Vasospasm Shortens Cerebral Arterial Time Constant

Abstract

Background

Cerebrovascular time constant (τ) estimates how fast cerebral blood arrives in cerebral arterial bed after each heart stroke. We investigate the pattern of changes in τ following subarachnoid hemorrhage (SAH), with specific emphasis on the temporal profile of changes in relation to the development of cerebral vasospasm.

Methods

Simultaneous recordings of arterial blood pressure (ABP) and transcranial Doppler (TCD) blood flow velocity (CBFV) in MCA were performed daily in patients after SAH. In 22 patients (10 males and 12 females; median age: 48 years, range: 34–84 years) recordings done before spasm were compared to those done during spasm. Vasospasm was confirmed with TCD (mean CBFV in MCA > 120 cm/s and Lindegaard ratio > 3). τ was estimated as a product of compliance of cerebral arteries (C _a) and cerebrovascular resistance (CVR). C _a and CVR were estimated using mathematical transformations of ABP and CBFV waveforms.

Results

Vasospasm caused shortening of τ on both the spastic (before: 0.20 ± 0.05 s vs. spasm: 0.14 ± 0.04 s, P < 0.0008) and contralateral side (before: 0.22 ± 0.05 s vs. spasm: 0.16 ± 0.04 s, P < 0.0008). Before TCD signs of vasospasm were detected, τ demonstrated asymmetry with lower values on ipsilateral side to aneurysm, in comparison to contralateral side (P < 0.009),

Conclusions

Cerebral vasospasm causes shortening of τ. Shorter τ at the side of aneurysm can be observed before formal TCD signs of vasospasm are observed, therefore, potentially reducing time to escalation of treatment.

Appendix

Cerebral Arterial Blood Volume (C _aBV)

The magnitude of the pulsatile changes in C _aBV (ΔC _aBV) used for calculation C _a (Eq. 1, Data analysis) was assessed based on a model proposed by Avezaat and Eijndhoven [16]. According to that concept the changes in cerebral blood volume (ΔCBV) during a cardiac cycle can be calculated as an integral of the difference between pulsatile arterial inflow (CBF_a) and venous outflow (CBF_v) of cerebral blood [17]:

$$ \Updelta {\text{CBV}}= \int\limits_{{t_{0} }}^{t} {\left( {{\text{CBF}}_{\text{a}} (t) - {\text{CBF}}_{\text{v}} (t)} \right){\text{d}}t} $$

(1)

t ₀ denotes beginning of cardiac cycle.

We made an assumption that a low pulsatility venous outflow (CBF_v) may be approximated by constant flow equal to averaged arterial inflow (meanCBF_a) [18]:

$$ {\text{CBFV}}_{\text{v}} = {\text{ meanCBF}}_{\text{a}} $$

(2)

Therefore, the pulsatile cerebral arterial blood volume (ΔC _aBV) can be expressed as:

$$ \Updelta C_{\text{a}} {\text{BV}} = \int\limits_{{t_{0} }}^{t} {\left( {{\text{CBF}}_{\text{a}} (t) - {\text{meanCBF}}_{\text{a}} (t)} \right){\text{d}}t} $$

(3)

Taking into account finite sampling frequency and assuming that cross-sectional area of the insonated vessel (the middle cerebral artery) is equal S _a we can rewrite the previous equation as a discrete time difference equation in terms of flow velocity (CBFV)

$$ C_{\text{a}} {\text{BV}}(n) = S_{\text{a}} \cdot \sum\limits_{i = m}^{n} {\left( {{\text{CBFV}}_{\text{a}} (i) - {\text{meanCBFV}}_{\text{a}} (i)} \right)\Updelta t(i)} $$

(4)

where Δt is the sampling interval and CBFV_a(i) is sample of cerebral arterial blood flow velocity.

Compliance of Cerebral Arterial Bed (C _a)

C _a was estimated as the pulsatile changes in cerebral arterial blood volume (AmpC _aBV) divided by the amplitude of arterial blood pressure (AmpABP) [5, 6].

$$ C_{\text{a}} = \frac{{{\text{Amp}}_{{C_{\text{a}} {\text{BV}}}} \cdot S_{\text{a}} }} {{{\text{Amp}}_{\text{ABP}} }}\left[ {\frac{{{\text{cm}}^{2} \cdot \frac{\text{cm}}{\text{s}} \cdot {\text{s}}}}{\text{mmHg}}} \right] $$

(5)

where AmpC _aBV and AmpABP—the amplitudes of fundamental components (first harmonic) of C _aBV and ABP pulse waveforms, respectively.

Resistance of Cerebrovascular Bed (CVR)

CVR was evaluated according to the following model [19]:

$$ {\text{CVR}} = \frac{\text{meanABP}}{{{\text{meanCBFV}} \cdot S_{\text{a}} }}\left[ {\frac{\text{mmHg}}{{\frac{\text{cm}}{\text{s}} \cdot {\text{cm}}^{2} }}} \right] $$

(6)

where S _a denotes a cross-sectional area of the insonated vessel.

Time Constant of Cerebral Arterial Bed (τ)

τ was assessed as a product of C _a and CVR:

$$ \tau = C_{\text{a}} \cdot {\text {CVR}} = \frac{{{\text{Amp}}_{{C_{\text{a}} {\text{BV}}}} \cdot S_{\text{a}}}}{{{\text{Amp}}_{\text{ABP}} }} \cdot \frac{\text{meanABP}}{{{\text{meanCBFV}} \cdot S_{\text{a}} }}({\text{s}}) $$

(7)

Substituting the Eqs. 5 and 6 into Eq. 7 allowed to eliminate unknown cross-sectional area of the arterial vessel and calculate in seconds the magnitude of time constant of cerebral arterial blood inflow (τ).