Computer-based system for continuous on-line measurements of tissue blood perfusion

COMPUTER-BASED SYSTEM FOR CONTINUOUS ON-LINE MEASUREMENTS OF TISSUE BLOOD PERFUSION H. Arkin, K.R. Holmes*

and M.M. Chen

Received March 1986; accepted April 1986 ABSTRACT We describe a new system for an almost continuous, on-line measurement of local blood perjiusion in living tisszz The technique uses a therm& method based on measurements of the tissue temperature decay after a short pulse (= 3 s) of local heating. The instrumentation system consists of six small thermistor microprobes, a probe interface unit and a DEC LSIII/23 microcomputer. The system is equipped with six thermistor channels, and the number can be increased withfirther signal Keywords:

blood perfusion, heat transfer

Blood flow,

NOMENCLATURE C

Heat capacity (J kg-’ K-l)

k

Thermal

conductivity

P

Supplied

power (W), (equation

R

Resistance

s

Integration

T

Temperature

t

Time (s)

V

Voltage (V)

‘W

(Wm-’

Tissue density (kgme3)

w

Non-dimensional by equation 7c

< > Key on a monitor

6)

perfusion

rate defined

keyboard

(Figure 3)

Subscripts

variable

(equation

5)

(K)

Tissue perfusion

P K-‘)

(Sz)

(mlt,lmin-’

Defined by equation

ml;‘)

6

;

C onstant reflecting processing

bead material

Y

Parameter

rl

Non-dimensional variable defined by equation 7b

8

Temperature

z

Non-dimensional equation 7a

defined by equation

and

7d

of integration,

rise (K) time, defined by

INTRODUCTION The continuous correlation of local blood flow with heat transfer is essential in physiological studies of thermoregulation’** and in many clinical applications such as hyperthermia3, and cryosurge?. Control of drug distribution by blood is crucial in medical practices and a sufficient supply of blood-borne oxygen and nutrients is Departments of Mechanical Engineering and *Veterinary Biosciences, Bioengineering Faculty, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA Reprints from Professor H. A&n 0 1987 Butterworth & Co (Publishers) Ltd 0141~5425/87/010038-08 $03.00 38

conditioning modules, threby increasing th locations at which blood pejusion can be measured. The results agree favourably with values for tissue bloodflow obtained simultaneously using either the microspheres method or an electromagnetic probe. i%e system has been in use for three years and there is good reason to believe that it can be reliably applied in many situations whre a continuous multichannel monitor of local blood pe$sion is necessary.

J. Biomed. Eng. 1987, Vol. 9, January

B

Bridge supply

b

Bridge balancing

bl

Blood

h

Heater supply (Figure 3)

hp

Heat pulse

k

At T=

0

Bridge output

P

Probe

S

Bridge arm

t

Tissue

311.15

arm

K

Superscripts 0

Unperturbed

conditions

important for effective surgical and medical treatmen@. This paper describes a thermal technique and the related computer-based system for essentially continuous, on-line monitoring of local blood perfusion. HARDWARE Six thermistor probes are connected to a probe interface unit (PIU) which consists of resistance bridges (one for each probe) connected through an A/D converter to a DEC LSI-1 l/23 microcomputer. The temperature transients

Tissue blood pjihm:

measured by the probes are stored and used for the calculation of local blood perfusion. Figure I illustrates the microprobe. In our experience, the microprobe is structurally strong and capable of piercing most tissues with minimal effort. The thermistor bead serves both as a source of heat and as the tissue temperature sensor (Figure 2). The small size of the probes allows the surgical wound to be closed during the course of an experiment, thereby preventing heat exchange, by evaporation or radiation, between the sampled organ and the operating room environment. Even if the skin wound cannot be closed completely, undesirable heat loss can be controlled and held to a minimum by covering the surgical field with a sheet of thin plastic film and suitable insulating materials.

