- THIS MATERIAL IS PUBLISHED AND PROTECTED BY U.S.
COPYRIGHT LAW - REPRODUCTION PROHIBITED UNLESS
FOR PERSONAL USE, EXCEPTING AUTHOR PERMISSION -
Peter F. Kelly, D.P.M., F.A.C.F.A.S. *
Diplomate, American Board of Podiatric Surgery
Fellow, American College of Foot and Ankle Surgeons
PERIPHERAL VASCULAR DISEASE: A PRACTICAL
MONITORING METHOD
PART TWO: CALIBRATION OF THE DOPPLER ULTRASOUND
*This work resulted in receipt of the Angiology Award, Pannsylvania
College of Podiatric Medicine, 1986
ABSTRACT
Until this time, no simple noninvasive method of calculating and
monitoring calibrated parameters of blood perfusion has existed.
The first section of this paper discussed various methods of
diagnosing circulatory deficiencies and used the example of intermittent
claudication, for it is a frequently encountered symptom of circulatory
inadequacy.
The second section of this paper introduces mathematical
fundamentals which show a practical method of calibrating circulatory
velocity and flow studies. With this the practitioner of Podiatric
Medicine or Surgery is better prepared to monitor blood flow through
the extremities with increased accuracy.
CALIBRATION OF THE DOPPLER ULTRASOUND--BLOOD
VELOCITY
The patient should be reclined in a supine, phlebostatic attitude,
having had ample time to accommodate to any environmental changes in
temperature or stimulation which might affect blood pressure or heart
rate. The doppler instrument and recorder should have been operating
for several minutes to allow voltages and internal heating to stabilize
baseline readings. The probe should be positioned over the vessel at an
angle which will give maximal reflectivity, thus amplitude of the
ultrasonic waves. As little direct pressure as possible should be used to
keep the vessel maximally patent. The sensitivity of the recorder is
adjusted to obtain maximum excursion of the stylus swing so as to
maintain boundaries within either side of the graph markings. The
authors use a chart speed of 25 mm/sec. The industry standard of
recorder sensitivity is 1000 Hz/cm., so models with a variable rheostats
should be set to this value.
Triangulation and calculation of the total curve area is then
performed (see figure 2). In tracing tangiential lines on the upswing and
downswing of one complete wave period, they should meet generally
slightly above the apex and extend below the baseline. Baseline
levels should be even for several consecutive wave periods. The area
under the curve may then be calculated:
a = 1/2 (b x h) where a = area (cm2 )
b = base (single wave length) (cm.)
h = height (cm.)
Velocity, if desired, may be calculated:
v = _a_ x 20.49 where l = single wave length (cm.)
l
The factor of 20.49 is condensed from the parameters of recorder
sensitivity, velocity of sound through tissue, cosine of intended probe
position angle, zero crossover processing factors, and several other
conversion factors. An explanation on this calculation will shortly
follow. Once calculated, this simplified equation represents a greatly
simplified and standardized approach for application of the calibrated
doppler in the office. It must be noted that this factor should be adjusted
for each individual doppler unit. Our factor resulted in the figure of
20.49, since the doppler frequency transmitted was 9.221 Mhz.
Transmitting frequencies will generally vary between units, even
those of the same manufacturer. Therefore, for frequencies being less
than 9.221 MHz multiply the factor of 20.49 by
_(value)_.
9.221
For frequencies greater than 9.221 MHz, multiply the factor by
_9.221_.
(value)
The doppler shift is always inversely proportional to the transmitting
frequency. A new factor must always be calculated when a new crystal
is used.
The above abbreviated factor in our equation is derived from the
larger velocity equation:
___ graph area (cm)__
v(cm/sec) = graph length (cm) X recorder sensitivity (cps/cm) X
___c(m/sec) x 100(cm/m) x K3_____________
2Ft(cps) x cos O x 6(Hz/MHz)
10
where:
v = velocity of blood,
c = speed of sound in tissue,
K3 = correction factor for zero-crossover processing,
Ft = doppler transmitted frequency,
O = incident angle (probe to surface), and
A = vessel cross-sectional area.
Cps/cm is the recorder sensitivity, being the same as Hz/cm, and using
the industry standard of 1000 Hz/cm. Hz/Mhz is a conversion factor
because the frequencies used are relatively high and would be
cumbersome to work with.(14)
Substituting for the above variables we have:
_a(cm)_ __ 1550(m/sec) x 100 (cm/m) x 1.724___
v = l(cm) X 1000(cps/cm) X 2 x 9.221(MHz) x cos 45 x 6 (Hz/MHZ)
10
to arrive at the final standardized velocity equation of:
_a(cm)_
v = l(cm) X 20.49
CALCULATION OF STANDARDIZED BLOOD FLOW
To find blood flow through a vessel, its diameter must be known.
