LOGO

Horkunenko A.B.

Department of medical physics diagnostic and therapeutic equipment

Medical instruments and devices for monitoring of hemodynamic processes

LOGO Doppler effect in acoustics

Doppler effect in acoustics is the change in frequency of a wave (or other periodic event) for an observer moving relative to its source.

LOGO

Doppler effect in acoustics It is commonly heard when a vehicle sounding a siren or horn approaches, passes, and recedes from an observer. The received frequency is higher (compared to the emitted frequency) during the approach, it is identical at the instant of passing by, and it is lower during the recession.

LOGODoppler effect

Doppler effect is used in various fields of human activity to measure the speed of objects at a distance. For example, in medicine by ultrasound measure speed of passage of blood through the vessels.

LOGO

The general formula for calculating frequency waves that are accepted by the receiver due to wave motion of the source

and receiver is:

- observed frequency;- emitted frequency;- is the velocity of the receiver relative to the medium;- is the velocity of the source relative to the medium;- is the velocity of waves in the medium

.0

.0..

gs

prgspr

.pr

.gs

.pr.gs

0

LOGO

In the medical Doppler device in the soft tissues of the body emitted ultrasonic wave, followed by a reception and analysis of the reflected echo from the moving elements of the blood in the blood vessels (mainly erythrocytes).

Doppler fetal monitor

LOGO

0

...

cos2

gsprgs

.. prgs Doppler frequency shift

Subtraction which depends on the velocity of blood flow elements, called the Doppler frequency shift.

LOGO Portable ultrasound device "Minidop" for the acoustic determination of blood flow and research of human heartbeat.

Scope of using: diagnostics in clinical vascular surgery and obstetrics. "Minidop" can be used in hospital and out-patient patients.

LOGO

At the modern Doppler ultrasound devices used B-scan and

Doppler research. The result of such devices is a color image of

blood flow in the vessels of researched tissues. This

particular color corresponds to the flow velocity.

Modern Doppler ultrasound devices

LOGO Examples of modern Doppler ultrasound devices

LOGO In modern medicine Doppler using the following methods:

Color Doppler Continuous Doppler Pulsed wave (PW) Doppler Duplex

LOGO Passage of viscous fluid in biological systems

Movement of liquid media (blood, lymph, interstitial and cellular fluids) in biological systems is important, ensuring normal living conditions of various physiological systems. Problem biophysics is to study the physical properties of liquid media and physical foundations of their movement. The flow of fluids occurs under the action of forces determine the nature of which is also one of the important problems of biophysics.

Liquid environments have some specific properties due to the characteristics of their molecular structure. One of the most important properties is the viscosity of the fluid.

LOGOViscosity of fluid

In the liquid media on the borders of layers moving internal friction forces act. There are many examples of these forces: they are the cause of the pressure drop along the flow of blood in the vessels, they determine the behavior of the fluid in the vessel, rotating, preventing the movement of bodies in fluids and so on.

Experiments show that the friction between layers of fluid moving with different velocities are tangent to the surfaces of these layers (Fig. 1) and designed so as to accelerate the layer moves more slowly, and brake the layer that moves faster.

LOGOShifting tangential stress

y)(yv

y

)( yy v

FFTP

LOGO

Figure. 1. Friction between the layers of liquid.

The fluid in this figure is between two plates, one of which is fixed and the other under the influence of forces applied to it F uniformly moving

at υ (Fig. 1). Effects of shear stress shifting SF causes deformation

displacement, and relative displacement per unit time dydv , called the velocity gradient, is proportional to the applied shear stress:

dy

d

S

F v

(1)

LOGONewton's equation

From equation (1) implies that

dy

dSF

v

(2)

Equation (2), known as Newton's equation describes waking is the internal friction. The proportionality factor in the equation is called the Newtonian viscosity and internal friction force is acting on a unit area of the surface layer in the velocity gradient, which is equal to one.

LOGO

Velocity profile y

y+dy

y

F

xv=0

v+dvdydv

v

v0

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I

liquid

Velocity profile that we see in this case (Fig. 2), due to the fact that between the layers of real fluid flows, are forces of internal friction F, which are proportional to the

square S layers, that touch and velocity gradient dydv

in the direction perpendicular to the direction of fluid flow.

