total evaporative heat loss E is divided into three parts: heat of vaporized moisture from the lungs during respiration, Eres; heat of vaporized water diffusing through the skin layer, Ediff; and heat of vaporized sweat necessary for the regulation of body temperature, Ersw. The sum, Eres + Ediff, is known as the insensible evaporative heat loss from the body while the component Ersw is the sensible loss.

A. Gagge Model The Gagge model [12], written in Fortran, includes the most recent concepts of the regulation of body temperature during rest and exercise and during transient and steady states. A forerunner of the Gagge model was the one proposed by Gagge, Stolwijk, and Nishi [13]. Their model was developed to determine an environmental temperature scale, based on

S=M- W-E±R±C

(1)

where S = rate of heating (+) or cooling (-) of the body, W; M = net rate of total metabolic heat production, W; W = net rate of work accomplished, W; E = rate of total evaporative heat loss, W; R = rate of heat gained (+) or lost (-) by radiation, W; C = rate of heat gained (+) or lost (-) by convection, W.

313

HWANG AND KONZ: ENGINEERING MODELS OF HUMAN THERMOREGULATORY SYSTEM THERMAL

SENSES

COMFORT

\ IN WARMTH

SKIN WETTEDNESS

XFp rswPCI

CLOTHING

INSULATI ON THE PHYSICAL ENVIRONMENT

To Tdew(or rh, Twet), MRT, AIR MOVEMENT, Clo.

Fig. 6. A concentric shell model of man and his environment [ 1 , 131.

The total rate of heat storage is

(2)

S =Ssk + Scr

The rate of change in skin (shell) temperature, Tsk, and central core temperature, T are given by

where

Tsk

=SskAICsk

Ssk = rate of skin shell heat storage, W/m2; Scr = rate of core storage, W/m2. The net heat flow to and from the skin shell is given by

Tcr

ScrA/Ccr

= DuBois surface area, m2; CSk = total thermal capacity of the skin shell, W(h)/0C; Ccr = total thermal capacity of the core, W(h)10C.

(3)

Kmin = minimum heat conductance of skin tissue,

Tcr

Tsk

Cbl

Vbl

DEsk

W/(m2 . 0C); = temperature of central core, = temperature of skin shell, 0C; = specific heat of blood, W(h)/(kg *

0C;

= rate of skin = evaporative

W/m2 .

°C);

blood flow, £/(h mn2); heat loss from the skin surface,

Scr = (M- Eres - W) - Kmin (Tcr - Tsk) CbI Vbl (Tcr

In the above equations the cooling and warming is considered as Newtonian for the core and shell. The core and shell are assumed uniform at temperature Tcr and Tsk, respectively. If the skin and core temperatures are at 34.10C and 36.60C, respectively, on initial exposure to an environment, then the values of Tsk and Tcr at any time are given by ~~~~Tsk=34l+f

Tskdt

(7)

t

The net heat flow to and from the core is given by -

(6)

A

-

where

(5)

where

Ssk = Kmin (Tcr Tsk) + Cbl VbI (Tcr -Tsk) -Esk - (R + C)

0C/h 0C/h

-

Tsk).

Tcr 36.6 =

+

Tcr

dt.

(8)

2) The Controlling System: As mentioned above, the Gagge (4) model assumes that the temperature signals from the skin shell

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, JULY 1977

314

and the central core are given by

(9)

sk = Tsk - 34.1

Icr = Tcr - 36.6.

Gagge's two-node model is one of the simplest models in the current literature and its use is limited for exposure times shorter than an hour. However, it does include all of the important parameters, coefficients, and controls for man and his environment necessary to predict the quasi-equilibrium status for the whole body and the probable values of the three principal parameters related to the judgement of comfort and thermal sensation-skin and core temperature and skin wettedness.