H. Arkin et al.

/ 10:

Rb

I?,= 22K$l y/R,=,,,,

L

to A/D

Converter

Figure 2 Basic thermistor (R,) pulse-heating and temperature sensing electrical circuit. V, and V, are the bridge and heater voltages, respectively

The thermistor microprobe functions as a temperature sensing element when it forms one arm of a resistance bridge (F@re 2). Typically, we use a thermistor bead having a resistance, I$,, of approximately 2000 Sz + 5% at 25°C. A variable bridge balance arm resistance Rt, provides a resolution of + 1 Sz over the range l-2 Ka. This encompasses the temperature range 27-45°C values which are not expected to be exceeded. The two bridge-arm elements (R,) are matched 22000 f 20 0 resistors. The thermistor resistancetemperature relationship can be expressed as

When the bridge is balanced (R,, = Rb) it measures the unperturbed probe temperature TpO,as given by equation (1); a heat pulse changes the local tissue (and probe) temperatures and unbalances the bridge. The change in thermistor bridge output V, for a given change in probe temperature Tp is derived from an analysis of the electrical bridge circuit

R, = Rpk exP[p(l/r,

Vo/T,

- l/Tk)l

(1)

Rpk is the bead resistance evaluated at Tk = 3 Il. 15 K, a value which represents the centre of the working range in living tissue. Temperature calibration against a thermometer traceable to NBS

ALTERNATE STRAIGHT PROBE CONFIGURATION

-WIRE LEAD TH TWISTED SHIELD

EPOXY

STRAIN

standard, establishes probe assembly.

= [ VB&/&

values for Rpk and p for each

+ RJ21

(~R,/~TP)~

(2)

Changes in the probe resistance with respect to deviations of the thermistor temperature from its unperturbed value, are obtained by differentiating equation (1)

(dR,/dT)’ = --P&k (Top )+

exP [fl(l/T,o - l/Tk)l@)

Typically, (dR,,ldT&’ is approximately 40 OK-’ at a tissue temperature q of 37°C. Rearranging equation (2) and substituting the relation given by equation (3), results in an expression for the perturbed probe temperature Tp = Vo (T;)?

RELIEF

I

I

(1 VB Rs/(&

PROBE LENGTH AS DESIRED

+ Rs

I21P RpkeXP[P(l/q

-

l/Tk)l?

GLASS FIBER REINFORCEMENT

THERM STOR (0.25 mm DIA. 1

1

(4) The evaluation of T,, in situ is derived from equation (4) where R,.is equal to the value of Rb observed when the bridge is balanced. SOFTWARE

1 t-

0.3 mm, NOMINALLY

Figure 1

Diagram of the thermistor probe

The software package, TPD, is written in FORTRAN; it consists of several routines for controlling the acquisition and storage of data, and for the on-line calculations of blood perfusion. A flowchart for the TPD software, Figure 3, shows the interrelations

J. Biomed. Eng. 1987, Vol. 9, January

39

Tissue blood pjiuion:

H. Arkim et al.

ia CdlC. Status

and

Filename

a

Q

n

Figure

3

A flowchart

of the TPD software

between routines and files; a brief description of the routines is given in Appendix 1. The flowchart also demonstrates the activation of the decision options necessary to conduct an experiment; each option is addressed by depressing a key on the monitor keyboard. Options include: selection of the measurement time interval (MTI) for the calculation of blood perfusion; specification of new data file names, which are automatically incremented by one after each sampling; and setting the presampling, heating and sam ling times. The calculated values of blood pe r! usion at each thermistor probe site can be displayed on the monitor screen and updated after each evaluation. Another option provides for the continuous (1 samples-‘) measurement and storage of the local tissue temperatures at times when the system is not used for measurement of perfusion rates. The external control of the system during an

40

J. Biomed. Eng. 1987, Vol. 9, January

experiment is contained in a subroutine MENU which prepares and updates the monitor window shown in Figure 4. A specific software package, CALC, is used to perform the on-line calculations of local blood perfusion. The algorithm is based on a comparison between the measured and a model-predicted temperature decay following a heating pulse (typically 3 s duration) delivered by the thermistor bead embedded in the tissue. The theoretical temperature decay at the probe site is obtained from a solution of the bioheat equation for the specified initial and boundary conditions10 and is given by

e,=

fhP

--& 6

(t--s)-1~5

exp [ -w(t--s)]

ds

(5)

Tissue

where

a=-

P(pc)“*5 87+

(6)

