blood pressure estimation

7/27/2019 Blood Pressure Estimation

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Estimation of Blood Pressure from Thermal

Video

COSC 6397, Spring 2005

Raja S. Kushalnagar

[email protected]

3rd

May, 2005
mailto:[email protected]:[email protected]


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Abstract

This paper presents a method for estimation of blood pressure of a major artery

from thermal video of the skin over the brachial artery. The method depends on a bio-

heat transfer model developed by Dr. Pavlidis that reflects the thermo-physiological

processes the skin region lying over that artery. The bio-heat transfer model enables us to

estimate blood flow speed from the temperature flux observed in the thermal video. From

blood flow speed, we can compute various associated parameters. A method is then

introduced to estimate the continuous arterial blood pressure from blood flow. This

method would enable the monitoring cardiological parameters, including blood pressure,

of patients continuously, safely and non-invasively.

Introduction

Overview of blood pressure and measurement

Blood pressure is the force per unit area the blood exerts against the blood vessel

walls as the heart pumps the blood through the closed cardio-vascular systemic blood

circulation loop in the body. Blood pressure is usually measured in mmHg. In the human

circulatory system, each kind of vessel has its own average pressure - the arterial,

capillary, venous blood pressure, left atrial and right ventricular blood pressure. The

pressure in the systemic blood vessels falls continuously from the aorta until the blood re-

enters the heart in the right atrium, as shown in Figure 1.


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Figure 1: Blood pressure at each segment of the cardiovascular system.

The difference between systolic pressure and diastolic pressure is termed pulse pressure.

It is directly related to stroke volume of the heart and inversely related to heart rate and

peripheral resistance. The pulse pressure is determined by the interaction of the stroke

volume versus the volume and elasticity of the major arteries. For example, when a

person exercises, stroke volume increases to meet increased oxygen demands of the body.

This increase in stroke volume is achieved by increasing systolic pressure more than

diastolic pressure, which causes a net increase in pulse pressure, flow and volume.


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Related Work

While direct measurement of blood pressure is the most accurate method of

measurement, it is invasive and is neither practical nor convenient for routine use. A

more indirect invasive method uses catheters that are directly inserted into an artery, and

connected to a small electronic transducer to give direct arterial pressure measurements.

While this indirect invasive method is now commonly used in research or in emergency

rooms where accurate measurement is essential, it is not practical in most other

situations. However, indirect methods only give an approximation of the actual blood

pressure, and are calibrated against direct measurements in the development stage.

The first documented direct measurement of blood pressure dates back to the

eighteenth century. In 1732, Stephen Hales, an English scientist, directly measured mean

blood pressure in a horse by inserting an open-ended tube directly into the animal's neck.

The blood entered the tube and rose upwards (to a height of 2.5 m) towards the tube

opening until the weight of the column of blood was equal to the pressure in the

circulatory system of the horse [1]. This is the basis of a simple pressure manometer

which is still used for measuring blood pressure. The same method is used to measure

cerebrospinal fluid pressures during a lumbar puncture.

In the eighteenth century, an Italian physiologist, Scipione Riva Rocci, invented

the sphygmomanometer (sphygmo = pulse and manometer = pressure meter hence the

meaning is pulse pressure meter) which enabled a non-invasive measurement of

systolic pressure. A rubber inflatable cuff is placed over the brachial artery and the

pressure in the cuff is raised until the cuff pressure exceeds that of the blood in the artery.


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At this point the artery collapses and no radial pulse can be felt as blood is not able to

flow through the brachial artery. The pressure in the cuff is then slowly released and the

radial pulse reappears. The pressure at which the pulse reappears corresponds to the

systolic pressure as it is the point at which the peak pressure (i.e. the systolic) in the

brachial artery exceeds the occluding pressure in the cuff. Even today, it is widely used

for assessing arterial pressure as it is cheap and accurate, especially when augmented

with electronic readouts, but its biggest disadvantage is that it cannot continuously

measure blood pressure.

For continuous blood pressure measurement, contact monitors use pressure

sensing techniques. The usual method is to place pressure sensors over a major artery,

and vary the force on the artery. Then, the counter-pressure in the artery produces a

signal which is digitized and used to calculate blood pressure parameters.

Non-contact methods are usually continuous imaging methods. Theyre all used

whenever the artery is not accessible to contact-pressure monitoring, due to their relative

technical immaturity with pressure sensing techniques. Examples of arteries not being

accessible to contact-pressure monitoring are cerebral, cervical or other major interior

arteries of interest. The three major imaging methods currently being used or researched

for estimating blood flow and pressure in the body are Near Infrared Spectroscopy,

Ultrasonic Imaging, and Infrared Imaging.

