FIGURE 1:  VELOCITY AND FLOW EQUATIONS

a) 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

         _a(cm)_	                ___1550(m/sec) x 100 (cm/m) x 1.724___
   v =   l(cm)   X 1000cps X 2 x 9.221(MHz) x cos 45  x   6 (Hz/MHZ)
						  10

           _a(cm)_
   v =	l(cm)	X  20.49


   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)
	     A = vessel cross-sectional area


FIGURE 1 (Continued)

b) Flow Equation:

   Q(ml/min) = v(cm/sec) X A(cm2) X 60(sec/min)

   substituting for v (velocity):

                  _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

				       __a___
   Thus:     for popliteal a.:	Q =  l	X     1229.5    X   0.196

		  _a_
	     or Q =    l	X    241.4


   For posterior tibial a.:

	      _a_
	Q =  l	X   1229.50   X    0.031416

	     _a_
   or	Q =  l	X 38.63


   For dorsalis pedis a.:

	     _a_
	Q =  l	  X    1229.50  X    0.031416

	   _a_
   or  Q =      l    X   38.63


FIGURE 2:  DOPPLER GRAPH FOR THE EXAMPLE OF 
COMPENSATED ANTIBIOTIC DOSAGE

	 Dorsalis Pedis A., Right	 Posterior Tibial A., Right
	 Dorsalis Pedis A., Left	Posterior Tibial A., Left


FIGURE 3:  WHOLE BLOOD VISCOSITY


FIGURE 3.: Viscosity of heparinized normal human blood relative to 
hematocrit, expressed in relation to viscosity of normal saline solution.  
Adapted from Williams, W.J., et al.  Hematology, McGraw Hill, 1983 P. 
61.

FIGURE 4:  SUMMARY OF CALCULATIONS

   Velocity = Height of Curve (in cm) X  20.49 (Constant)   Recorder 
Gain


   Adjustment for	       20.49    X	_(     )MHz_   if < 9.221 MHz
   Frequency Change:		9.221 MHz

		       20.49 X	_9.221 MHz _   if > 9.221 MHz
				(     )MHz


Flow = Height of  X Pop= 241.4  Recorder =100 -  _(     )_ = % Increase
	  Curve (cm)		Gain	           0.089      in Dosage 

			PT= 38.63	     =	100 -  _(     )_
						           0.068

			DP= 38.63	     =	100 -  _(     )_
						            0.099


   Resistance = K-A Distance X Popliteal= 0.53 X _0.040 poise 
Viscosity x 8 ii

Cross-Sectional Area

			      PT= 0.81	     Popliteal= 0.196
			      DP= 0.87	     DP or PT = 0.0314

FIGURE 4: SUMMARY OF CALCULATIONS
 
1. Height of curve = instantaneous blood velocity at any given time. 
   The peak velocity is measured (height in cm), corresponding with  
   the peak frequency shift.   

2. Velocity =  wave period length  X factor (standardized measurement  
   parameters). 

3.  Flow = velocity X averaged vessel parameters ^ recorder gain 

4.  Flow and velocity are calibrated to the practitioner's frequency  
    used and recorder gain. 

5.  Vessel length is factored for vessel knee-ankle distance. 

6.  Resistance = (factored vessel length X viscosity X constants) ^  
    the square of averaged vessel parameters. 


PHOTOGRAPHS

Photo 1:
One of the earliest signs of circulatory inadequacy is intermittent 
claudication.  Historically, this has been measured in the number of 
blocks walked or the number of steps climbed before the onset of pain. 


Photo 2: 
Angiogram of partial obstruction of the femoral profunda artery.  Note 
multiple athrosclerotic areas, and how collateral circulation attempts to 
comprimise to supply blood distally. 
 
Angiogram courtesy of Roanoke Memorial Hospitals. 

 
Photo 3:
Angiogram of the foot, which is normal for this patient, but doppler 
measurements show decreased blood flow.  Although blood supply is 
patent distally, proximal collateral circulation is responsible for 
circulatory adequacy of this limb.  The calibrated doppler measurement 
of these arteries enable closer monitoring of a more proximal 
pathological obstruction. 
 
Angiogram courtesy of Roanoke Memorial Hospitals. 


Photo 4: 
The Podiatric Physician may be consulted to monitor cases involving 
vascular trauma should the foot become a high risk of loss.  Note 
circulatory embarrassment of the Popliteal Artery as it rides over the 
crest of a fractured tibial epiphysis.  Calibrated blood flow measurement 
provides early non-invasive measurement of circulation deficiency as 
fracture healing continues.   Bone callus formation in this area could 
gradually constrict flow to the distal leg and foot. 
 
Angiogram courtesy of Roanoke Memorial Hospitals. 


REFERENCES

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