8 is the temperature elevation due to a heat pulse, k and w are the local thermal conductivity and blood perfusion, respectively. Applying the relations 7 =

7) = +hp w = wthp o! 7 = ~l.Stff$

(7)

it was shownrO that the solution given by equation (5) can be expressed as an infinite series

(8) In practice, this infinite series is truncated when the absolute value of the nth term is less than 0.1 percent of the first term (n=O). This series equation is solved by subroutine TEMPER, (see Figure 5 and Appendix 2) which has three parameters: TS = r, PS = w, PONE = y. A data acquisition system is used to sample (10 samples s-l) the temperature transient whilst the tissue cools after the cessation of the heat pulse. Tissue conductivity and perfusion rate are then calculated simultaneously so that the sum of the

H. Arkin et al,

squares of deviations between the predicted and measured temperatures is minimized (only the perfusion rate is displayed on the monitor). The flowchart of the calculation process is shown on Figure 5. The iterative algorithm chosen for this nonlinear least sauares fitting has been described by Bevington’ and an examge of the convergence of the fitted curve to the experimental data is shown in Figure 6. The theoretical background of the TPD method, its applications and restrictions have been described elsewhere839*10. EXPERIMENTAL

t/th,,

bloodjqfiiion:

PROTOCOL

At the beginning of an experiment on the anaesthetized subject the microprobes are inserted through a skin incision into the tissue or organ in which blood perfusion is to be measured. Probe insertion is generally made easier if the tissue surface is gently punctured with the point of a syringe needle just before the probe insertion. The skin incision is then closed to minimize heat losses to the surrounding environment and the microprobes are connected to the computer through the PIU. Next, several experimental parameters are either retrieved from stored files or are entered following prompts using the options previously described. These updated parameters include the selection of the names of the raw data files, setting the presampling, heating and sampling durations, identification of each probe, balancing of the bridges and testing the configuration of certain switches on the PIU. The probe heating, temperature sampling and blood perfusion calculations can be carried out manually, or in an automatic mode. If the automatic mode is chosen, the interval between measurements, and number of successive measurements, are defined by the user from prompts on the monitor. Although a typical calculation of blood perfusion takes = 8 s per probe, a refresh time of around 3 min has been found to provide sufficient time for the tissue temperature to recover from the perturbation caused by the heat pulse. This period also allows for the adjustment of experimental parameters and options. In addition to the continuous, on-line monitoring of blood perfusion at the six probe sites, the data collected during each experiment is stored on a flexible disk. The stored data can subsequently be used for off line diagnostics, statistical analysis or plotting. RESULTS

Figure 4 Typical view of the monitor window during experiment. The current values of perfusitm rate at six locations are displayed in the line named ‘Last Perfusion’

The instrument has been extensively used during the last three years in our laboratory. We have measured local blood perfusions in organs such as kidney, spleen, liver and myocardium in a variety of animals. Some of these experiments compared perfusion rates obtained using the TPD method with simultaneous values obtained using the microsphere trapping technique and/or the total organ blood flow measured with an

J. Biomed. Eng. 1987. Vol. 9, January

41

Tissueblood pefi&n:

H. A&n et

al. Define the Measurement Interval on the Decay Curve Store 4Presanple

Data

J

HEAT PULSE +> Store Sample Data

accounting for the PRESAMPLE temperature trend

Define initial values for conductivity (ko) and blood perfusion (w,) T (x2), = 50.0

FCHISO TEMPER

No

Figure

5

A flowchart for on-line measurement

of blood perfusion

electromagnetic flowmeter. Due to space limitations, we present here the results from a single experiment, which will demonstrate the performance and the advantages of the TPD system. In this experiment an electromagnetic (EM) flow probe (Zepeda Instr., Seattle, WA, USA) was placed around the renal artery of an anaesthetized dog. Systemic arterial blood pressure was measured using a Statham-Could P23Id pressure transducer connected to a cannula placed in the femoral

42

J. Biomed. Eng. 1987, Vol. 9, January

artery. At three different times 8, 15 and 25 w spheres was injected in a manner previously reported by others, 11g12.Data presented in Figure 7 show that there was a general correlation between the total kidney blood flow measured with the EM probe, and the local cortex blood perfusion measured with the TPD method. Changes in the renal artery flow and local cortex perfusion appear to be moderately correlated with changes occurring in systemic blood pressure. In this experiment, the 15 pm spheres provided better average estimates of the cortex perfusion than did either the 8 or the 25 pm spheres.