LOGO

Instability curveRatio S

F called shear stress

Quantity

dy

d in rheology called shear rate and

schedule of functional dependence і shown in this slide called instability curve.

τ

τ0

b

а

α

γ

LOGOThe effective viscosity

Movement Newtonian fluid (viscosity which is constant and independent of shear rate) can be described by Newton's law. These liquids include pulmonary gas, water, urine, low fluid schedule is a straight line passing through the origin (figure on the previous slide). Slope of the line to the x-axis is

equal to

and is the only rheological parameters for Newtonian fluids. In analogy with Newtonian fluids for

visco-plastic liquids notion of effective viscosity: ef

LOGO The viscosity of the blood. Index hematocrit Не.

Blood is an example of a complex in its liquid content. It is a suspension formal elements (erythrocytes, leukocytes, platelets) in the aqueous colloidal solution - plasma total protein concentration which is 6.9%. The experiment showed a significant dependence of blood viscosity on its composition, which is not determined by hematocrit (Figure 3 on the next slide), which is the ratio of volume elements formennyh Vf to plasma volume Vpr:

pr

f

V

VHe

(4)

Since the volume element formal mainly accounted for erythrocytes, hematocrit index characterizes the content of red blood cells.

LOGOChanges in blood viscosity by changing the uniforms of the blood (Fig. 3, a)

As shown in Figure shows the dependence )He(fdep , Blood viscosity varies in a very wide range with respect to normal (N). It increases with polycythemia and reduced anemia.

Empirical formulas relating the viscosity index of blood hematocrit:

= 0 (1+ Hе) або = 0 е Не,

where 0 – plasma viscosity, , , – empirical constants whose values depend on the concentration and form of elements.

a) 15

10

5 1

0.5N N 2N

Hematocrit

відн

LOGOChanges in blood viscosity by changing the rate of shear deformation (Fig. 3b)

Investigation of blood viscosity on the rate of deformation of shear (velocity gradient) suggest that the blood is not a Newtonian fluid. For large velocity gradient (for example, in arterial vessels) blood viscosity is close to the viscosity of water, while for small values of strain rate shear viscosity in five or more times the viscosity of water (fig. 3b).

6

4

2 1

б)

1 0.1 10 100 1000 1/c grad V

LOGODiagnostic value of relative viscosity

The value of the relative viscosity of the blood can be used in the diagnosis of diseases (Table 1). Dependence of viscosity on the

velocity gradient dydv due to the ability of erythrocytes to

aggregate formation "coin column" and conglomerates. With increasing velocity gradient columns are destroyed, and the viscosity decreases due to deformation and disaggregation of erythrocytes.

table 1.

Relative viscosity of blood dep result 4,2–6,0 norm < 2,0 anemia > 10,0 politsytymiya

Reducing blood viscosity during its transition from venous to arterial physiologically justified. In this case, significantly reduced myocardial muscle energy expenditure to promote blood along the arterial bed in which the value of velocity shear strain is quite significant.

LOGOBasic equations of fluid motion. The concept of tube current

a) в)б)

Вихрові лінії

Напрямок руху

v1

v2

1S

2Sv1

v2

Figure. 4. Line current at steady state (a) and turbulent current (b), tube current (c).

Movement of liquid media is subject to the same laws of mechanics, and motion of solids and gases. In a continuous medium are the elementary volume of fluid dV (or element mass , - density environment),consider the forces acting on it and write equations of statics (equilibrium) or dynamic. When moving in space each such elementary volume moving along a certain path - line current. Tangent to any point of the line current in the direction of the velocity vector particles at this point. Isolate area closed path S. All current lines that pass through this loop, forming a tube current. Thus, the tube current is a flow of fluid bounded by a line current

LOGO

Stationary and turbulent flow of liquid

Describing the flow of fluid, often use the terms - velocity field and velocity profiles that are in accordance with the value of velocity at all points of space and points of cross-section tube current in a fixed time. If the line current and the velocity field does not change with time, the fluid motion is called stationary.

At steady state current trajectory of the particles remain unchanged. Light particles may change during its motion along the line current, but at each point of the line current is stored in magnitude and direction. If the velocity field and current lines change with time, then the flow is called transient. In this case, the line current during the current disappear and reappear in some cases in the form they resemble a vortex fluid flow is called turbulent or vortex.