(10) The values 34.1 and 36.6 have been observed as the mean temperature of the skin and core when there is minimal regulatory effort in maintaining body temperature either by any vascular effort or by sweating. When these temperatures occur simultaneously during rest, the body is in a state of physiological thermal neutrality. B. Wyndham-AtkinsModel When Isk is negative, the skin senses "cold," and positive, The simple mathematical model of Wyndham and Atkins "warmth." Likewise, when Zcr is negative, the core senses [2, 41, 42], for which an analog computer was used to solve "cold," and positive, "warmth." A "cold" signal from the the equation describing the several highly nonlinear control skin primarily governs "vasoconstriction" in the vascular bed characteristics, gives good agreement between a computer of the skin and thus reduces the blood flow from core to skin. prediction (a model simulation) and an actual experimental A "warm" signal from the skin governs sweating. A warm result. signal from the core will cause dilation in the vascular bed Figure 7 illustrates the relatively simple physical model, and evoke sweating. The corresponding cold signal from the from which the mathematical model was constructed. The core will cause vasoconstriction but not as rapidly or effec- body is considered to consist of a single cylinder divided into tively as one from the skin. four concentric sections (the core, the muscles, the deep skin The skin blood flow, Vbl, at any time is given by and fatty tissue, and the outer skin). The core includes the (1 1) skeleton and all organs with the exception of those associated Vbl = (6.3 + 75Zcr)/(l - O.SZsk), V/(h * i2). the circulatory system. The muscles form a This equation is based on a multicompartment model of directly with thick around the core. Heat generated in the fairly layer Stolwijk and Hardy [29], who estimated for a cold Zsk that, muscles during body exercise is transferred to the deep skin for each degree centimeter drop, skin blood flow will enand tissue by vascular convection and by conduction. The counter a proportional increase in resistance. For the hands and feet alone, this resistance factor may be twice as great outer skin is a very thin layer with negligible blood flow. with each degree drop; for the head, vasoconstriction may be Heat transfer to the surface through the skin is limited ennegligible. For the core, each degree centimeter rise will cause tirely to direct conduction. For each layer the tissue and skin are assumed to be homogeneous, so that the thermal an increase in skin blood flow of 75 Q/(h mi2) above a normal the rate of metabolic heat production, and the conductivity, skin blood flow of 6.3 Q/(h iM2 ), a value which occurs at rest of rate heat absorption by the blood stream are uniform. during thermal neutrality. When Icr represents a cold signal, Direct conduction in and between these zones is assumed to that is, Tcr < 36.6, and/or when Isk represents a warm signal, in the radial direction. The circulation of blood has be only that is, Tsk > 34.1, the numerical value of Z in either case is the very important task of conveying heat by convection considered as zero. from one portion of the body to another. All arterial blood The rate of sweat production is written as is assumed to have the same temperature, there being no heat (12) exchange between main arteries and adjacent tissue or counter mrsw = 250 Zcr + 10(Zcr) (ask). heat exchange between main arteries and veins. Heat exchange The regulatory sweating, m rsw, in g/(h mi2) at the skin occurs only in a distributed nature from the smaller capillaries surface, necessary for temperature regulation by evaporation, within each zone. Perfect heat exchange is assumed; that is, is activated both by the core signal ,cr and by the product the temperature of the venous blood leaving an area will be (ask) (Ycr) The first constant is from Saltin et al. [261, who equal to the temperature of the tissue in that area. observed that each degree change in core temperature above The control center is shown separately in Fig. 7. Reference 36.60C during exercise caused an average increase in sweating temperature receptors exist in three places-near the skin secretion of 250 g/(h C m2). The second constant is surface, within the spinal cord, and within the hypothalamus. from Stolwijk and Hardy [29], who have shown that the The latter is separated from the bulk of the core, but it has a sweat drive during rest has the factor 100 g/(h -C2 _M2), good blood supply. Internal reference temperature is assumed representing the dual effect of a gain controller with an equal to the arterial blood temperature. The deviation from output described by the product (cr) (ask). reference temperatures initiates or controls the blood flow, The heat loss from regulatory sweating is given by the rate of heat production, and the sweat rate at the surface Ersw = 0.7 Mrsw [2(Tsk 34:1)'3] (13) of the skin. 1) Mathematical Model of Heat Flow: Radial heat flow is where 0.7 is the latent heat of sweat in W(h)/g. The 2-to- expressed by an equation a-power term is from Bullard et al. [8], who showed 1 a aT p aT h that skin temperature can modify locally the production - -_ =1r (14) r ar-~ ar k at k of sweat. Stolwijk [28] later modified equation (13). -

-

-

r

HWANG AND KONZ: ENGINEERING MODELS OF HUMAN THERMOREGULATORY SYSTEM

315

where Mn = rate of blood flow in a unit volume of tissue, m3 blood/(m3 tissue s); = Cb thermal capacitance of blood per unit volume, -

T, Tn

cal/(0C m3 blood);

= temperature of blood entering capillary bed (assumed to be equal to arterial blood temperature), 0C; = tissue temperature (assumed to be equal to venous tem-

perature), 0C. The blood will gain heat in the muscle and core and lose heat in the skin. At steady state, if heat loss by respiration is neglected, the net heat exchange is zero, that is lhb =O. During transient conditions the change in heat storage of the

blood must be taken into account as follows: Tc I2hb = 2Mn Cb (TC - Tn) = Chl ~~~~~~dt Fig. 7. A simple physical model of heat flow and control in the human body [2] .

where h = rate of heat production, cal/(s m3 k = conductivity, cal/(s - m C); r = radial coordinate, m; T = temperature, 0C; ca = specific heat of tissue, cal/(g - C); p = density of tissue, g/m3.

C

{Kn+1/2 (Tn+1

-

Tn) - Kn-112 (Tn - Tn-l)}

+ Hn

(15)

Cn

C = total thermal capacitance of each step, cal/°C; H = total rate of heat production in each step, cal/s; K = thermal conductance of step, cal/(s °C). -

The rate of heat production per unit volume h is the net heat gain by metabolism, hm, plus heat exchange with the blood capillaries, hb. That is

(16)

The rate of heat exchange with the blood may be represented by hb

=MnCb(Tc- Tn)

AR = radiation area, m2;

AC = convection area, m2 TS = skin temperature, °C; Ta = air temperature, °C; TR = mean radiant temperature of surroundings, 0C;

V = air velocity, m/s; Pa = air pressure, mmHg; PA = saturated water vapor pressure at air temperature, mmHg; = saturated water vapor pressure at skin temperature,

mmHg.

where

h=hm + hb*

(20) (21)

A = body area, m

Equation (14) is solved by the finite difference technique, where the cylinder is divided into a number of finite steps and an ordinary differential equation is allocated to each step. The difference equation to step n is given by

d-t

where Chl (cal/(0C * m3 blood)) is the thermal capacitance of the blood, including that in the heart-lungs. The equations for heat loss from the body are Radiation: q, [kcal/hJ = 5.58 (T7S - TR) AR (19)

Convection: q, [kcal/h] = 6.23 (PJ/760)o 6 V0.6 * (Ts - Ta)Ac Evaporation: qe [kcal/hJ = 1.84AV-37 (PS - PA) where

-

(18)

