- 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.