Transcranial Doppler Pulsatility Index: What it is and What it Isn’t

Abstract

Background

Transcranial Doppler (TCD) pulsatility index (PI) has traditionally been interpreted as a descriptor of distal cerebrovascular resistance (CVR). We sought to evaluate the relationship between PI and CVR in situations, where CVR increases (mild hypocapnia) and decreases (plateau waves of intracranial pressure—ICP).

Methods

Recordings from patients with head-injury undergoing monitoring of arterial blood pressure (ABP), ICP, cerebral perfusion pressure (CPP), and TCD assessed cerebral blood flow velocities (FV) were analyzed. The Gosling pulsatility index (PI) was compared between baseline and ICP plateau waves (n = 20 patients) or short term (30–60 min) hypocapnia (n = 31). In addition, a modeling study was conducted with the “spectral” PI (calculated using fundamental harmonic of FV) resulting in a theoretical formula expressing the dependence of PI on balance of cerebrovascular impedances.

Results

PI increased significantly (p < 0.001) while CVR decreased (p < 0.001) during plateau waves. During hypocapnia PI and CVR increased (p < 0.001). The modeling formula explained more than 65% of the variability of Gosling PI and 90% of the variability of the “spectral” PI (R = 0.81 and R = 0.95, respectively).

Conclusion

TCD pulsatility index can be easily and quickly assessed but is usually misinterpreted as a descriptor of CVR. The mathematical model presents a complex relationship between PI and multiple haemodynamic variables.

Appendix

Mathematical Methods

The input circuit to cerebrovascular space (Fig. 5) can be reduced to cerebrovascular resistance (R _a) and compliance (Ca) of arteries. Under the assumption that input pressure is low, and systolic–diastolic distance is totally contained within the range of autoregulation, the system may be treated as semi-linear.

Fig. 5

Simplified input circuit used for the derivation of the formula (4) describing PI (calculated for fixed frequency of heart rate). a Input circuit representing a model of cerebral circulation. b Diagram of cerebrovascular impedance |Z(f)| as a function of frequency. Two frequencies are considered: f = 0 (i.e., DC component) and f = HR. Module of impedance for f = 0 is equal to R _a, and may be estimated as CPPm/FV_m. a1 pulse amplitude (first harmonic) of ABP, ABP arterial blood pressure, C _a cerebrovascular compliance, CPPm mean cerebral perfusion pressure, f frequency, f1 pulse amplitude (first harmonic) of blood FV, FV _m mean blood flow velocity in the middle cerebral artery, HR heart rate, PI Gosling pulsatility index, R _a cerebrovascular resistance (in the main part of manuscript expressed as CVR), |z| cerebrovascular impedance, |z₁| cerebrovascular impedance with frequency equal to HR

The pulsatility of the flow (PI), described as the ratio of the fundamental amplitude of the FV waveform divided by mean FV (1)

$$ {\text{PI}} = \frac{{{\text{f}}1}}{{{\text{FV}}_{\text{m}} }} = \frac{a1}{{{\text{CPP}}_{\text{m}} }} \times \left| {\frac{{{\text{z}}(0)}}{{{\text{z}}({\text{HR}})}}} \right|\quad\quad\left| \begin{gathered} {\text{f}}1 = \frac{a1}{{\left| {{\text{Z}}({\text{HR}})} \right|}} \hfill \\ {\text{FV}}_{\text{m}} = \frac{{{\text{CPP}}_{\text{m}} }}{{\left| {{\text{Z}}(0)} \right|}} \hfill \\ \end{gathered} \right. $$

(1)

where f1 is the fundamental harmonic of FV, FV_m is the mean FV, a1 is the fundamental harmonic of arterial pulse pressure, CPP_m is the mean cerebral perfusion pressure, |z(0)| is the cerebrovascular impedance at zero frequency, |z(HR)| is the cerebrovascular impedance at frequency equal to heart rate.

Cerebrovascular impedance (Z(jω)) can be described as a complex function of frequency (2).

$$ z\left( {j\omega } \right) = \frac{{\frac{{R_{\text{a}} }}{{j\omega {\text{Ca}}}}}}{{R_{\text{a}} + \frac{1}{{j\omega {\text{Ca}}}}}} = \frac{{R_{\text{a}} }}{{j\omega R_{\text{a}} {\text{Ca}} + 1}} $$

(2)

where ω is the 2πf, j is the imaginary unit, R _a is the cerebrovascular resistance, Ca is the compliance of arteries and arterioles.

Z(f)| is described in (3)

$$ \left| {z(j\omega )} \right| = \frac{{R_{\text{a}} }}{{\sqrt {R_{\text{a}}^{2} {\text{Ca}}^{2} \omega^{2} + 1} }} $$

(3)

where R _a is the cerebrovascular resistance, Ca is the compliance of arteries and arterioles.

From here we can derive formula describing the pulsatility index:

$$ {\text{PI}} = \frac{a1}{{{\text{CPP}}_{\text{m}} }} \times \sqrt {(R_{\text{a}} {\text{Ca}})^{ 2} {\text{HR}}^{2} (2\pi )^{2} + 1} $$

(4)

where PI is the pulsatility index (for fundamental component of HR), a1 is the pulse amplitude (first harmonic) of ABP, CPP_m is the mean cerebral perfusion pressure, R _a is the cerebrovascular resistance, Ca is the compliance of arteries and arterioles, HR is the heart rate.

For the Gosling pulsatility index (PI) a1 should be substituted by the peak-to-peak amplitude of the ABP pulse. Also, Ca should be derived in a far more complex way, taking into account all harmonics of the ABP pulse and modules of impedances at these frequencies. But the general description of TCD pulsatility as a function of cerebral haemodynamic parameters remains the same.