When the diameter is not known, as happens in most situations, a
standard, averaged diameter may be assumed is shown substituted in the
flow equation as follows:
Q(ml/min) = v(cm/sec) X A(cm2 ) X 60(sec/min)
substituting for v (velocity), as previously discussed:
_a(cm)_ _1550(m/sec) x 100(cm/m) x 1.724___
Q(ml/min) = l(cm) X 1000cps X 2 x 9.221MHz x cos45 x 6(Hz/MHz)
10
X A(cm2) X 60(sec/min)
_a(cm)_
Q(ml/min) = l(cm) X 1229.50 X A
thus for the popliteal artery:
_a_
Q = l X 1229.5 X 0.196
_a_
or Q = l X 241.4
for the posterior tibial artery:
_a_
Q = l X 1229.50 X 0.031416
_a_
or Q = l X 38.63
for the dorsalis pedis artery:
_a_
Q = l X 1229.50 X 0.031416
_a_
or Q = l X 38.63
The two factors of 241.4 and 38.63 above have been derived from
standardized values of vessel diameters of 0.2 cm. for the dorsalis pedis
and posterior tibial arteries, and 0.5 cm. for the popliteal artery. These
represent a composite of normotensive individuals as measured by real-
time ultrasonography, with other experiments calculating vessel diameter
by using flow and velocity values.(14,16) Adjustment correction for
these factors should also be applied for doppler frequency variations
from those used by the authors, as was described above in the flow
section.
As was true of calculating blood velocity, these resultants are also
corrected according to any changes in recorder sensitivity used to
maximize stylus excursion to get the final result in ml/min. For finding
blood flow, the area "a" in the equations above is found by multiplying
length times height only, and not subsequently dividing by two.
The factor of two is built into the simplified equation. See
"Example of Calculating Calibrated Blood Flow".
The normal values for calibrated flow are:
dorsalis pedis: 9.9 - 14.5 ml/min.
posterior tibial: 6.8 - 10.4 ml/min.
popliteal: 89 - 108 ml/min.
These values were obtained from a subject pool of normotensive
individuals (average brachial blood pressure of 118 mm.Hg.) having an
average calf ischemic index of 1.17 0.01 and average calf blood pressure
of 139 mm.Hg.(14)
EXAMPLE OF CALCULATING CALIBRATED BLOOD FLOW
A PVD patient, M. H., presents with an acute ulcerative cellulitis of
the dorsomedial area of her right foot. She also has a stenotic lesion of
the trifurcation of the popliteal artery, as evidenced by segmental
plethysmography. The doppler graph on this patient (see Figure 2.)
reveals a blood flow through the right dorsalis pedis artery to be
(.90 cm2 x 1.0 cm.) x 38.63 = 35.67, and 35.67 5 (chart gain) = 7.13
ml/min.
The posterior tibial artery measures (2.10 cm x 1.4 cm2) x 38.63 =
57.95, and 57.95 10 (chart gain) = 5.80 ml/min.
The physician realizes that the calibrated blood flow through the
dorsalis pedis is normally 9.9 to 14.5 ml/min, and through the posterior
tibial artery is normally 6.8 to 10.4 ml/min. It appears that this patient is
experiencing a reduction in blood flow through the right dorsalis pedis
of approximately 30% minimum. Circulation on the left in this example
appears generally normal.
The physician wishes to treat nonsurgically but aggressively with
systemic antibiotics at dosages which will achieve effective blood levels
at the infected area. The antibiotics selected are ticarcillin, at a 3 gm.
I.V. loading dose and 200 mg/kg/day I.V. in six divided doses, as well as
gentamicin, 2 mg/kg. loading and 3 to 5 mg/kg/day in three divided
doses. However, these dosages must be compensated for by the net loss
in perfusion to achieve an effective concentration required at the site of
infection. Additionally, gentamicin is nephrotoxic and ototoxic at
plasma trough concentrations of more than 2 ug/ml., and the
compensated dose should not exceed this for sustained periods.
Therapeutic drug monitoring should be monitored closely with this
patient, because the effective therapeutic range is reduced due to the
minimal amount of the antibiotic that must be maintained.
Therefore given the parameters of blood flow in this patient, and the
determination of a 30% decrease, the physician would adjust the dose
upward by approximately 30% so that an equivalent effective level of
antibiotics would reach the tissue in question at a comparable rate to that
of a normally perfused site. The adjustment of therapeutic correction
also depends on the source of arterial perfusion to the site being treated.