Near Infrared Spectroscopy (NIRS)

NIRS is unique among the three contact-free techniques in that it is a

spectroscopic technique rather than imaging technique, and as such, it cannot gather

dimensional information. Instead, it relies on sensing the flux of oxygenated blood over


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time, and computing inferences from that. Typically, light from two light-emitting diodes

at two different wavelengths [usually 660 nm (red) and 940 nm (infrared)] passes through

the tissue and is sensed by a photodiode. It ignores all absorption in the steady-state tissue

and measures only the absorption in the tissue that is expanded by the pressure pulse.

This expanded volume contains arterial oxygenated blood. There are two

transmitter/sensor geometries. In the transmission mode, the light source and sensor are

on opposite sides of the tissue being measured (such as a finger or ear lobe); the light

passes through the tissue. In the reflective mode, the sensor and light source are on the

same body surface, such as the cerebellum, and the light reflects from the tissue [9].

Figure 2: Pulse Oximetry J. T. B Moyle.

Beer-Lambert law: A=ebc, where A is absorbance, e is the molar absorptivity, b is the

path length of the sample and c is the concentration of absorptant. When we combine this


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with Ficks principle (the relationship between oxygenation and blood flow), we get an

estimate of the total blood flow: MVO2 = CBF x (AO2 VO2), where BF = blood flow

(ml/min), and AO2 VO2 is the arterial-venous oxygen content difference (ml O2/ml

blood).

Ultrasound Imaging (UI)

UI utilizes short wavelength sound waves to image internal structures non-

invasively. Doppler ultrasound exams is usually used for fetal scanning, but can also be

used to scan vascular anatomy as well as blood flow within the vessels see figure 3 for

an example [8].

Figure 3: Human carotid artery at about 2 mm resolution with 80% blockage.

In order to examine a structure at a given depth within the body, the ultrasonic transducer

emits brief pulses of sound and times the reflected pulses. By increasing the time interval

before the receiver can hear the echo, the operator increases the roundtrip distance the

sound has traveled, thereby increasing the depth. In this way, three-dimensional

visualizations can be created. A major virtue of ultrasound imaging is that sound reflected

from a moving structure will have its frequency shifted up or down, according as the


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structure is moving toward or away from the receiver. This phenomenon is called the

Doppler effect. The relative magnitude of the shift is f/f = (r x v)/us, where r is the

unit vector pointing from receiver to moving object, v is its velocity, and us is the

speed of sound. (Thus an object moving toward the receiver has a negative velocity and

so the relative change of pitch is upward.) In particular, the Doppler effect permits the

radiologist to measure the speed of flowing blood, or the speed of moving walls or valves

in the heart [10].

Infrared Imaging (IRI)

IRI is the newest technique to be used, and no substantial body of research has

been developed on it for finding blood flow parameters, especially blood pressure. It

depends on accurate thermoregulatory models. Fortunately, such models were proposed

over 50 years ago, and have been refined progressively since. The first continuum model

was introduced by Pennes to analyze heat transfer in resting human forearm [0]. While

this model cannot model the blood flow of large vessels close to the skin as it does not

account for the heterogeneity of the tissues as well as the position and shape of large

vessels, it worked well for decades. Then for IRI, which needed accurate modeling of

vasculature and thermoregulatory mechanisms, more refined models were needed, and

the bio-heat model was developed to deal with environmental boundary conditions, the

thermal properties of the tissue, and the physical responses of the thermoregulatory

system [11]. This paper presents a general procedure to solve the problem by recovering

missing information on vessel morphology and blood flow fluctuations. As outlined

earlier in the paper, it strives to compute cardio-vascular parameters indirectly by

analyzing the thermal flux over a major artery in the body.


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Proposed Methodology

Overview

We present a simplified hydrodynamic model, and add on cardiovascular variables to

enable it to approximate the human cardiovascular system sufficiently to allow for

computation of the blood pressure from the blood flow, and justify related variables that

are required to be pre-computed and adjusted as needed. We then show the imaging and

computation steps needed to implement this. Ultimately, we compute the blood pressure

from the thermal image sequence as follows:

1. Compute temperature flux from linear sequence on region of interest2. Compute pulse waveform from temperature flux3. Compute blood flow velocity via inverse A&M bio-heat transfer model4. Compute blood pressure gradient from flow velocity5. Compute the blood flow volume from velocity6. Finally, compute the blood pressure from flow volumeThis paper does not cover the first 3 steps, as they are covered in detail in M. Garbey,

A. Merla, and I. Pavlidiss paper: Estimation of Blood Flow Rate and Vessel Location

from Thermal Video [11], and covers in detail the 3rd

through 6th

steps.

