MODELING SKIN BLOOD FLOW

A Neuro-physiological Approach

Boris R. M. Kingma, Wim H. Saris

Department of Human Biology, NUTRIM School for Nutrition, Toxicology and Metabolism of Maastricht Universitary

Medical Centre+, Universiteitssingel 50, Maastricht, The Netherlands

Arjan J. H. Frijns, Anton A. van Steenhoven

Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands

Wouter D. van Marken Lichtenbelt

Department of Human Biology, NUTRIM School for Nutrition, Toxicology and Metabolism of Maastricht Universitary

Medical Centre Maastricht, The Netherlands

Keywords: Thermoregulation, Neural pathway simulation.

Abstract: In humans skin blood flow (SBF) plays a major role in body heat loss. Therefore the accuracy of models of

human thermoregulation depends for a great deal on their ability to predict skin blood flow. Most SBF-

models use body temperatures directly for calculation of skin perfusion. However, humans do not sense

temperature directly, yet the information is coded into neuron fire rates. The aim of this study was to

investigate whether SBF can be adequately modelled through simulation of temperature sensitive neurons

and neuro-physiological pathways of excitation and inhibition. Methods: In this study a mathematical model

for SBF was developed based on physiological knowledge on neural thermo-sensitivity and neural

pathways. The model was fitted on human experimental data. Mean squared residuals (MSR) were

estimated through k-fold cross-validation. Results: The model adequately explains the variance of the

measurements (r

=0.91). Furthermore the averaged MSR is close to the natural variation in the

measurements (AMSR=0.087 vs. 

=0l.080) indicating a small bias. Conclusion: In this study we

developed a model for skin perfusion based on physiological evidence on thermo-reception and neural

pathways. Given the highly explained variance this study shows that a neuro-physiological approach is

applicable for modelling skin blood flow in thermoregulation.

1 INTRODUCTION

In order to maintain the core temperature within

narrow limits, the human body balances both heat

gain and heat loss (Hardy and Dubois, 1937).

Conservation of body heat during mild cold

challenges is primarily achieved by vasoconstriction

(i.e. constriction of blood vessels), which decreases

skin blood flow (Kellogg, 2006). Thereby heat

transport from the core to the skin is diminished and

eventually heat loss to the environment is decreased.

Hence, the accuracy of models of human

thermoregulation depends for a great deal on their

ability to predict skin blood flow. In the past various

models predicting skin perfusion responses have

been developed (Parsons, 2003). What these models

have in common is that they require an explicit set-

point; i.e. a reference temperature which is

compared with the actual body temperatures to

generate error signals. The effector response (in this

case vasoconstriction) is assumed to be proportional

to the error signal (Mekjavic and Eiken, 2006).

Although from an engineering perspective the

meaning of a set-point might be clear, application of

the concept in human physiology is still under

debate as it is not clear how this set-point could be

contained (Romanovsky, 2007). Alternatively, it is

hypothesized that thermoregulatory effectors could

also be modelled by using bell-shaped neural

156

Kingma B., Saris W., Frijns A., van Steenhoven A. and van Marken Lichtenbelt W..

MODELING SKIN BLOOD FLOW - A Neuro-physiological Approach.

DOI: 10.5220/0003059001560162

In Proceedings of the International Conference on Fuzzy Computation and 2nd International Conference on Neural Computation (ICNC-2010), pages

156-162

ISBN: 978-989-8425-32-4

 2010 SCITEPRESS (Science and Technology Publications, Lda.)

activation patterns of thermo-sensitive neurons, and

reciprocal cross inhibition (RCI) (Bligh, 2006). An

advantage of this approach is that the model

structure remains true to current neurophysiologic

knowledge on thermoregulation. For instance, the

thermoregulatory system does not sense temperature

directly, yet the information is coded into neuron fire

rates (Nakamura and Morrison, 2008a). Hence skin

blood flow is modelled from first principles instead

of simple regression.