Equation (21) defines the maximum evaporation rate when the skin is saturated. When the skin is not saturated the only term that varies, and which is determined by the control, is PS. The term Ps may be replaced by PsKe, where Ps is the maximum value for a saturated skin and Ke is the evaporation control constant with a value varying between zero and one. 2) The Control of Sweat Rate by Core and Skin Temperature: Figure 8 shows a simple physiological scheme for the control of sweating and heat conductance by the thermal receptors in the hypothalamus and in the skin. The main feature is two integrating centers. One center is concerned with heat loss from the body; facilitation of the effector neurones in this center by incoming impulses from the heat receptors in the hypothalamus, or in the skin, or from both

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, JULY 1977

316

HOT

COLD

HEAT

HOT

COLD

SKIN

RECEPTORS

Fig. 8. Physiological scheme of the control of sweating and heat conductance by the hypothalamus and the skin [42].

areas, leads to sweating and an increase in heat conductance. The other integrating center is concerned with heat conservation; facilitation of the effector neurones in this center results in vasoconstriction in peripheral blood vessels and in shivering. The second feature of the scheme is that facilitation of one of the centers leads to inhibition of the effector neurones in the other center. The experimental findings by Wyndham and Atkins [42] for understanding the characteristics of the temperature regulatory mechanism for the control of sweat rate Sw, (W/h) is

S, = 0.55 (Tr - 36.5) - 0.455 (Tr - 36.35) [1 - exp (-2.7(33 - Ts))] (22) and may be approximated by Sw = (Tr - 36.5) [0.1 + 0.455 exp (0.27(Ts - 33))]. (23) These complex equations represent highly nonlinear control characteristics as a function of core and skin temperature. -

C. Kawashima- Yamamoto Model Wyndham and Atkins [41, 42], in modeling a human body as a single cylinder, divided the cylinder into four concentric sections (the core, the muscles, the deep skin and fatty tissue, and the outer skin). Wissler [36] utilized the functions of the heart and lungs to interconnect all the elements. Stolwijk and Hardy [291 considered the blood compartment to be in the center of all the elements. Kawashima and Yamamoto [23], as shown in Fig. 9, employ all the concepts to depict the complex thermal behavior of the human body. See Table I for symbol definitions.

The human body is divided into three portions; an inner part (Vs), which has a relatively steady temperature, an outer part (V4), which is affected by the environmental temperature, and the circulating system (1I + V2 + V3), which connects the inner and outer parts. The circulating system is: 1) the large blood vessels as heart and aorta (which have small surfaces in comparison with their volumes) lumped together as VI, 2) the small vessels (distributed in various organs and muscles) lumped together as V2, and 3) the cutaneous circulating system lumped together as V3. The volume of the inner part, which does include V1 and V2, is designated as Vet. The volume of the outer part, V4, does not include

V1/, V21, V3, and V15. The heat produced in the inner part (Vat) by metabolism and shivering is transmitted to the outer part (14) directly through the boundary surface (A5) by conduction and indirectly with blood flow (F3). Heat dissipation through the circulating system is carried out so that the heat gained at V2 is transported to V3 and dissipated into the outer part (14) through the surface of V3. The volumetric blood flow into V3 is regulated by a valve VF, which is located between

V2 and V13.

1) Mathematical Model: Since the model was originally presented in Japanese, the development of the mathematical model is presented in some detail here. The heat balance of VI is VICbvb

dtj = CbYbF2T2 + CbebF3T3 -A'h1(T1

-

Ts).

-

CbzYbFITt

(24)

The terms of the right-hand side are, respectively, the heat

HWANG AND KONZ: ENGINEERING MODELS OF HUMAN THERMOREGULATORY SYSTEM

---

NOMENCLATURE

--

A1

1I

A.

to

L-

r-

t

- --

F0=

I

I

_! + I

F1

to

V5,

m

I

,

V5.,

2

Kcal/(Kg-C)

a reference blood flow rate, b y), 1 1 b~'/ volumetric blood flow rate from VV, m

volumetric blood flow rate to V1, m /h

3'

volumetric blood flow rate to V3. a /h 3~~~~~ upper limit of F3, m /h

F3u=

= equivalent heat transfer coefficient at the surface of A1, to

Q=

A.,

Kcal/(h-C-m 2)

metabolic rate, Kcal/h

QL= L Q0

CbybFoT0,

Qr=

upper limit of Q, Kcal/h

lower limit of Q

system [23 .

S

WLW = lower limit of

Q0/(rA4),

W0

carried into V1 by blood flow from V2, into V1 from V3, the heat carried out by blood flow from V1, and the heat dissipation from VI to Vs. These terms expressing heat flow in and out of V1 are equal to the time rate of change of heat storage of Vl expressed on the left-hand side of the equation. Similarly, heat balance equations for V2 through Vs are

SWU

evaporation, Kcal/kg

sweating from skin surface, Kg/(h-m

=

SW

basal metabolic rate, Kcal/h

=

a reference quantity for metabolic rate, Kcal/h

r = latent heat for

Fig. 9. Kawashima-Yamamoto model of human thermoregulation

m3/h

= lower limit of F3,

h5

to

m3/h

3/h

F2= F3=

hI

dt

of V

(Ah )/(C

=

F

V2CblbdT2 = Cbtb F2T

area

Cb = specific heat of blood, Kcal/(Kg-C)

II

-1-I__

I I

heat transfer

C5 = mean specific heat of

I

I

L-- --- 0, the theoretically controllable range is B < Ta < C. However, the real range should be E3 < Ta < E4, since the blood circulation cannot have zero or infinity as its lower or upper limit. When Ta >E4, body temperature will be controlled by blood circulation and evaporation; when Ta E7, the core temperature increases, and the steady-state solutions from eqs. (40) through (43) for F3 =F, Q'= Q, SW = SU, are (

When

environmental

(40) through (43) are

\+ 1

I

0a3

low

ZL

11

(1 aI

At

F= F eqs.