Hydrodynamic model

By starting with a simple hydrodynamic model, we hope to get a reasonable

approximation of the behavior of this very complex system and subsequently refine it to

fit the model. Flow through a closed blood circulation loop can be reasonably


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approximated by the classic hydrodynamic model of liquid flowing through a closed

loop. We start by balancing the force causing the flow against the resistance to flow

offered by the blood vessel walls and the internal viscosity of the blood. The relationship

between the blood flow (F), the pressure (P) that causes the flow and resistance (R) to the

flow is represented by Poisueilles law [3], which assumes laminar (smooth) flow:

F = P/R (1)

The pressure P drives the liquid flow around the loop at a specific volume flow rate F.

R = 8l/r4

(2)

By combining (1) and (2), we get

F = ( pressure x radius4)/(8/ x viscosity x length) (3)

Flow is expressed as liters/min., pressure is expressed as mmHg, and resistance is

expressed as peripheral resistance units.

Cardiac Cycle

In order to model blood flow through the closed loop, we have to take into

account the fact that the blood flow is semi-periodic and has different phase lengths.

During each cardiac cycle, or one heartbeat, the heart relaxes for about twice as long as it

contracts, thus spends diastole is about twice as long as systole. As a result, the mean

arterial pressure is not the mathematical average of systolic and diastolic pressure but

rather an approximation of the geometric mean. Mean Arterial Pressure (MAP) can be

calculated as follows:

MAP = Pa = (systolic pressure x (2 x diastolic pressure))/3 (4)


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For a small segment of the brachial artery, we can assume that the flow through is

straight and laminar, and that Pa is the mean pressure approximation for steady flow. We

can then apply (4) to Poisueilles law (1) and derive the following:

Pa = Q x R, (5)

Plugging in (2) into (5), we get:

Pa = Q x 8l/r4

(6)

Where Q is the blood flow rate in the artery, and R is the resistance in the artery. For

either left or right brachial artery, the average radius is about 1.4 +/- 0.09mm for men,

and 1.16mm +/- 0.07 for women; and depth is about 3-4mm from the radial position [7].

However, our assumption of constant viscosity is not strictly true, as the viscosity of

blood actually changes with velocity, since blood is not a uniform fluid. Although arteries

are not straight, uniform pipes, for sufficiently short segments, like in a inch long

segment of the brachial artery, this assumption holds true.

Varying each component enables the body to regulate arterial pressure, and by

extension, blood flow and oxygen supply in order to meet external demands. Q is the

product of heart rate and stroke volume; the sympathetic and parasympathetic systems

control the heart rate and stroke volumes. R changes with age, as arterial elasticity

decreases. TPR fluctuations are much slower than CO fluctuations, and depend mostly on

arterial diameter and resistance; the sympathetic and parasympathetic systems influence

release of chemicals that alter the diameters of blood vessels. TPR also depends on the

viscosity of blood, which in normal humans is about 3.2 centipoise. As blood flow is

proportional to the fourth power of the radius, it is critical to accurately measure the


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radius of the artery in order to get an accurate estimate of total flow. Diseases and

malfunctions can affect any of these variables in unpredictable ways.

Imaging

The common brachial artery is easily identified by its pulsatile walls against the

skin. We select either the left or right brachial artery or use it throughout, for there can be

differences between the left or right brachial arterial dimensions or depth.

Figure 4: Brachial artery (http://www.bartleby.com/107/illus526.html)
http://www.bartleby.com/107/150.html


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For the purposes of this method, we assume that R is constant, and use the

computed average of R from previous studies with the only dependent variable being age.

From a sample image (Figure 5), we can draw an ROI around the artery:

Region of Interest

Figure 5: High Resolution Thermal Image of the wrist

Computation

We preview a sequence of thermal images of a close-up view of the forearm from

an infrared camera. We then draw a region of interest [ROI] around the brachial artery

(right or left). We then apply the inverse of the A&M Bioheat Transfer Model to extract

the mean blood flow along the brachial artery.

