Some Aspects of the Applied Hemodynamics in Diagnostic Angiology

Abstract

Sometimes physical principles of some technologies, which are used very effectively by the human, are so confused and nebulous that many year passes when people clearly realize laws and rules, which these technologies were based on.

Full text

Author - Ulyana B. Lushchyk, MD, PhD, DSc
Co-author - Novytskyy V. Viktor, Prof. D.Ph.&Math.Sc.

Sometimes physical principles of
some technologies, which are
used very effectively by the
human, are so confused and
nebulous that many year passes
when people clearly realize laws
and rules, which these
technologies were based on.
М. H. Maxon, М. Аlbert, F.Hedowry

Hemodynamics
(of Greek haima – blood, dynamis – force)
is a science, which appeared and is
developing on the crossroads of
hydromechanics and biology,
it studies blood movement in the closed
vascular system of the human organism taking
into account morphological structure of blood,
its physical-chemical characteristics, specific
features of vascular wall, dynamics of the live
system with applied adoption of the
hydrodynamic postulates. 

1. The gradient of the hydrostatic pressure in
various segments of the vascular system
that is formed due to the pumping function
of the myocardium.
2. Rheological properties of blood as the
dispersion of the forming elements with
properties of the non-Newton liquids.
3. Blood carrying vessels as the viscous-
elastic tubes, whose properties
(geometrical - size, branching and physical -
viscosity, elasticity, penetration) vary in
diameter and length.

HYDROMECHANICS
Theoretical Technical
hydromechanics hydromecanics
(hydraulics)
Hydrodynamics Rheology
Hydrostatics
Hemodynamics 

Ideal Newton liquids –
itisanabstractmodelthatisusedinordertosimplify
analyticalinvestigationsandischaracterisedwiththe
absolutelyunchangeablevolumeandcompleteabsence
ofviscositythat’sfrictionforcesundertheirmoving.
The profile of the velocity of movement of the ideal
Newton liquid
(viscosity = 0, F friction = 0)


Real Newton liquids
areallliquidsthatexistsinthenatureandcharacterised
by the viscosity - the force of the internal friction that
appearsinthemwhilethelayersaremoving.
Decreasing of their viscosity under increasing of the
temperature is the characteristic feature of the real
liquids (honey, tar, jam).
The profile of the velocity of
the real Newton
liquid’s movement


Non-Newton liquids
presentvariousmaterials,whoseonlycommonproperties
are their fluidity and deviation from the friction law of
Newton(marsh,emulsion,suspension,paint,blood).
The profile of velocity
of non-Newton liquids’ movement (viscous liquid)

As non-Newton liquids
increase their viscosity
under increasing of
temperature, patients under
hyperthermia and in the heat
require more careful
treatment.

The law of Hagen-Pausel
A loss of liquids is proportional to decreasing of
pressure per a unit of tube’s length and radius of the
tubeinthefourthpower.
Appliedessence:
is maintained with practically achieved velocities of
movementofliquidsinnarrowtubes.
This proportionality is not maintained for non-
Newton liquids - with decreasing of velocity of the
liquid’s movement the blood viscosity increases.

Москва, 2005
Hydrodynamic resistance with the pressure movement of real
liquids
1.Thevariantofthepressuremovementoftheidealliquid.
2.Thevariantofthepressuremovementoftherealliquid.
3.Thevariantofdecreasingofthepressuremovementofthe
real liquid in the conditions of the increased friction of the
wall.





Parameters In hydrodynamics In hemodynamics
Tube'swall unchangeablehard elastic,pulsating
Porosityofthetube'swall absent
thereareeffectsofpenetrationof
theliquidthroughthevacularwall
insmallvessels
Thetube'scontent
constantdensityofthereal
liquid
variabledensityonnon-Newton
liquids
apump
constantparametersofthe
pumpfunctioning
pumpingfunctionofthe
myocardiumisthevariablequantity
Segmentsofawatersupply
system
intakeandoutletmainlines thirdlinkapppears-capillarybed


Parameters In hydrodynamics In hemodynamics
Autoregulatingmechanisms
absentorarecontrolled
outside
present
characterofmovement pressure
isnotapressureoneinthe
classicalunderestanding,itdiffers
bythepossibilityofformationofa
blooddepotduetostretchingof
vascularwalls
Dempfers almostabsent present
Dynamicsystem absent present
corespondingtothe
gravitationforces
constant
constantlyvariabledueto
variationsofbodypositions


Москва, 2005
The section that
corresponds to
the capillary net
has the largest
area

Москва, 2005
According to the
condition of the
stream’s continuity in
case of increasing of
the system’s cross
section area the
velocity of blood flow
decreases in the
corresponding areas

Hemodynamics Laws
1. The law of continuous movement
Stream of liquid can be continuous under condition
of laminar stream and constant volumetric velocity
(multiplication of velocity and cross section is the
constant value): Sv = const
Volumetric velocity of blood flow is constant in any
section of the cardio-vascular system.