In this study a mathematical model for skin

blood flow during cold exposure was developed

based on physiological data on neural thermo-

sensitivity and neural pathways. The aim of this

study was to investigate whether skin blood flow can

be adequately modelled through simulation of

thermo-sensitive neurons and neuro-physiological

pathways of excitation and inhibition.

2 METHODS

The model for the central control of skin blood flow

was based on thermal reception and neural pathways

that were mostly established by in vivo animal

experiments. To underline the importance of

modelling physiological responses from first

principles we first address the physiological

mechanisms, thereafter a mathematical translation is

described.

2.1 Physiology of Vasoconstriction

Physiological experimental evidence indicates that

skin blood flow is regulated by both reflex (neural)

and local mechanisms (Kellogg, 2006). Neural

control of vasoconstriction is mediated by the

sympathetic nervous system. Under thermoneutral

conditions blood vessels are under a baseline

sympathetic vasoconstrictor tone. During a cold

challenge an increase in sympathetic vasoconstrictor

tone causes blood vessels to constrict (Savage and

Brengelmann, 1996).

The ability of the body to react to a cold

challenge is determined by thermal reception, neural

integration of thermal information and vessel

responsiveness to the increased vasoconstrictor tone.

2.1.1 Thermal Reception

Thermal reception is mediated through temperature

sensitive neurons. The steady state fire rate vs.

temperature has a characteristic bell-shaped form.

In addition to steady state fire rates, temperature

dynamics influence the neuron fire rate such that

cold sensitive neurons will fire more often (also

referred to as bursts) during cooling than during

warming in the same temperature range (Zotterman,

1953, Mekjavic and Eiken, 2006). Likewise a warm-

sensitive neuron will fire more often when heated

rather than cooled. Although there is spatial

variation in the actual fire rate of neurons, the

general response of individual temperature sensitive

neurons has been accepted widely.

Figure 1: Figure after Zotterman (Zotterman, 1953),

steady-state fire rate of cold sensitive neuron (open circle)

and warm-sensitive neuron (closed circle).

2.1.2 Neural Integration

The specific integration of neural information

through neural pathways is still enigmatic. However

Nakamura and Morrison recently identified neural

control of cold defensive responses to skin cooling

in the rat (Nakamura and Morrison, 2008b,

Nakamura and Morrison, 2008a). For the

mathematical model we used their description of

sensory pathways, effector pathways and related

neuronal circuits (see Figure 1). Nakamura and

Morrison showed that in a neutral situation, when

there is virtually no cool input from the skin, cold

defence pathways are inhibited by warm sensitive

neurons in the hypothalamus. Hence, no

vasoconstriction occurs. However, during

environmental cooling, cold sensitive neurons at the

skin are excited and increase their fire rate.

Information of individual neurons is combined in

neurons of the spinal cord where it is transmitted to

the hypothalamus. There the warm sensitive neurons

in the hypothalamus are inhibited, which leads to the

increase of sympathetic adrenergic tone and

ultimately vasoconstriction.

2.2 Modelling of Vasoconstriction

The description of thermal reception and neural

integration was schematized in a diagram (See

Figure 2).

MODELING SKIN BLOOD FLOW - A Neuro-physiological Approach

157

In the left part of the figure local skin

temperatures are transduced into neural coded

information by cold and warm sensitive neurons. In

the spinal cord section information from individual

neurons is combined and transmitted to the

hypothalamus. Warm sensitive neurons in the

hypothalamus transduce core temperature and are

inhibited by cold sensitive neurons from the

periphery, whereas peripheral warm sensitive

neurons perform an excitatory role. Control neurons

responsible for cold defence pathways are inhibited

by the warm sensitive neurons in the hypothalamus.

Figure 2: Schematic of neuronal model for control of skin

blood flow. + and – denote excitatory or inhibitory

pathways;



1 denotes the averaged combined effect of

other inputs than thermoreception on skin blood flow;



and



3 denote weighing of the inhibition of the cold

defense pathway by warm sensitive neurons in the

hypothalamus.