-

(1 +1 +

b)

(55)

+ Ta.

a4

+a5

+

(a3 +a4 +as)F;L a3 (F3L + 1)

(60)

Let QU be the upper limit of Q'. As Ta is lower than El, Ts shall decrease as shown in Fig. 11. When Ta E1, let F3 = F3L, Q'= QU, and Sw = SWL. Then solving eqs. (40) through

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, JULY 1977

320

(43) gives ( a3 + 1) Q1 +

-

T1

=aS (F3 + 1

St, QU I- SWL

a + a3)

QU

a4

T.

(61)

+ Ta

(62)

+

I

T;

(Fa3

F3L

a4

+-3+ a3d a)

TaL

Q'-

T

+ I

+

a4

3

I + a3

(63) U

+QU

SWL + + (64) Ta. a4 a3 + + a3 + a3 as as F3L Figure 11 shows the steady-state condition, where for maintaining the core temperature, Ts, at a constant, T'SS thermoregulation is indicated by the peripheral blood flow, sweating, and shivering. This regulatory mechanism is similar to that presented by Crosbie et al. [9]. The difference, however, is that Crosbie et al. assume that sweating and shivering occur at the initial condition of 280C. When the environmental temperature is greater than 280C, sweating starts; when lower than 280C, shivering. In the present model there exists a region (E3 < TA < E4) where the thermoregulation is controlled by only peripheral blood flow. T

=

4. MULTISEGMENT MODEL A. Stolwijk Model

Stolwijk [281 presented an extensively detailed model Fig. 12. Schematic representation of the six-element man [36]. written in Fortran for a digital computer. The model is a summary and extension of models by Crosbie et al. [9], Stolwijk and colleagues [29], [30], [311, and Wissler [35, as an input to modify sweat rate on the skin, blood flow rate 36, 37]. in the skin layer, and heat production rate (shivering) in the In contrast to the one cylinder of the Gagge model, the muscle layer. Wyndham-Atkins model, and the Kawashima-Yamamoto 1) Controlling System: In the first step for the controller, model, the Stolwijk model divides the body into six segments. the error, which represents the thermoreceptor output, is A hypothetical central blood compartment links the six calculated for each of the 25 compartments segments together via the appropriate blood flows to each (65) ERROR(N) = T(N) - TSET(N) + RATE (N)* F(N). of the segments. The six-segment model was originally proposed by Wissler [35, 36, 37], as shown- in Fig. 12. Each In addition to the difference between the instantaneous segment is sub-divided into 4 layers (core, muscle, fat, and temperature, T(N), and the set-point temperature, TSET(N), skin). Figure 13 shows a block diagram of the head segment. Stolwijk included the RATE(N)* F(N) term for those who Therefore, there are a total of 25 compartments; 25 basic feel there might be a multiplicative effect; RATE(N) is a heat-balance equations form the core of the model. "dynamic sensitivity factor" and F(N) is the rate of change The heat balance is composed of heat generation (metab- of temperature. olism), heat input, and heat output. Metabolism is composed The second step is to check whether the sign of the error is of basal metabolism and activity metabolism. For the three positive or negative, that is, whether the compartment is too interior layers (core, muscle, and fat), heat input and output warm or too cold. If ERROR(N) is positive, it is redefined as is through conduction and convection (blood flow). The outer WARM (N); if negative it is redefined as COLD(N). The model layer (skin) has, in addition, exchange with the environment assumes that thermal receptors are only in the head core and in the skin. The total warm receptor output from the skin, through evaporation, convection, and radiation. The key concept of the controlling system as shown in WARMS, is obtained by summing SKINR(I)* WARM(4*I) for Fig. 2 is to use the temperature of each of these 25 elements the skin compartments of all six segments (I). SKINR(I) is

HWANG AND KONZ: ENGINEERING MODELS OF HUMAN THERMOREGULATORY SYSTEM

321

Fig. 13. Block diagram of the controlled system for one segment: the head [281.

stant and equal to the basal blood flow

the relative area of skin of each segment in determining skin output. The total cold receptor output from the si integrated from a similar summation. The third step calculates the controller commands tc body to sweat on the skin layer (SWEAT), modify skin b flow (DILAT or STRIC), or to shiver in the muscle (CHILL).

BF(N) = BFB(N).

Blood flow in the fat layer also is considered constant. BF(N+2) = BFB(N+2).

(73) Muscle blood flow consists of the basal blood flow plus activity blood flow. One Q/h of blood flow is added for each kilocalorie/hour of heat production due to work or shivering by the muscular compartment in question. That is

SWEAT = CSW * ERROR (1) + SSW * (WARMS - COLDS) + PSW *ERROR(1)*(WARMS-COLDS) DILAT = CDIL*ERROR(I) + SDIL*(WARMS-COLDS)

+ PDIL*WARMS(1)*WARMS (67) STRIC = - CCON *ERROR (1) - SCON * (WARMS - COLDS) + PCON *COLD (1) * COLDS (68) CHILL = -CCHIL*ERROR(1) - SCHIL*(WARMS-COLDS) + PCHIL*ERROR(1)*(WARMS-COLDS). (69)

Each command is the result of a signal from the hypothalamus, ERROR(l), and the skin (WARMS-COLDS). If YOU believe the two signals add, then set PSW, PDIL, PCON and PCHIL = 0. If you believe the two signals multiply, then set SSW, SDIL, SCON, and SCHIL = 0 and CSW, CDIL, CCON, and CCHIL = 0. The fourth step is to translate the command into action. Evaporation for the skin (N+3) is the basal (diffusion) plus sweat for cooling. E(N+3) = EB(N+3) + SKINS(I)*SWEAT*2.**((T(N+3) - TSET(N+3))/4.).