LOGOThe equation of continuity jet Consider the steady flow of liquid. Denote by υ the average velocity

of flow of fluid to randomly selected cross-section S tube current. Mass of liquid flowing through the cross section per unit time remains constant because the liquid is broken and compressed under normal conditions, namely

dm/dt = const. Because

dm = Sdl = Sυdt,

from equation (5) we obtain.   For an incompressible fluid the continuity equation ( = const)

gives the relationship between jet planes jet tube and an average

flow rate of fluid:

Sυ = const

or for different sections of the tube current S1υ 1 = S2υ 2

LOGOVolumetric flow rate of liquid

Value

Q = dV/dt = Sυ[m3 / s]

equal to the volume of fluid flowing through a tube power section per unit time is called the volumetric flow rate of fluid. If it remains steady current of constant magnitude. Analogues of this value is in the physiology of blood flow or cardiac output of blood (Hawk). Based on the apparent velocity of fluid flow, minute volume of blood can be calculated as the ratio of stroke volume of blood Vud the period T of the heart, or the product of Vud heart rate

HR = 1 / T

LOGO The tube current

Consider the steady flow of an ideal fluid. Isolate the space tube current (Fig. 5) and consider the power of small volume element of the fluid mass m = V, flowing through the cross section of the tube current for a while.

2h

h

1h

1S 1P

2P 2Sv1

v2

x

Fig. 5 The tube current

LOGOBernoulli equation

Since the fluid is ideal and the work of friction is zero, the total energy of a fluid volume element in this case will remain constant value when moving along the tube current:

E = Ec + + Ect Ep = const, 

where Ek =mυ2/2 - kinetic energ, En = mgh - potential energy, and Ect = РV - internal energy of an ideal fluid. Substituting these expressions in the formula and introducing volumetric energy density w = E/V we obtain the Bernoulli equation, which is the law of conservation of energy for a unit volume of fluid that moves

LOGOThe physical meaning of the Bernoulli equation

 Volumetric energy density w an ideal fluid with its steady current value is constant. Note that the dimension of the volumetric energy density is

[w] = [E]/[V] = J/м3= Н/м2

ie it coincides with the dimension of pressure

[p] = Pa = N/m2.

Therefore hydraulics components volumetric energy density w is called:

υ2/2 - dynamic and gh – hydrostatic Р - static pressure. In this

case, the Bernoulli equation indicates that the total pressure is constant

along the tube current at steady flow of an ideal fluid.

LOGOPump function of the heart

When the blood moves through the vascular tube, the value of volumetric energy density changes abruptly at the transition from venous to arterial. This change is due to the activity of the heart as a pump. Pumping function of the heart is the change in volumetric energy density of blood. Cardiac pump function can be characterized by the difference of volumetric energy density at the inlet and outlet of the heart, in the largest

wc = wart – wven.

LOGO The equations of motion and fluid balance

Isolate the liquid elementary volume V cylindrical cross-section S and up х (fig. 7).

According to Newton's second law: i

idt

mdF

)( v,

or for bulk power:

i iii V

dt

dfF /

)( v. (11)

Figure. 7. The forces acting on an element of fluid volume.

L

P1P2

FTP

F(x) F(x+dx)

dxR

r

x

mgS v

LOGO The flow of Newtonian fluid in a horizontal tube

Figure. 7. The forces acting on an element of volume of the liquid.L

P1P2

FTP

F(x) F(x+dx)

dxR

r

x

mgS v

The flow of viscous fluids in cylindrical tubes which is of special interest for medicine. Vascular system can be represented by a grid of cylindrical labor Bock different diameters, linear and volumetric flow rate of fluid which depends not only on the properties of fluids, but also on the geometric dimensions of the vessels. Define the linear and volumetric flow rate for steady flow of a viscous fluid through a vessel radius R, length L, with a pressure drop at its ends P1 - P2 (Fig. 7).