Tissue blood pefksion:

k=QSlO, ~~4.355, chi=3.82e-5

-.-l1-21 ----lt=5;

OOOI”

8 4

H. Arkin et al.

k=O.500, p=4.?64*

I

5

chi=8.53e-6

I

I

I

6

7

8

I 9

b 6

5

0

Time ;sec)

Time (set) Figure 6 a, Typical iterative convergence of the fitted curve to the experimental b, Insert showing detail of convergence (iterations 1 and 2) and the final solution

data during the least squares (iteration 5)

TPD VS EM PROBE & MICROSPHERES BHTW 4-10 Set August 2, 1985 n=Kid 3 X=Total RBF o=Kid 1 O=Kid 4 i-=Blood Press. O=Kid 2

fitting

process.

MTI

I ,

“0. 0 ,-

I

20.

0

TIME

40.

0

(minutes)

60.

0

80.

0

Figure 7 Local kidney cortex perfusion measured at four sites (Kid) in an anaesthetized dog, using the TPD method (open symbols) and the microsphere (8, 15, and 25 p diameter) method (solid symbols). T0ta.l kidney blood flow (RBF, ml min-’ g-‘) and arterial blood pressure (+) are also shown

J. Biomed. Eng. 1987, Vol. 9, January

43

T&U blood@$Gon:

H. A&n et al.

ACKNOWLEDGEMENTS The authors wish to express their thanks to Mr William Ryan and Dr Walter Bottje for their technical assistance and to Mr Stuart Jacobson for his computer programming effort. The skillful typing and graphic artwork of the Publication Office, Department of Mechanical and Industrial Engineering, is gratefully acknowledged. The research described in this paper was supported in part by NIH-NHLBI Grant HL27011.

CALC *

A package for the calculation of local tissue blood perfusion. Subroutine LINFIT uses the presample data for calculation of parameters to compensate for possible significant variations in the reference temperature during the heating and sampling period. Subroutine CURFIT performs non-linear curve fitting, using an algorithm suggested in reference 7. The current 2 value is calculated by subroutine FCHISQ while the theoretical tern erature decay is calculated by su 1 routine TEMPER (see text) and Appendix 2

CH78

Sets up calibration coefficients for two channels used for measurement of blood pressure or for measurement of additional temperatures, with auxiliary, external instrumentation

FILER

Stores the raw data in file AAAXXX.DAT

MENU

Refreshes

OPTION

Enables execution of certain options in the system operation e.g. change of the raw data file name, the window file name, (see Figure 3)

PARAM’

Stores current data displayed on the screen at the end of an experiment (STORE) in file PARAMS; reads the stored data to the program memory at the beginning of an experiment (RESTORE) from file PARAMS

PROBE

Reads from file PROBEXXX previously stored calibration parameters (R+ p in equation 3) for each probe used during an experiment

SAMPLE

Manipulates the duration of presamplin , pulse heating and sampling o f the temperatures. If the calculation option is chosen, the perfusion rates are calculated by calling CALC

SUBS”

Manages the cursor monitor position (CURSOR); screen change (refreshment) (CLAREA); and character presentation (TTYIN)

TEST

Tests configuration of various switches on the probe interface unit (PIU)

WINDOW

Stores sampled temperatures (1 sample s-i) for all the channels, in a file WINXXX.DAT

REFERENCES Brengleman, G.L. Circulatory adjustments to exercise and heat stress. Ann. Rev. Physiol. 1983, 45, 191-212 Rowell, L.B. Cardiovascular aspects of human thermoregulation. Circ. Rex 1983, 52, 367-379 Thermal Characteristics of Tumors: ApPlications in Detection and Treatment (Eds R.K. Jain, P.M. Cullins), New York Academy

