Cerebral Critical Closing Pressure: Is the Multiparameter Model Better Suited to Estimate Physiology of Cerebral Hemodynamics?

Abstract

Background

Cerebral critical closing pressure (CrCP) is the level of arterial blood pressure (ABP) at which small brain vessels close and blood flow stops. This value is always greater than intracranial pressure (ICP). The difference between CrCP and ICP is explained by the tone of the small cerebral vessels (wall tension). CrCP value is used in several dynamic cerebral autoregulation models. However, the different methods for calculation of CrCP show frequent negative values. These findings are viewed as a methodological limitation. We intended to evaluate CrCP in patients with severe traumatic brain injury (TBI) with a new multiparameter impedance-based model and compare it with results found earlier using a transcranial Doppler (TCD)–ABP pulse waveform-based method.

Methods

Twelve severe TBI patients hospitalized during September 2005–May 2007. Ten men, mean age 32 years (16–61). Four had decompressive craniectomies (DC); three presented anisocoria. Patients were monitored with TCD cerebral blood flow velocity (FV), invasive ABP, and ICP. Data were acquired at 50 Hz with an in-house developed data acquisition system. We compared the earlier studied “first harmonic” method (M1) results with results from a new recently developed (M2) “multiparameter method.”

Results

M1: In seven patients CrCP values were negative, reaching −150 mmHg. M2: All positive values; only one lower than ICP (ICP 60 mmHg/ CrCP 57 mmHg). There was a significant difference between M1 and M2 values (M1 < M2) and between ICP and M2 (M2 > ICP).

Conclusion

M2 results in positive values of CrCP, higher than ICP, and are physiologically interpretable.

Appendices

Appendix 1

Our hypothesis was that THAM (tromethamine), a drug which decreases ICP [16], would improve cerebral autoregulation in these patients. It was a prospective, interventional, controlled trial. Each patient was its own control, studied pre- and during tromethamine administration. The results of this trial have not yet been published but have been presented in different meetings. The patients were studied in a basal phase, without THAM, with no hemodynamic changes performed initially. After 30 min of basal data acquisition, ABP was increased with the use of noradrenaline. In the second part, the patients were administered THAM, and new basal and hypertensive phases were acquired.

Appendix 2

The new model is of calculating CrCP based on cerebrovascular impedance. Resistance is a concept used for DC (direct current), whereas impedance is the AC (alternating current) equivalent. In this model, impedance is used instead of resistance, based on the pulsatile characteristics of cerebral circulation. Arterial compliance and resistance are set in parallel, giving an impedance spectrum across the frequencies of the cardiac cycle.

Modulus of impedance is defined as a function of circular frequency

$$ \left| {Z(\omega)} \right| = {{\text{Ra}} \mathord{\left/ {\vphantom {{\text{Ra}} {\sqrt[2]{{\left( {{\text{Ra}}*{\text{Ca}}*\omega } \right)^{2} + 1}}}}} \right. \kern-0pt} {\sqrt[2]{{\left( {{\text{Ra}}*{\text{Ca}}*\omega } \right)^{2} + 1}}}} $$

(1)

where Ra is the cerebrovascular resistance, Ca is the cerebral arterial circuit compliance, and ω is the circular frequency.

The amplitude of the fundamental harmonic of MCA FV (F1) can be expressed as a function of cerebrovascular impedance

$$ F 1= {{A 1} \mathord{\left/ {\vphantom {{A 1} {\left| {Z\left( {f{\text{HR}}} \right)} \right|}}} \right. \kern-0pt} {\left| {Z\left( {f{\text{HR}}} \right)} \right|}} $$

(2)

where |Z(fHR)| is the modulus of cerebrovascular impedance at heart rate frequency (fHR).

CPP pulsation (i.e., ABP–ICP) should be used instead of A1. The use of A1 is justified because the pulsation of ICP is much lower than the pulsation of ABP (average proportion 1:25).

If FV is expressed using this model at a heart rate of zero, blood flow acts as a direct current. In this case, arterial compliance is saturated and impedance depends only on arteriolar resistance (Ra) (Fig. 6).

$$ {\text{FV}} = {{\text{CPP}} \mathord{\left/ {\vphantom {{\text{CPP}} {\left| {Z(0)} \right|}}} \right. \kern-0pt} {\left| {Z(0)} \right|}} = {\text{CPP/Ra}} $$

(3)

Fig. 6

Simplified electrical model of the cerebrovascular bed, with scheme showing an unscaled shape of the frequency (f)-dependent modulus of impedance $({\left| {Z(f)} \right|})$. Ca cerebral arterial compliance; CVR cerebrovascular resistance; CPP mean cerebral perfusion pressure; FV mean cerebral blood flow velocity, AMP_ABP and AMP_FV first harmonics’ amplitudes of pulse waveforms of ABP and FV, respectively, HR heart rate frequency (beats/min). (Modified from reference [10])

The combination of the equation A with (1), (2), and (3) results in the formula (B):

$$ {{{\text{CrCP}} = {\text{ ABP }} - {\text{ CPP}}} \mathord{\left/ {\vphantom {{{\text{CrCP}} = {\text{ ABP }} - {\text{ CPP}}} {\sqrt[2]{{\left( {{\text{Ra*Ca*}}2\pi * {\text{HR}}} \right)^{2} + 1}}}}} \right. \kern-0pt} {\sqrt[2]{{\left( {{\text{Ra*Ca*}}2\pi{\text{*HR}}} \right)^{2} + 1}}}} $$

(B)

This formula takes into account ABP, ICP, Ra, and Ca.

The product of Ra and Ca is the “time constant” of the cerebral circulation [17–20].