2. Bernoulli’s equation (1738) –
itisacorrelationforconstantmovingoftubeofflowof
idealincompressibleliquid.
Aproductofgeometric,piezometricandvelocityheight
remains constant on the whole distance of the given
flowoftheliquidstream:
z+p/γ+v2/2g=const,
γ= ρg
( γ – specific gravity of the liquid )
“energetic”presentationoftheequation:
zpg + p +
ρ
v2 / 2 = const,
Zpg – hydraulic pressure,
p – static pressure,

ρ
v2/2 – velocity (kinetic) pressure, that’s kinetic energy
of the mass unit of the moving liquid.

A sum of three pressures -
hydraulic, static and
velocity (kinetic) - makes
up complete pressure of
the moving liquid and it is
constant

That’s why separate kinds of mechanic
energy can vary, but their sum remains
the constant value - it is the law of the
energy conservation of moving liquid,
which is fundamental for the whole
hydromechanics.
Applying the Bernoulli’s equation to
real liquid they take into account
friction force too, which arises under
liquids’ moving.

3. The Puasel’s formula
A magnitude of the volumetric
velocity of liquid stream Q
depends on the radius of the
vessel r and is proportional to
r4 under condition of the
relative stability of difference
between pressure and length of
the vessel.

Amount of blood that flow through a blood
carrying bed per time unit is determined by the
presence of two factors:
1) pressure gradient in the circulation system;
2) resistance of the blood carrying bed that
depends on a degree of variance of the lumen
of vessels and character of their branching.

All methods of the life-time investigation of the
vascular system can be conditionally divided
into the following directions:
1. Assessment of the heart’s and vessels’
structures
2. Assessment of the functional activity of the
heart as a pump
3. Assessment of functions of vessels
4. Assessment of perfusion in organs and
tissues
5. Assessment of the pressure in the vascular
system
6. Assessment of the rheological features of
blood flow

It is necessary to observe in order to realize
and to realize in order to operate.
Roman Rollan

Assessment of the venous channel and signs of the intracranial
hypertension
ASTd
ASTs
VJIs
VJId
ACCs
ACCd
AVd=s
ACMd=s
ACPd
ACPs
ACId=s
AB

Hemodynamic efficiency of revascularization
VJId
VJIs ACCs
VSTd
ASTs
VVd
VVs
ACIs
ACId
AB

Assessment of elastic- tonic features of vessels

Assessment of the hemodynamic importance
ACCd ACCd after operation
ASTd
ASTs
ASTd after operation
ACCs after operation
ACCs

Integrated approach to assessment of functioning of
the hemodynamic system

Screening of ischemization of the myocardium with the
correction of hemodynamics in the organism

Peculiar features of the cerebral
angioarchitectonics
control
group
DE I DE II DE III
1. Predominating caliber of cerebral arteries
Мicrocaliber 2 18,5 24 32
Middlecaliber 72 74,5 68 48
Macrocaliber 26 7 8 20
2. Type of angioarchitectonics
Magistral 74 68 54 46
Diffused 26 32 46 54
3. Tortuosity of cerebral arteries
ofoneartery 2 4 14 38
oftwoarteries 4 4 14 34
4. Type of division
Dichotomic 94 55,6 34 34
Pathologicalatypical 6 44,4 66 66

Mathematical Modeling of Possible Tracts of Revascularization
Present level of non-invasive investigation of the vascular bed
requires  profound knowledge of basics of hemodynamics and
potential of the ultrasound devices not only from physicians, USD
functional diagnostics, but also from vascular surgeons and
neurosurgeons
•Calculation of the size of the hydraulic stroke
•Calculation of the required caliber of a vessel
•Correction of the arteriovenous-liquor balance
•An angle of incline of an artery in case of transposition
Theoptimumangleup
to60°

2 approaches:
macrolevel of
blood circulation;
microcirculation