(72)

(70)

The SKINS(I) term considers the varying amount of sweat glands on different parts of the body. The 2-raised-to-a-power term attempts to let the local skin temperature modify the "brain's" sweat command. A final precaution is to calculate the maximum rate of evaporation possible (EMAX). It is a function of environmental vapor pressure and air velocity. Actual sweat and thus evaporation in any skin element is limited to EMAX (in watts).

BF(N+l) =

BFB(N+1) + Q(N+l) - QB(N+1).

(74)

Basal skin blood flow is modified by DILAT or STRIC. BF(N+3) = (BFB(N+3) + SKINV(I)*DILAT)/(l.+SKINC(I)* STRIC)

(75) where SKINV(I) and SKINC(I) represent the relative responsivity of the skin of different segments. Since some regions such as the hand and feet are more responsive than other regions such as the trunk, each of the 6 segments has its own coefficient for dilation (SKINV) and for constriction (SKINC). The third controller command, affecting only the muscle layer, is shivering (CHILL). Metabolic rate in this layer is the sum of basal metabolism, activity metabolism (work), and shivering. WORKM(i) allocates activity metabolism to the 6 segments; CHILM (I) allocates shivering to the 6 segments. Q(N+l) = QB(N+l) + WORKM(I)*WORK + CHILM(I)*CHILL.

(76) Metabolic heat production in the core, Q(N), in the fat, Q(N+2), and in the skin, Q(N+3), remain at the basal level. The detailed Fortran program is given in Stolwijk [28].

5. MODEL WITH EXTERNAL THERMOREGULATORY SYSTEM EMAX(I) = (PSKIN -PAIR)*2.14*(HC(I))*S(I)) (/1) A. Webb Model Water cooling in space suits [24] is a powerful means of where PSKIN and PAIR are the water pressures at the skin surface and in the environment in mmHg; 2.14 * HC(I) is the extracting metabolic heat, so effective that a man can be evaporative heat transfer coefficient (calculated from the overcooled even while working hard. The problem is how to Lewis relationship and convective heat transfer coefficient control the cooling. Manual control by the subject has been in W/(m2 C)); S(I) is the skin surface area in Mi2. used, but man is a poor judge of his own thermal state and Blood flow to the core of each segment is considered con- often reacts too late or too strongly. Automatic control

322

based upon physiological changes is presented by Webb, Troutman, and Annis [33, 34] for astronauts who might work hard during extra-vehicular activity while relying on water cooling to prevent heat accumulation and sweating in space suits. The automatic control has to be accurate and timely despite changing activity levels. Two different automatic controllers have been successfully operated by Webb et al. [33, 34]. The whole purpose of automatic control of cooling was to minimize sweating as the space suit had "no place" to put the sweat. 1) The Cooling Loop: Cooling water is recirculated through a closed loop, as shown in Fig. 14, where the man is the heat source and a thermoelectric (TE) cooler is the sink. The box labeled "automatic controller" represents the V12 controller. The V02 controller may be replaced by the AT controller. Since the thermoelectric cooler has a continuously variable setpoint, it is easy to connect the command signal from the automatic controller to the setpoint mechanism. In a water cooled suit, the cooling is varied either by adjusting flow at a constant water temperature or by adjusting inlet cooling water temperature at a constant flow. After experiments with both methods, Webb et al. picked a constant flow rate of 1.5 Q/min, at which rate a resting subject could be kept comfortable with water temperature in the range of 26 to 320C; yet the flow rate would be sufficient to remove all the metabolic heat a man brought to his surface during hard work. 2) The V;2 Controller: A signal proportional to metabolic rate (M) as an input which would generate the cooling water inlet temperature (Twi) was considered, since the metabolic rate (M) can be indicated from a continuous measurement of oxygen consumption, (VO2). The metabolic rate is quick to change and is quantitatively related to work level making it a good candidate for an input signal to an automatic controller. But the rate of heat removal (H) and inlet cooling water temperature (Twi) change slowly; that is, the time constants for H and Twi are on the order of 10 min. Thus there is a temporal dissociation between heat production (M) and heat dissipation (H). An automatic controller would have to match this temporal pattern if it were to maintain physiologically neutral conditions. The key transfer function which relates change in M to the required change in water inlet temperature, Twi, is expressed by (77) XTow = -Twi + B(Mo - M)

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, JULY 1977

D2-

l

_

4

AUTOMATIC CONTROLLER

PUMPl'TwI

. r COP

I

:~~~~~~~~~~

Fig. 14. Diagram of the water loop with the VO2 controller and a thermoelectric (TE) cooler, a recirculating pump, and a man in the insulated water cooled clothing assembly [34].

