## Introduction

## Materials and Methods

*f*) at the sampling site of Doppler sonography can be expressed as the inverse of the total impedance, which is the vector sum of electrical resistance.

*f/P*=1/

_{in}*Z*(

*f*, flow velocity;

*P*, input pressure;

_{in}*Z*, impedance)

*P*-

_{in}*P*=

_{out}*fR*+

*f*

_{1}*R*+

_{1}*f*

_{2}*R*

_{2}*C*

_{1}*d*(

*P*-

_{in}*R*

_{1}*f*)/

_{1}*dt*=

*f*-

_{1}*f*

*C*

_{2}*d*(

*R*

_{2}*f*+

_{2}*P*)/

_{out}*dt*=

*f*-

*f*

_{2}*P*, and

_{in}*R*is the resistance at the measuring point of

*f. R*is expected to be a very small value. Impedance was graphed along with the resistance and compliance of the proximal and distal areas by using the above four equations in Mathematica (Wolfram Research, Champaign, IL, USA). Changes in impedance were simulated in response to changes of the variables that affect blood flow.

*in vivo*cardiac cycle, the pulse rate was set at 1 Hz (60 beats per minute) with a 50% systolic and a 50% diastolic component, the maximum pressure was set at 50 mm Hg, and the diastolic pressure was set at 0 mm Hg (Fig. 2). Several types of waveforms reflecting changes in the proximal and distal values of resistance and compliance were drawn using Mathematica. Subsequently, the influence of these factors on flow velocity and the RI was evaluated according to changes in each variable. The RI was obtained using the formula [(PSV-minimum diastolic velocity [MDV])/PSV]. The basic standard waveforms are presented as a thick line when the regular pulse in Fig. 2 is provided with proximal compliance (

*C*) set to 1.3, distal compliance (

_{1}*C*) set to 0.9, proximal resistance (

_{2}*R*) set to 1.0, and distal resistance (

_{1}*R*) set to 0.8. These are arbitrarily chosen values that result in a waveform similar to renal arterial Doppler waveforms. In order to draw Doppler waveforms representing the influence of each component, the waveforms resulting from a threefold increase of each variable were presented as a thin line and compared with the basic waveforms. Nevertheless, non-uniformity may occur depending on the degree of hardening of the arteries, since our model implies that the proximal and distal compliance values are changed at the same ratio as arteriosclerotic changes progress evenly throughout the arteries. Basic waveforms were compared with the waveforms created when the proximal and distal compliances were increased threefold or decreased by one third in order to evaluate the effects of atherosclerotic changes. In order to evaluate the impact of pulse rate on the RI independently, differences in the basic waveforms were evaluated by altering the pulse rate and maintaining a consistent magnitude and shape of the pressure ripple. Since a reduced blood flow quantity is associated with a decreased heart rate, the pressure ripple and resistance must be increased in order to maintain a consistent quantity of blood flow. Therefore, the effect of changes in the pulse rate on the RI was also examined by altering the magnitude of the pressure ripple.

_{2}## Results

## Discussion

*in vivo*by evaluating the effect of changes in each component using a simulated electrical circuit model, and assessed the effect of each variable independently by isolating and changing interdependent variables. Taking into consideration the fact that

*in vivo*vascular flow is more likely than electrical current to be affected by many variables, this analysis is limited because only some factors were evaluated. This study determined that impedance and RI were influenced by both proximal and distal resistance and compliance. Nevertheless, a significant difference in the degree of changes in vascular resistance and compliance must be accounted for. While vascular resistance can range from zero to infinity, the degree of changes in vascular compliance is small, despite the effects of arterial hardening, interstitial edema in the distal peripheral region, cellular infiltration, and other factors. Thus, it may be anticipated that these factors will have impacts of different levels on Doppler waveforms and on the RI

*in vivo*.