LOGO Hydraulic resistance

Equation ( 17), which connects three-dimensional velocity liquids

ful pressure difference at the ends of the vessel, has a form similar to Ohm's law :

Q = (P1 – P2)/W, (19)

because the value of W = 8L/(R4) called hydraulic opposition rum Graphics Communications (Q;P) we call diagram expenditures , and pressure." They look for a Newtonian fluid and fluid viscosity which depends on the velocity gradient (in for example , for blood) are shown in Fig. 9

LOGO

Pulse wave The existence of the pulse wave is easy to detect. To do

so, press your finger radial or carotid arteries and feel " beating " the walls of blood vessels . Sensitive devices can register vibrations of the walls and veins , which are much weaker than fluctuations in blood vessels.

The flow of blood through the bloodstream causes different variations : this longitudinal pressure waves that propagate in a liquid medium with the speed of sound , this periodic change of velocity of the fluid associated with the intermittent ejection of blood in the heart, vascular , this periodic change in vessel lumen by changing its blood supply . All these processes are interrelated, they describe a single phenomenon - the movement of blood through a complex vascular tree .

LOGO The origin of the pulse wave

Consider a simplified model of the origin of pulse wave in elastic vessel. It is clear that their origin is connected with the activity of the heart. When used at the exit of the heart blood flow was stable , no pulsations would not arise . On the other hand , if blood vessels are very hard , even with pulsating movement of the walls of blood flow would be almost unnoticeable. Thus , the origin of the pulse wave associated with the reaction of elastic vessel walls in the pulsating blood flow that occurs when the heart periodic .

LOGOModel plots elastic vessels

We select a small section of elastic vessels ( Fig. 10), at one end of which the piston. In short piston a force F. Fluid around the piston due to its inertia does not have time to move along the vessel , the action force is increasing pressure on the wall - part extends until the wall tension does not compensate for increased pressure inside the vessel. As the tension in the wall region is higher than in the adjacent liquid will move further along the vessel. Moving fluid will reduce the pressure on this area , the vessel will restore the original volume at the time, as the volume of neighboring areas will increase. The process is repeated after a new impetus to the piston. For elastic wall will extend pulse wave.

Figure. 10. Model plots elastic vessels.

LOGOPulse wave equation

The equation of the pulse wave . In this con - Nemo ideal fluid

motion in an elastic tube under the action of pressure forces alone .

Select the area long DX and volume V. Let changing area tubes with

radius extending through e, then the current value of the radius is

equal wool

R(x,t) = R0 + (x,t). (22)

Pulse wave equation , which describes the process of diswives of

changes in vessel radius along its axis, is as follows:

2

22

2

2

xu

t

, (23)

where

u – the velocity of the pulse wave

LOGO Moensa - Korteweg formula for the velocity of the pulse wave

In the absence of longitudinal tension ( so that the tubes can be reduced when expanding ) volume modulus of elasticity tion for thin cylindrical vessel of radius R and wall thickness h is given by = 2hE(1 – 2)R with multiplier

1 – 2. After putting into Moensa - Korteweg formula for speed :

R

hEu

2

. (24)

Thus, the velocity of the pulse wave depends on the geometrical

parameters of the vessel ( radius and thickness ) and the elastic

properties of the vascular wall .

Poisson's ratio for the vessel is constant and equal to about 0.5. Young's modulus , as shown above, the value remains constant for the vessel , so velocity of the pulse wave can significantly change , to challenge

LOGOExamples of changes in pulse wave velocity distribution

Speed pulse wave varies in different vascular diseases , in this regard, its clinical definition allows to obtain further information to assess the functional state of the vessel walls .

Figure. 11. a) change in velocity with increasing pressure (1, 2, 3 -, respectively, for elderly, the middle and younger), b) velocity change with age.

LOGO

Vascular system Vascular system - a closed system of elastic tubes ( vessels) of different

diameters . Heart blood moves first in the aorta - the elastic tube with a diameter of 2-3

cm farther from the heart , the more branching vessels , directing blood to all branching vessels - arteries. The diameter of the arteries decreases with distance from the heart.

Upon entering the tissues of the arteries also branch out and move in very small vessels - arterioles. Arterioles give rise to the hair have multiple vessels - capillaries . The walls of the capillaries have a specific property - similar to " filter ". In the opening between the cells that form a layer of cells in the tissue easily penetrate oxygen and nutrients . Capillaries do not end , and gradually increasing their diameter and they turn into venules that connect the veins that carry blood to the heart. The circle ends and the " start point " blood returns after about 20 seconds.