Construction details of the controller, its calibration, and other information are given in Webb et al. [33]. 3) The AT Controller: This controller (Fig. 16) uses rate of heat removal (H) as one input and a special skin temperature signal (Tc,) as another. H is derived from matched thermistors which are placed in the inlet and outlet manifolds of the water cooled suit. Their difference, ATw, is the output of a Wheatstone bridge, as two arms of the bridge are those two thermistors. The excitation voltage of the bridge is scaled to represent the flow rate of water (mh) so that any difference in temperature between Twi and T~O represented H directly as in H = rCp (Two -

Twi)

(78)

The skin temperature input is derived from four disk thermistors placed between cooling tubes on the inner surface of the water cooled suit. These four temperatures represent a mean skin temperature with emphasis on the temperature of the skin over active muscle groups. The four locations are: over where the thigh muscle, over the biceps, over the lower abdomen, and over the kidney. The mean of these four temperature r = time constant, min; is the control input, TCSI signals Twi = rate of change in water temperature at the suit inlet, The control concept is as follows: 'C/min; 1) At rest, Tj, TOs, andHhold steady. Twi = instantaneous inlet water temperature, 0C; When work begins, Tcs increases, and H must increase 2) B = gain of the system, degrees change in Twi per W; since Twi is still constant. (or liter of oxygen consumed per minute), 0C/W; The increase in H causes the controller to lower Twi. 3) M = measured metabolic rate, W; The lowering of TWi lowers Ts and increases H still 4) MO = reference metabolic rate, W. further until the system seeks to stabilize; stabilization arises Starting with a signal which is continuously proportional from: a) too low a Tw, (over cooling), causing cutaneous vasoto M, one may generate Tj1 as expressed in eq. (77). Imple- constriction, a reduction in H, and an exaggerated lowering mentation of this equation with a circuit is shown in Fig. 15. of TCS; this causes the controller to allow Twi to rise; or b) if

HWANG AND KONZ: ENGINEERING MODELS OF HUMAN THERMOREGULATORY SYSTEM

323

GAIN ADJUST

Y

+wi *-Twi

B

(Mo-M)

Fig. 15. Analog diagram of the VO2 controller, using the V0 signal from the metabolic rate monitor (MRM) for metabolic rate (M) compared with a reference metabolic rate (M6) as the input. The gain of the summing amplifier is adjustable to match individual suit characteristics; the time constant (T) and the initial condition (IC) of the integrating amplifier are also adjustable [33, 34].

Ho

T, Tll; TWi 7,TWi

HO) {BTCS TCS )

-i;C (HH

Fig. 16. Analog diagram of the AT controller with adjustable proportionality constants, a and j, modifying the two signal inputs, H, for heat removal rate, and T, for the mean of four skin temperatures [33, 34].

T5i goes too high, TCS is too high for the simultaneous value the control of sweat rate by core and skin temperature is of H, which causes the controller to lower T, again. presented to some extent, the feedback controls of vasomotor For the steady state, the controller equation is activity and shivering are not explicitly given. The setpoint or reference temperatures are assumed as Twi = Twio ~ (79) constant in most of the models. Moreover, the same setpoint -Ho)-U (Tcs Tcso) is associated with activating appropriate signals for both cold where the subscript 0 indicated initial condition at rest, and and warm conditions or responses from the feedback elements. However, the Kawasima-Yamamoto model presents a neutral a and f3 are proportionality constants. zone or band, within which the body regulatory functions 6. CONCLUDING REMARKS AND DISCUSSION are not actually activated (a region where the thermoreguAll major models reviewed are for simulation and design lation is controlled by only peripherial blood flow). The purposes for engineers and scientists. Gagge's two-node model Kawasima-Yamamoto model has not yet been developed to is one of the simplest models in the current literature. The include a dynamic regulatory system. They present only an Wyndham-Atkins model demonstrated good agreement initial estimation for the basic constants and parameters used between a computer prediction (a model simulation) and in their model. Extensive validation of the model by experiactual experimental results. However, in their model, although mental data has not yet been carried out.

(HC

324

The Stolwijk model has been substantially updated with extensively modified values for constants and parameters in the model (for example, heat capacitance, thermal conductance, basal metabolic heat production, basal evaporative heat loss, and basal blood flow). This information should be obtained from Dr. Stolwijk of the Pierce Laboratory [441. After critically reviewing these major models and testing some of the models reviewed here (Gagge model and Stolwijk model) and others, for example, the Wissler model in our laboratory [43, 44], the following remarks are in order. Since all models are quantitative approximations of the complex physical system, appropriate values for many constants and parameters used in the models are needed. In all models the main problem has been to find the appropriate parameter values for the different theoretically reasoned empirical formulas. This problem becomes very important when the model is used for different subjects and different physiological and environmental conditions, although the models are supposed to take care of these variations. Experimental verification of models by investigators other than the ones who proposed the model is needed. Each model tends to claim good agreement with an individual set of experimental data (generally limited to a specific environmental condition for a specific standard person). The existing (published) data are inadequate to be used for comparison vs other models. Therefore, the comparative study of models definitely needs a design of experiment, considering all these major models, which will collect data which can be used for all models. That is, use the same set of data for comparative study of the models. In these experiments and analyses of the comparative study, the objective should not be merely to reproduce the results for the models, but to determine which are the predominant forms of control, how they interact with one another, and where their limits exist. Another drawback in the current models, which at first glance may seem trivial but in actuality has a great influence on the simulated results, is that they do not incorporate any sort of limit on the physiological regulatory actions. Human body regulatory actions have physiological limits. Limits become more important when the body is subjected to severe stress, either physiological and/or environmental stresses. The literature on medical physiology, for example, [14], has dealt with this matter extensively. Some of the physiological limits which affect the model output are: cardiac output, blood flows to different segments of the body, total sweating rate, and rise in core or mean body temperature. A further complication to the thermoregulatory functions occurs because many of the regulatory actions are greatly affected by acclimatization. This long term adaptive change, as shown in Fig. 3, has not been considered in the models reviewed. A main purpose of building mathematical models is to predict man's thermal response to any given environment. It is essential to have a thorough understanding of man's thermoregulatory mechanism. There is no doubt that the thermoregulatory system is very complex and it will take much time and effort before general agreement can be reached on how the basic mechanism functions [2]. The mathematical