In this case, the dorsomedial aspect of the right foot, the dorsalis pedis
predominates. Should the site have been supplied by two arteries, an
averaged adjustment might have been made.
Another convenient way to adjust medication when the patient is on
oral antibiotics, in this case after M. H. is discharged, would be to
simply increase the tablet doseages from three times per day to four
times per day, or to prescribe a higher strength.
CALCULATION OF CALIBRATED RESISTANCE
This section on resistance is included in the academic interest of
completing the presentation of the aspects of the Poiseuille equation.
These are the interrelations of velocity, flow, and resistance. These
sequentially increase in usefulness in measuring peripheral perfusion.
However, it is unfortunate that obtaining parameters for these
measurements are also sequentially more difficult. This is because of the
number of variables which must be included and difficulty in obtaining
them.
For example, in clinical or research studies of vascular resistance,
knee-ankle distance and viscosity must be measured. To increase the
spectrum of vascular analysis, it might be suggested to include the rate
of perfusion as it relates to the equivalent mass of the extremity as a
truncated cone; however this and other parameters are beyond the scope
of this article.
Resistance may be roughly calculated for theoretical considerations
from velocity and blood viscosity. The following formula assumes a
normal whole blood viscosity of n= 0.040 poise. Williams (1983) states
that the viscosity of whole blood at a normal hematocrit is three to four
times that of water.(17) (See Figure 3.) Note that viscosity decreases in
a linear mode in states of severe anemia and increases exponentially past
a hematocrit of about fifty percent.
vascular _L n 8 ii_ where: L = length of artery
resistance = A2 n = viscosity
A2= A squared
A = cross sectional area
of the artery
ii= pi
Therefore when calculating resistance, correction for viscosity should
be performed in anemic or erythrocytic (polycythemic) states. Patients
having macroglobulinemia (Waldenstrom's) in most cases show an
elevation of plasma viscosity to three times normal due to large
asymmetrical IgM molecules. The same is true in plasma cell myeloma,
due to IgG or IgA molecules or aggregates. Sickle cell disease patients
frequently present with variable viscosity values depending upon the
state of oxygenation and HbS polymer/crystalloid configuration. Thus
multiple parameters must be considered.(17)
Length of the arteries may be derived from the knee-ankle distance by
applying a percentage. For the anterior tibial artery, use 87% of the
knee-ankle distance. For posterior tibial use 81%, for popliteal use 53%,
and for dorsalis pedis use 18% of the knee-ankle distance. In adult
human cadavers, the average measured length of the anterior tibial artery
was 31.7 cm., the posterior tibial artery was 29.4 cm., the popliteal
artery was 19.7 cm., and the dorsalis pedis was 6.6 cm. The average
cross-sectional area for the popliteal artery is 0.196 cm2. , for the
anterior tibial artery, dorsalis pedis, and posterior tibial artery, it is
0.0314 cm.2.
The approximate normal values for vascular resistance are:
-5
anterior tibial artery = 32,000 dyne-sec/cm .
-5
posterior tibial artery = 30,000 dyne-sec/cm .
-5
popliteal artery = 514 dyne-sec/cm .
-5
dorsalis pedis artery = 6,700 dyne-sec/cm .
It can be seen that despite the identical values of all other parameters,
the considerable difference in the vascular resistance of the anterior
tibial artery and dorsalis pedis artery is entirely due to variation in
length.
SUMMARY
Various methods of diagnosing intermittent claudication have been
discussed. None are completely advantageous in comparison, and each
presents unique faults. The example of intermittent claudication has
been used within the larger setting of diagnosing circulatory deficiencies,
and a simplified method of calculating parameters of blood perfusion has
been presented so that the practitioner might be able to increase the
accuracy in monitoring blood flow through the extremities.
Using this method, small changes in the status of blood flow of the
extremity may be accurately and easily documented. In situations of
infection when utilizing nephrotoxic drugs having low toxic doses and a
narrow therapeutic range, a more exact dosage may be administered
once compensation for a reduced flow is known. Should the blood flow
be so low as to make the dosage adjustment exceed the toxic range in
these cases, this information would provide a clearer differential for
more aggressive surgical considerations, such as administrating direct
arteriolar bolusing to the area, or possibly employing investigational
procedures such as antibiotic-impregnated polymethylmethacrylate
beads.
It is anticipated that the clinician might find the greatest usefullness
and rapidity in using predominantly the calibrated velocity and flow
measurements. The vascular surgeon and research scientist might want
to explore the effects of changes in vessel diameter on viscosity
(Fahraues-Lindqvist effect), or the effect of metabolic disease on
viscosity, and changes of vessel length as they relate to resistance. A
methodology which simplifies the determination of peripheral resistance
might be well received in the arena of the vascular sciences.