Blood in arteries from 1c is approximately 0.5 meters in veins - 10-20 cm in capillaries - 0.05-0.1 cm

LOGO. The pressure and velocity of the blood vessels in various

Vessels Diameter , mm

cm / s

Pressure

mmHg

.

Aorta 20 50 50 – 150 Arteries 10 – 5 50 – 20 80 – 20 Arterioles 0, 1 – 0, 5 20 – 1 50 – 20 Capillaries 0, 5 – 0, 01 0, 5 – 0, 1 20 – 10 Venules 0, 1 – 0, 2 0, 1 – 1 10 – 5

Vienna 10 – 30 10 – 20 (-5) - (+5)

Speed decreases blood from the aorta to the capillaries and the veins increases.

Thus, the pressure should be greater in capillaries and smaller - in the aorta and

veins (by Bernoulli equation ). But this statement is unjustified because blood

can only move in the direction of reducing the pressure. This contradiction

explains the work of the heart, which " pumps " blood into the aorta and creates

pressure to 150 mmHg , then the pressure falls, and the veins become even

negative values.

LOGOFeatures of the movement of blood through ? Cardiovascular system

The movement of blood through the cardiovascular system is quite complex phenomenon. Complex structure has the bloodstream , which is a complex system of elastic vessels of various types. The very fluid - blood - is a complex suspension rheological properties which depend on the conditions of flow. Circulatory system has active energy ( ventricles and atria of the heart) . Various active physiological processes (mechanisms of reflex changes in vascular tone and cardiac output ) change the physiological properties of the circulatory system, and thus the conditions of blood . Any description of the processes hemodynamics ( from simple cases mechanics of blood to the complex processes of reflex control of circulation ) are based on experimental data accumulated over many years of research.

LOGOThe cardiovascular system

LOGO Indicators of hemodynamic in different parts of the vascular tube

Indicators of hemodynamic in different parts of the vascular tube

A - disruption of blood

B - blood pressure, total vascular lumen and linear flow speed

Indicators of hemodynamic in different parts of the vascular bed

LOGOHuman heart

Human heart is a hollow muscular organ that rhythmically pumps blood into vessels of large and small circulation. Heartbeat starts in utero (in the womb) and does not stop to work throughout life. Heart pumps 4.5 liters of blood per minute and more than 7 thousand liters a day. During heavy exercise the volume of blood that is pumped per minute increases 3-4 times. Over a lifetime, the human heart can pump about 150 million liters of blood. Thanks to the heart function the process of blood circulation, which provides all important vital body functions, is continuous and permanent.

LOGO

Human heart

Human heart is a hollow muscular organ that rhythmically pumps blood into vessels of large and small circulation. Heartbeat starts in utero (in the womb) and does not stop to work throughout life. Heart pumps 4.5 liters of blood per minute and more than 7 thousand liters a day. During heavy exercise the volume of blood that is pumped per minute increases 3-4 times. Over a lifetime, the human heart can pump about 150 million liters of blood. Thanks to the heart function the process of blood circulation, which provides all important vital body functions, is continuous and permanent.

LOGOCardiac cycle

cycle of heart rate:1 - atrial diastole; 2 - atrial systole;3 - ventricular diastole; 4 - ventricular systole.

LOGOWork and power of the heart

The work of the heart is the sum of work performed ventricles. The bulk of the work takes the left ventricle. The work of the right ventricle is 0.2 hours from the left. ago:

Аc =Аn + Ал= Ал + 0,2Ал =1,2Aл The work of the left ventricle is directed to overcoming the

resistance movement of blood throughout the vascular system and giving it kinetic energy.

Ал = pVуд + mV2 / 2= pVуд + ρVудV2 / 2 = Vуд (p + ρV2/ 2) , where р — average pressure at which blood is ejected into the

aorta, even ~ 1,3-10* Pa, ρ — density of blood (1,05*103 кг/м3), V — rate of blood (approximately 0,5 m / s), stroke volume of blood (at rest 6*10-5 м3).