2.2.1 Thermal Reception

The neural input for the model is based on activation

patterns of thermo-sensitive neurons on the skin and

in the core region of the body. Simulation of both

the static and dynamic components of thermo-

sensitive neurons is based on the approach of

Mekjavic and Morrison (Mekjavic and Morrison,

1985). In their study they performed a polynomial fit

of the static fire rate of temperature sensitive

neurons. However, a typographical error seems to

have slipped in their table of coefficients. Here we

corrected the coefficients of the 2

order of the

polynomial for warm receptors as 0.7707699 x 10

and the coefficient of the 6

order of the polynomial

for cold receptors as -0.26343323 x 10

, see Table 1

for the used coefficients.

Equations 1 to 3 describe the simulation of the

neuron fire rate (adjusted from Mekjavic, 1985):

i,t



t

 A

1  e

 j













 P  Ae

 j

 e

 j

































j  0

j 

1



(1)

Here C

i,t

is the neural response at location i and

time t (C for cold sensitive neurons, W for warm

sensitive neurons);



t is the time interval (60 sec); F

is the static neuron fire rate at t=t-1. A

and A are

static gain factors that depend on the difference

static fire rates between two moments in time.





(2)



5.0



(3)

Table 1: Coefficients for the 10

order polynomial

function of static neuron fire rate as given in Mekjavic and

Morrison (1985). Coefficients in bold are corrected values.

Polynomial

order

Cold sensitive

neuron

Warm sensitive

neuron

-0.19005313e6 0.1526647e5

0.85318078e5 -0.5147704e4

-0.16974919e5

0.7707699e3

0.19724509e4 -0.67475955e2

-0.14833377e3 0.38244284e1

0.75486723e1 -0.14664175e0

6 -0.26343323e0

0.38526706e-2

0.62289589e-2 -0.68496075e-4

-0.95563808e-4 0.78889647e-6

0.85949930e-6 -0.53173142e-8

-0.34432887e-8 0.15936041e-10

Figure 3: Example of simulated neuron response using

Equation 1. The peak indicates an excitatory response,

after which the fire rate returns to its static level. The

dynamic component is larger for larger variations in

temperature. The average fire rate during 1 minute was

used as the input fire rate for the model.

K=5.5, K

=3.3 and K

=5.5 are static, inhibitory and

excitatory gain factors respectively. P is a sign

operator indicating an inhibitory or excitatory res

ponse. When cold sensitive neurons are heated P is

negative, when the same neurons are cooled P is

positive; vice versa for warm sensitive neurons. See

Figure 3 for an example of neuron simulation.

ICFC 2010 - International Conference on Fuzzy Computation

158

2.2.2 Neural Integration

As can be seen in Figure 2, neural information from

skin sites was integrated at the spinal neurons. From

then on, neuron response was considered as a neural

drive. The resulting neural drive (N) from cold (C)

and warm (W) sensitive neurons was defined as the

average fire rate over all locations.

Skin,Cold



i,t



loc

(4)

Skin,Warm



i,t



loc

(5)

It should be pointed out that due to the non-linear

characteristics of neuron fire rates, as a function of

temperature and temperature history, the mean skin

temperature was not used to calculate the neural

drive. For example, given two temperatures

=25C and T

=35C, due to the bell-shaped form

of the static neuron fire rate, the neuron fire rate of

the averaged temperature (30C) is not equal to the

averaged neuron fire rates at T

and T

The hypothalamic neural drive was calculated as

the neural response to core temperature. The

response of neurons in the body core is shifted by

2C (Mekjavic and Morrison, 1985). Inhibition of

core neural drive by peripheral cold neurons was

calculated by subtraction of cold peripheral neural

drive from the core neural drive. Likewise,

excitation of core neural drive by peripheral warm

neurons was simulated by addition of warm

peripheral neural drive on the core neural drive.

cold



Core,Warm



Skin,Cold

(6)

warm



Core,Warm



Skin,Warm

(7)

Here H denotes the net hypothalamic neural

drive of either warm or cold pathway and N denotes

the neural drive of neurons given their position and

type.