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, JULY 1977

model of a complex system, such as the human thermoregulation system, develops gradually and is never complete. Development of the model should be a continuous process and be combined with experimental work [29]. Therefore, the authors are currently developing a KSU model to improve the existing models. REFERENCES [1] ASHRAE, "Physiological Principles, Comfort and Health," Chapter 7 of ASHRAE Handbook of Fundamentals ASHRAE, New York, 1972, pp. 119-150. [2] Atkins, A. R. and C. H. Wyndham, "A Study of Temperature Regulation in the Human Body with the Aid of an Analogue Computer," Pflugers Arch, Vol. 37, pp. 104-119 (1969). [3] Benzinger, T. H., C. Kitzinger, and A. W. Pratt, "The Human Thermostat," in Temperature, its Regulation and Control in Science and Industry, Volume Three, Part 3 Biology and Medicine, J. D. Hardy (Editor). Reinhold, New York, 1963, pp. 637-665. [4] Bligh, J., "The Thermosensitivity of the Hypothalamus and Thermoregulation in Mammals," Biol. Rev., Vol. 41, pp. 317367 (1966). [5] Bligh, J., Temperature Regulation in Mammals and other Vertebrates, North-Holland-Amsterdam, American Elsevier-New York, 1973. [6] Bligh, J. and R. E. Moore (Editors), Essays on Temperature Regulation, North-Holland-Amsterdam, American Elsevier-New York, 1972.

[7] Bullard, R. W., M. R. Banerjee, and B. A. MacIntyre, "The Role

[8]

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[11] [12] [131

[14] [151 [16] [17]

[18]

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of Skin in Negative Feedback Regulation of Eccrine Sweating," Int. J. Biometeor, Vol. 11, pp. 93-107 (1967). Bullard, R. W., M. R. Banerjee, F. Chen, R. Elizondo, and B. A. McIntyre, "Skin Temperature and Thermoregulatory Sweating, A Control System Approach," Chapter 40 in Physiological and Behavioral Temperature Regulation, J. D. Hardy et al. (editors), Charles C. Thomas, Springfield, Ill., 1970. Crosbie, R. J., J. D. Hardy, and E. Fessenden, "Electrical Analog Simulation of Temperature Regulation in Man," in J. D. Hardy (Ed.): Temperature, Its Measurement and Control in Science and Industry, Part III, New York, Reinhold, 1963. Ch. 55, pp. 627-635. Downey, J. A., D. Phil, and R. C. Darling, "Thermotherapy and Thermoregulation," International Review of Physical Medicine and Rehabilitation, Vol. 43, pp. 265-276, December 1964. Fan, L. T., F. T. Hsu, and C. L. Hwang, "A Review on Mathematical Models of the Human Thermal System," IEEE Trans. on Bio-Medical Eng., Vol. BME-18, pp. 218-234 (1971). Gagge, A. P., "A Two-Node Model of Human Temperature Regulation in FORTRAN," in Bioastronautics Data Book, J. F. Parker, Jr. and V. R. West (editors), NASA SP-3006, Washington, D.C., 1973, pp. 142-148. Gagge, A. P., J. A. J. Stolwijk, and Y. Nishi, "An Effective Temperature Scale, based on a Simple Model of Human Physiological Regulatory Response," ASHRAE Transactions, part one (1971), pp. 247-262. Guyton, A. C., Text Book of Medical Physiology (4th ed.), W. B. Saunders Co., Philadelphia, Pa. 1971. Hammel, H. T., "Regulation of Internal Body Temperature," Annual Review of Physiology, Vol. 30, pp. 641-710 (1968). Hardy, J. D., "Physiology of Temperature Regulation," Physiological Reviews, Vol. 41, pp. 521-606 (1961). Hardy, J. D., "Models of Temperature Regulation-A Review," in Essays on Temperature Regulation, Bligh, J. and R. E. Moore (editors), North-Holland-Amsterdam, American Elsevier-New York, 1972, pp. 163-186. Hardy, J. D. (editor), Temperature-its Measurement and Control in Science and Industry, Volume Three, Part 3 Biology and Medicine, Reinhold, New York, 1963. Hardy, J. D., A. P. Gagge, and J. A. J. Stolwijk, (editors) Physiological and Behavioral Temperature Regulation, Charles C. Thomas, Springfield, Illinois, 1970. Huckaba, C. E., J. A. Downey, and R. C. Darling, "A Feedforward-Feedback Mechanism for Human Thermoregulation,"

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[27] [28]