Then: Ал = (1,3*104 + (1,05*103*0,52)/2)*6*10-5 = 0,81 (J.). In view of the right ventricle heart function equal: Аc = 1,2 Ал = 1,2*0,81=1 J Work performed heart during systole (0.3 s), and therefore the

power developed by the heart muscle during a reduction will: Nc=Ac/t=1/0,3=3,4 W

LOGO Methods for determination of blood viscosity

The set of methods used to measure the viscosity coefficient, called viscosimeter, and devices that are used for this purpose viscometer. Viscosity coefficients whose values lie in the range 10–5–104 Pa*s, determined using capillary viscometers.

Capillary method is based on using Hagen-Poiseuille formula whereby fluid volume V, occurring during t through the capillary length l and radius R in the presence of differential pressure ΔP at the ends of the capillary, is:

tl

PRV

8

4

(25)

LOGO Capillary method for determining blood viscosity

For vertical capillary pressure drop caused by the hydrostatic pressure of the liquid column height h, namely

ΔP = ρgh, (26)

where ρ – density of the liquid. By the formula (25), (26) find the viscosity of the fluid

tlV

ghR

8

4 (27)

Given that the value of V, l, R and h is constant for a given capillary viscometer and put the new constant:

c = πR4gh/(8lV), (28)

we can determine the viscosityη = cρt (29)

LOGOCapillary method for determining blood viscosity

Time course of the test liquid through this capillary depends on its parameters, density and viscosity of the liquid. By measuring the time for the occurrence of equal volumes of the investigated (tx) and reference (tет) fluids, we obtain a formula for determining the relative (ηвід) and absolute (ηабс) viscosity of the liquid:

eтeт

xx

eт

xвід t

t

, (30)

ηx = ηабс = ηет ηвід. (31)

Instead of the reference fluid, usually using distilled water, the viscosity of which (ηет).

LOGO The structure of the capillary viscometer

Figure. 12. Capillary viscometer.

The basis of the capillary viscometer is 3 out of tank 2. Tags М1

and М2 to serve as a reservoir for fixing the amount of fluid flowing through the capillary. Pear 4 is used for suction of fluid into the re-servoir 1.

LOGO Determination of the viscosity of the fluid through the viscometer ВК-4

Geppler VC-4 is a capillary viscometer for determining the blood viscosity. From the Hagen-Poiseuille formula that describes the flow of a viscous fluid in a cylindrical tube, it appears that under the same conditions of flow at the same time, the volume of material V, flowing through this tube is inversely proportional to the viscosity of the fluid: V = 1/η .

The magnitude of the volume V we can estimate the length of capilar L during of: V = πr2L. Thus, the ratio of viscosity of liquids volumes which occur over time, will be equal to the volume or relative lengths

η=η/ηет = Vет /V = Lет /L.

Thus, by measuring L та Lет, You can determine the relative viscosity of the test liquid

ηвід = η/ηет = Lет /L. (32)

Knowing the viscosity of the reference liquid (water) at the temperature of the experiment, one can easily obtain the absolute value of the viscosity of the test liquid.

LOGOMethods of measuring blood pressure

There are maximum (systolohichnyy) pressure which is the pressure of blood on the walls of the arteries during systole (contraction) and ventricular minimum (diastolic) pressure - the same during the diastole (relaxation) ventricles. The difference between them is called the pulse pressure. An important indicator is the average pressure that represents the average of all instantaneous values of blood pressure during the cardiac cycle. This value characterizes the energy costs of maintaining the real value of blood pressure during the cardiac cycle.

Blood pressure can be measured by direct method (kateterizatsiyi in which using a plastic probe into large vessels introduced a miniature pressure gauge). This method is used in surgical practice, or in animal experiments. In clinical practice, using the indirect method (bloodless), measuring blood pressure, known as the Korotkoff method.

LOGO Blood pressure measuring devices

LOGO Mean Arterial Pressure

LOGOMean Arterial Pressure

The mean arterial pressure (MAP) is the average blood pressure during the cardiac cycle. The mean arterial pressure depends on: Cardiac output(Q or CO ) Vascular resistance (VR) Central venous pressure (CVP)

MAP= (CO* VR)+ CVP

MAP can be determined from the values of systolic and diastolic blood pressure by normal heart rate (pulse).The formula for calculating the mean

arterial pressure is :

LOGO

Thank you for your attention.