4

5

6

7

8

of Sciences, 1980, 335 Trezek, G.J. Thermal analysis for cryosurgery. In: Heat Transfer in Medicine and Biology (Eds A. Shitzer and R.C. Eberhart), Vol. 2, Plenum Press, New York, NY, USA, 1985, 239-255 Heat Transfer in Medicine and Biology (Eds A. Shitzer and R.C. Eberhart), Vol. 2, Plenum Press, New York, NY, USA, 1985 Seylaz, J., Pimard, E., Dittmar, A. and Birer, A. Measurement of blood flows, tissue PO, and tissue PCO, continuously and simultaneously in the same structure of the brain. Med. Biol Eng. Comput. 1979, 17, 19-24 Bevington, P.R. Data Reduction and Error Analysis for tti Physical Sciences, McGraw-Hill, New York, NY, USA, 1969, 235-240 Holmes, K.R. and Chen, M.M. Local tissue heating: microprobe pulse-decay technique for heat transfer parameter evaluation. In: Measurement of Blood Flow and Local Tissue Energy Production by Therm& Methods, Evaluation Methodology. (W. Muller-Schauenburg, et al.), Thieme-

9

10

11

12

Stratton Inc., New York, NY USA, 1983, 50-56 Arkin, H., Holmes, K.R. and Chen, M.M. A sensitivity analysis of the thermal pulse decay method for measurement of local tissue conductivity and blood perfusion. J. Biomech. Eng. 1986, 108, 54-58 Arkin, H., Holmes, K.R., Chen, M.M. and Bottje, W.G. Thermal pulse decay method for simultaneous measurement of local thermal conductivity and blood perfusion: a theoretical analysis.f. BWm& Eng. 1986, 108, 208-214 Casellas, D. and Mimran, A. Measurement of cardiac output and its distribution in rats under various sodium intakes, using 15 and 10 micron spheres. Cardiovas. Res. 1977, 14, 577-581 Fan, F.C., Schuessler, G.B., Chen, R.Y.Z. and Chien, S. Determinations of blood flow and shunting of 9 and 15 pm spheres in regional beds. Am. J. Physiol. 1979, 231, H25-H33

APPENDIX 1 BRIEF

DESCRIPTION

OF SOFTWARE

Subroutines TPD (Main)

44

of

Prompts the different options for performing an experiment

J. Biomed. Eng. 1987, Vol. 9, January

‘Denotes a set of subroutines

the monitor

screen

Tissue blood pe@sion:

APPENDIX 2

Files AAAXXX.DAT

Ouput file, contains the raw data

PROBEXXX

Input file, contains the calibration parameters (Rpkand fi in eqUatiOn 3) for probe number XXX

WINXXX.DAT PARAMS

H. Arkin et al.

Output file, contains sampled temperatures Input/Output file; on completion of the TDP program, contains the data last displayed

LISTING

OF SUBROUTINE FVNCTlON

TEMPER

TEnPER

0001 0002 0003

TSO-TS+l.

0004

TSODr1./8DRT(TSO)

(TS.PS.PONE)

TSDul.tSDRT(TS)

0003

PP.1.

0006

TwONr-0.

0007

TSER-PP*tTWON TREP.TSCS

0008

IF

0009 0010

s

(P8)P.P.S

IF(PS.CT.10.)

S

0013

DO

0013

4

0014

PP.PP*PStN TWON-T”ON+l.

001s

TSO-TSQ*TS

0016

TSOD-TSOO*TSO

0017

TCRX.PP”(TSOD-TSO~IWON

0013

TSER-TSER+TERtl IF~ABS(TCRH)tTREF

0019 0021

4

0033

7

002s

3

.LE.

ZE-4)

COT0

7

0

IF(TSER.GT.O.0)

0026

TSS-TS+0.3 TSSS-TSS*TSS

0027

CT-EIP(-TSS*PS)tTSS*+1.S

0023

PTSrPS+l.StTSS

GOT0

9

PTSS-PTS*PTS

0039 0030

GT3-(PTSS+l.StTSSS)*CT

0031

TSER-CT+3.*CTPt44.

0033

3

CONTINUE COT0

0022

COT0

N-l.30

9

TC,‘,PER-PONE*TSCR

0033

RETURN

0034

END

J. Biomed.

Eng. 1987, Vol. 9, January

45