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Symposium on Simulation of Physiological Systems, Paper No. 64f, AIChE 62 Annual Meeting, Nov. 16-20, 1969. Mitchell, D., J. W. Snellen, and A. R. Atkins, "Thermoregulation during Fever: Change of Set-Point or Gain," Arch. Ges. Physiol., Vol. 321, p. 293 (1970). Mitchell, D., A. R. Atkins, and C. H. Wyndham, "Mathematical and Physical Models of Thermoregulation," in Essays on Temperature Regulation, Bligh, J. and R. E. Moore (editors), NorthHolland-Amsterdam, American Elsevier-New York, 1972, pp. 37-54. Nangun, J. (editor), Physiological System (in Japanese), NikanIndustrial Press, Tokyo, 1971. Nunneley, S. A., "Water Cooled Garments: A Review," Space Life Sciences, Vol. 2, pp. 335-360 (1970). Randall, W. C., R. 0. Rawson, R. D. McCook, and C. N. Peiss, "Control and Peripheral Factors in Dynamic Thermoregulation," J. Appl. Physiol., Vol. 18, pp. 61-64 (1964). Saltin, B., A. P. Gagge, and J. A. J. Stolwijk, "Body Temperatures and Sweating during Thermal Transients Caused by Exercise,"J. Appl.Physiol., Vol. 28, pp. 318-327 (1970). Shitzer, A., "Mathematical Models of Thermoregulation and Heat Transfer in Mammals," NASA Technical Memorandum, NASA TM X-62,172 (1972). Stolwijk, J. A. J., "Mathematical Model of Thermoregulation," in Physiological and Behavioral Temperature Regulation, edited by J. D. Hardy, A. P. Gagge, and J. A. J. Stolwijk, Charles C. Thomas, Publisher, Springfield, Illinois (1970), Chapter 48, pp. 703-721. Stolwijk, J. A. J., and J. D. Hardy, "Temperature Regulation in Man-A Theoretical Study," Pflugers Archiv, Vol. 291, pp. 129-162 (1966). Stolwijk, J. A. J., B. Saltin, and A. P. Gagge, "Physiological Factors Associated with Sweating during Exercise," J. Aerospace Med., Vol. 39, pp. 1 101-1 105 (1968). Stolwijk, J. A. J., and E. R. Nadel, "Thermoregulation during Positive and Negative Work Exercise," Problems in Temperature Regulation and Exercise, Federation Proceedings, Vol. 32, No. 5, pp. 1607-1613, May 1973. Van Beaumont, W. and R. W. Bullard, "Sweating: Direct In-

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fluence of Skin Temperatures," Science, Vol. 147, pp. 14651467 (1965). Webb, P., J. F. Annis, and S. J. Troutman, "Automatic Control of Water Cooling in Space Suits," NASA Contractor Report, NASA CR-1085, 1968. Webb, P., S. J. Troutman, Jr., and J. F. Annis, "Automatic Cooling in Water Cooled Space Suits," Aerospace Medicine, Vol. 41, pp. 269-277 (1970). Wissler, E. H., "Steady-State Temperature Distribution in Man," J. Appl. Physiol., Vol. 16, pp. 734-740 (1961). Wissler, E. H., "An Analysis of Factors Affecting Temperature Levels in the Nude Human," in Temperature-Its Measurement and Control in Science and Industry, J. D. Hardy, Ed., Vol. 3, part 3, Reinhold, New York, 1963, pp. 603-612. Wissler, E. H., "A Mathematical Model of the Human Thermal System," Chem. Eng. Prog. Symp. Ser., Vol. 62 (1966). Wissler, E. H., "Review of Thermoregulation in the Human," paper presented at 162nd National Meeting of American Chemical Society, Washington, D.C., Sept. 12-17, 1971. Wyndham, C. H., "The Physiology of Exercise under Heat Stress," Ann. Rev. Physiol, Vol. 35, pp. 193-220 (1973). Wyndham, C. H., "The Role of Core and Skin Temperature in Man's Temperature Regulation," J. Appl. Physiol., Vol. 20, pp. 31-36 (1965). Wyndham, C. H., and A. R. Atkins, "An Approach to the Solution of the Human Biothermal Problem with the Aid of an Analogue Computer," in Proc. 3rd Internat. Conf. Med. Electron., London, 1960. Wyndham, C. H., and A. R. Atkins, "A Physiological Scheme and Mathematical Model of Temperature Regulation in Man," P/ligers Arch, Vol. 303, pp. 14-30 (1968). Hsu, F. T., C. L. Hwang, S. A. Konz, and L. T. Fan, "An Integrated Human Thermal System and Its Unsteady-State Simulation," International J. of Biomedical Eng., Vol. 1, pp. 55-78

(1972).

[44] Konz, S. A., C. L. Hwang, B. Dhiman, J. Duncan, and A. Masud,

"An Experimental Validation of Mathematical Simulation of Human Thermoregulation," Comput. Biol. Med., vol. 7, pp. 71-82, 1977.

Angular Dependence of Scattering of Ultrasound from Blood KOPING K. SHUNG, MEMBER, IEEE, RUBENS A. SIGELMANN, MEMBER, IEEE, AND JOHN M. REID, MEMBER,

Abstract-The angular scattering of 5-MHz ultrasonic waves by blood 1500. Experimental and theoretical results agree very well. A discussion on the use of angular scattering for determining the mechanical properties of the erythrocyte is presented. was measured in the range from 60 to

Manuscript received January 3, 1975; revised October 6, 1975, January 6, 1976, and May 17, 1976. This work was supported in part by the National Institutes of Health under Grant GM-16436. K. K. Shung and J. M. Reid were with the Department of Electrical Engineering, University of Washington, Seattle, WA 98122. They are now with the Institute of Applied Physiology and Medicine, Seattle, WA 98122. R. A. Sigelmann is with the Department of Electrical Engineering, University of Washington, Seattle, WA 98122.

IEEE

I. INTRODUCTION

A KNOWLEDGE of the dependence of the ultrasound waves scattered from blood as a function of frequency, concentration, angle, and mechanical properties of blood has long been sought both for the practical design of ultrasonic blood flowmeters and for aid in interpretation of their output. Our effort to characterize the scattering from blood was begun almost ten years ago. It has resulted in a theory which allows the reduction of these experimental results to an apparatusindependent form, allowing the quantitative determination of scattering cross-sections [1], and a number of preliminary experimental results [2] - [4]. This paper presents the results