From the blood flow, we can compute the blood pressure gradient from Newtons

1st

law: mass x acceleration = force, and apply it to classic hydrodynamics:

density x (transient acceleration + convection acceleration) = -(pressure gradient +

divergence of normal and shear stresses + gravitational force per unit volume) (7)

Acceleration is trivially computed from the blood flow flux as:

v = v(t) v(t+1) (8)


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If we consider the blood vessel as a long smooth-walled tube with laminar flow, by

combining with (8), we can simplify (7) to:

Blood density x v = -pressure gradient (9)

We can then put (9) in (6) to find the mean arterial pressure P a for the artery.

For example, if in the ROI of the artery, we have a blood flow rate of 25 mL/s, a viscosity

of 0.032 poise, artery length of 1cm, radius of 0.5mm, the mean arterial pressure Pa is

then: Pa = Q x R = 25 mL/s x (8 x 0.032 poise x 1cm)/ x (0.05cm)4

= 24.46 mmHg,

given that 1mmHg is 13.6 x 980 dyne-s/cm2.

Future Work

The computations depend upon setting default values for several variables, such

as blood viscosity, total peripheral resistance and arterial diameter. As these variables can

vary with the individual depending on age and environment, as well as between

individuals, this introduces a significant amount of inaccuracy into the computations.

For arterial dimensions, we hope to implement algorithms to extract them, such as a fully

automatic and tracking real-time tracking algorithm by Abolmaesumi et. al. [5]. We hope

to enhance accuracy by computing R fluctuations by using a Total Peripheral Resistance

quantification algorithm developed by Mukkamala, et. al. [2]. We also hope to better

quantify blood viscosity and adjust it dynamically, depending upon blood temperature

and hemocrit at least.

References


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[0] H.H. Pennes, Analysis of Tissue and Arterial Blood Temperature in the Resting

Human Forearm, Journal of Applied Physiology, Vol. 1, pp.93-122,1948.

[1] Hales S., Haemestaticks,London: Innys and Manby, 1733, via

http://www.drbloodpressure.com/05-mesurer.shtml

[2] Mukkamala R, Toska K, Cohen RJ., Noninvasive identification of the total

peripheral resistance baroreflex, Am J Physiol Heart Circ Physiol. 2003

Mar;284(3):H947-59. Epub 2002 Nov 14.

[3] Interactive web program for Poisueilles Law: http://hyperphysics.phy-

astr.gsu.edu/hbase/ppois.html

[4] Biophysics of the Human Cardiovascular System:

http://www.rwc.uc.edu/koehler/biophys/3a.html

[5] P. Abolmaesumi, M.R. Sirouspour, S.E. Salcudean, Real-Time Extraction of Carotid

Artery Contours from Ultrasound Images,

13th IEEE Symposium on Computer-Based Medical Systems (CBMS'00).

[6] Brains blood supply: Visualizing and measuring blood flow to the brain,

http://science.exeter.edu/jekstrom/Br_Bld/BlBr_Tch.pdf

[7] Joannides R, Costentin A, Iacob M, Compagnon P, Lahary A, Thuillez C, Influence

of vascular dimension on gender difference in flow-dependent dilatation of peripheral

conduit arteries, Am J Physiology Heart Circ Physiol. 2002 Apr; 282(4):1262-9

[8] Physics of diagnostic methods,

http://galileo.phys.virginia.edu/classes/304/diagnose.pdf

[9] J. T. B. Moyle, Pulse Oximetry, 2nd Edn, Published by BMJ Books, London.
http://hyperphysics.phy-astr.gsu.edu/hbase/ppois.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/ppois.htmlhttp://www.rwc.uc.edu/koehler/biophys/3a.htmlhttp://science.exeter.edu/jekstrom/Br_Bld/BlBr_Tch.pdfhttp://galileo.phys.virginia.edu/classes/304/diagnose.pdfhttp://galileo.phys.virginia.edu/classes/304/diagnose.pdfhttp://science.exeter.edu/jekstrom/Br_Bld/BlBr_Tch.pdfhttp://www.rwc.uc.edu/koehler/biophys/3a.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/ppois.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/ppois.html


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[10] David F Moore et. al., Arterial Wall Properties and Womersley Flow in Fabry

Disease, BMC Cardiovascular Disorders 2002, 2:1.

[11] M. Garbey, A. Merla, and I. Pavlidis, Estimation of Blood Flow Rate and Vessel

Location from Thermal Video.

[12] Kim-Keen Wee, Blood Pressure Computation, Infrared Imaging Class at

University of Houston, Fall 2004.

[13] Geddes, L.A; Babbs, C.F; Bourland, J.D; Tacker, W.A, Pulse Transit Time as an

indicator of Arterial Blood Pressure Psychophysiology, 1981, Vol 18, No.1 PP71-74

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