An impedance index in normal subjects and in subarachnoid hemorrhage

The impedance of a hemodynamic system is defined as the ratio of each harmonic component of blood pressure to that of flow. Calculation of impedance cures has been extensively performed in the systemic circulation, leading to the recognition of reflected pressure and flow waves and clarifying the shape of ultrasound waveforms. Impedance in the human cerebral circulation has not been measured primarily because of the relative inaccessibility of simultaneous flow and pressure data in the human cerebral circulation. We defined an impedance index using the transcranial Doppler waveform for that of flow and a noninvasive applanation measure of the carotid artery pressure waveform. Middle cerebral artery velocities and carotid artery pressure waveforms were simultaneously recorded in 16 vessels from 10 normal volunteers, 42 vessels in 14 patients with aneurysmal subarachnoid hemorrhage, and 14 vessels in 7 subjects during conditions of hypocapnia, normocapnia and hypercapnia. Impedance was calculated by dividing the harmonic associated with pressure divided by that of flow, and averaging 10 to 20 such calculations. Relative impedance curves were calculated by dividing by the impedance at the first harmonic. Impedance was also studied in an electrical model consisting of a Windkessel element containing inductance in series with a second Windkessel to model the large vessel and vascular bed, respectively. Model parameters were taken from the literature for these calculations. For the normal subjects, the shape of the impedance index curve was similar to those found in the systemic circulation. The impedance index curves for patients in vasospasm (middle cerebral velocity was greater than 180) showed a peak at the second or third harmonic, which appeared more frequently than the nonspasm group (p < 0.01). Furthermore, the ratio of the second harmonic to the first harmonic was significantly > 1.0 in the spasm group but significantly < 1.0 in the normal group (p < 0.05). Calculations from the electrical model replicated the appearance of these peaks at the second or third harmonic for vasospasm parameters. A statistically significant peak appeared at the second or third harmonic in the impedance index curves for patients in vasospasm, which was replicated quantitatively by our electrical model. Although such peaks can be explained in the systemic circulation by the presence of reflected waves, the distance to the reflection site is larger than expected for the cerebral circulation. This suggests the importance of the inertia of blood as a stenosis worsens and as the origin for the observed changes in the impedance index curves.