Weighting factors for the neural drive on cold

sensitive neurons (



2 and



3 in Figure 2) were

estimated by least squares regression using the

following model:

y 







cold





warm

(8)

Here y denotes the perfusion response. The

constant



1 can be interpreted as the averaged

combined effect of other factors on skin blood flow.

2.3 Validation

The model is validated by k-fold cross validation.

This method maximizes the available data by fitting

the model on the average response of n-1 subjects

and calculating the mean squared residuals (MSR)

on the remaining subject.

MSR 

 fx









(9)

Where y

is the measured perfusion at time point

t, f(x

) is the model prediction at t and n is the

number of measurement points in one recording.

The MSR provides a measure of the quality of the

model prediction, irrespective of the length of

measurement. This process is iterated k times (k=n)

where each fold the model is fitted and tested on a

unique subset. Hence k-fold cross validation

provides a measure of the ability of the model to

predict the vasoconstriction response over

individuals whilst maintaining the experimental

conditions constant. The average MSR over k

iterations is used as general measure of the

capability of the model to predict perfusion.

2.4 Experimental Protocol

Eight young adult males (18 to 28 yrs) were

included (characteristics in Table 2). All subjects

were healthy, non-obese and not taking medications.

Subjects were in fastened state and refrained from

caffeinated or alcoholic beverages in the morning

prior to the test. The medical ethical committee of

Maastricht University Medical Centre+ approved the

study. Each subject gave verbal and written

informed consent prior to participation in the study.

All procedures conformed the standards of the

Declaration of Helsinki.

Table 2: Subject characteristics.

Variable

Mean ± SE

Age, yr

23.63 ± 1.05

Height, m

1.81 ± 0.02

Mass, kg

69.05 ± 3.49

BMI, kg/m

21.07 ± 1.07

Mean BP, mmHg

85.00 ± 1.98

Whole body fat, %

15.93 ± 1.60

Leisure Activity Level

3.34± 0.19

2.4.1 Protocol

Subjects arrived at the laboratory at 9:00 a.m. Skin

temperature was measured in 1-minute intervals by

MODELING SKIN BLOOD FLOW - A Neuro-physiological Approach

159

i-buttons (type DS1921H; Maxim/Dallas

Semiconductor Corp., USA) at the 14 positions of

the ISO standard for mean skin temperature

(Parsons, 2003, van Marken Lichtenbelt et al.,

2006). Core temperature was measured in 1-minute

intervals using a telemetric pill (Coretemp,USA).

Whole body skin temperature was controlled by a

water perfused suit (DTI, TUBEsuit) in combination

with a water temperature control unit (Blanketrol II,

Cincinnati Sub-Zero). Skin perfusion was sampled at

8Hz using laser-Doppler flowmetry (Perimed, PF

5000, Sweden) at the ventral side of the hand

between the base and metacarpal of the thumb.

Custom made Peltier elements in the casing of the

probe allowed for local temperature control. Whole

body fat percentage was measured using Dual X-ray

absorptiometry. Leisure activity level was indexed

by a Baecke questionnaire. Subjects were in supine

position and were able to watch TV. Room air

temperature was kept at 24C. A small draft in the

room was allowed to assure sufficient ventilation.

Before starting the measurements subjects

maintained in supine position for 1 hr to become

accustomed to the environment. During this period

the temperature of the water suit was maintained at

33.5C. Measurements were divided in a 15-minute

baseline period where the water temperature of the

suit was kept at 33.5C followed by 15-minutes of

whole body cooling where the temperature control

unit was set to 10C. Short term cooling was

preferred to minimalize the influence of other factors

than acute sympathetic activation of the nervous

system on vasoconstriction (Johnson, 2007). To

avoid interference from local skin perfusion

regulation, local skin was clamped at 33C

throughout the entire experiment (Kingma et al.,

2010).

2.5 Data Handling

Data handling and model development was

performed using Matlab R2007a, figures were

created with Microsoft Excel 2008 for Mac;

statistical tests on subject characteristics were

performed with SPSS16.0 for Mac. Perfusion data

was resampled to 1-minute intervals using a

(lowpass) FIR filter and normalized over the

baseline period. Temperature data were sampled on

a minute base. Peripheral warm and cold neuron fire

rates were simulated in 1-minute intervals for each

measured location and sequentially averaged over

subjects.

3 RESULTS

Estimated coefficients, regression statistics and k-

fold cross validation results of the neural model are

presented in Table 3.

Table 3: Estimated model coefficients, 1: model

constant; 2: integrated pathway of peripheral cold

neurons and hypothalamic warm neurons; 3: integrated

pathway of peripheral warm neurons and hypothalamic

warm neurons. Regression statistics: p-value, r

and

averaged mean squared residuals (MSR).



25.48



-1.44



3.26

-value

0.91

p-value

p<0.001

Averaged MSR

0.087

Averaged variance

0.080

Neural model regression analysis yielded

significant fits on the measured data. Given the high

–values the majority of the measured variance

could be explained by the model (Table 3).

Furthermore the averaged MSR of the k-fold cross

validation is close to the time-averaged variance in

the measurements, indicating that there is a small

bias in the model prediction.

Perfusion measurements and the model

prediction are shown in Figure 4. After t=15 subjects

were cooled and vasoconstriction is observed

immediately. After 10 minutes of cooling perfusion

reached a nadir. The fitted line through the data

points represents the prediction of the neural model.

Figure 4: Measured and fitted perfusion response. After 15

minutes whole body cooling was performed. Error bars

represent SEM.

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4 DISCUSSION

In this study a model for skin blood flow during cold

exposure was developed based on neuro-

physiological concepts. Simulation of thermo-

reception through warm and cold sensitive neurons

was adapted from work by Mekjavic and Morrison

(Mekjavic and Morrison, 1985). Pathways of neural

integration were based on animal experiments by

Nakamura and Morrison (Nakamura and Morrison,

2008a, Nakamura and Morrison, 2008b). Neural

drives that were calculated by the model were fitted

to human experimental data on hand skin perfusion.

Given the high value of explained variance, the

model predicts vascular responses to a mild thermal

cold stimulus adequately. Furthermore, the averaged

MSR values are close to the variance of the

measurements. Therefore, this study shows that an

explicit declaration of a set point is not necessary for

modelling skin perfusion during short term cooling.

4.1 Limitations

The neuron response and neural afferent pathways

are established in small mammals and projected on

human response. Therefore, the modeled pathways

might deviate from the actual pathways in humans.

However, as long as no detailed human studies on

neural pathways and integration are available we

have to rely on these elaborate animal studies.

In general the thermoregulatory response is

subject to both thermal factors and non-thermal

factors like exercise or pathologies like motion-

sickness and fever (Mekjavic and Eiken, 2006). The

experimental set-up was developed to minimize the

influence of other factors than central sympathetic

regulation on vasomotor response. Also, other

factors such as humoral effects, or local regulation

-effect) are now neglected, but are known to

affect vasoconstriction. Therefore no conclusion can

be made on the relative influence of factors that

work either before or after the reciprocal cross-

inhibition.

The authors acknowledge that the current model

coefficients were not validated against data sets with

different experimental conditions. Therefore it is not

possible to conclude that the coefficients hold for

other types of thermal challenges.

In this study we did not incorporate the effect of

differences in spatial thermo-sensitivity. With a

greater dataset it might be possible to assign weights

to the individual branches of thermo-sensitive input

(face, hand, chest, etc.). It is however not possible to

use data of published studies, because usually mean

skin temperatures are presented. Our model instead

requires local skin temperature data.

5 CONCLUSIONS

In summary, this study presents a mathematical

model for skin blood flow during cold exposure

based on thermo-sensitive neurons and neuro-

physiological pathways. The model was fitted to

experimental data where young adult males were

exposed to a short mild cold exposure. The model

explained over 90% of the variance in the

measurements (r

=0.91). Hence, although further

research is warranted, the results of this model based

on first principles of neuro-physiological control of

skin blood flow are promising.

ACKNOWLEDGEMENTS

This study was sponsored by Senter Novem, The

Netherlands.

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