This study introduces a new technique, based on the Hilbert-Huang transformation [12, 18], termed multimodal pressure-flow analysis, for assessing the relationships between systemic blood pressure and cerebral blood flow changes associated with provocative maneuvers. Development of this method was motivated by the facts that 1) that the duration of the VM stages and resulting BP and BFV responses vary over time and among subjects, and 2) these types of time series are short and nonstationary, and therefore, not suitable for analysis using standard Fourier transform and autoregressive type approaches. We implemented the MMPF method to evaluate the dynamics of cerebral autoregulation using the instantaneous systemic BP and MCA BFV phase relationships during the VM. The frequency and corresponding BPR and BFVR amplitudes were computed for each data sample to construct a continuous phase diagram. The BPR and BFVR profiles were similar over the course of the VM, but the phase relationships were different. The autoregulation indices, calculated using the standard methods, did not differentiate the groups.
Cerebral vasoregulation compensates for rapid BP and BFV transitions over the course of the VM. A sudden and parallel increase in intrathoracic  and cerebrospinal fluid  pressures is associated with a rapid decline in BP and an initial increase of cerebrovascular resistance, resulting in a rapid decline in BFV. With active autoregulation, cerebrovascular resistance diminishes, enabling BFV to recover in the face of falling perfusion pressure, and BFV responses in the MCA precede the systemic BP changes. Therefore, in healthy controls, the phases corresponding to the BFVR minimum and maximum were smaller than BPR phases, reflecting an active vasoregulatory process. With delayed or impaired autoregulation, BFV becomes synchronized with blood pressure. In the stroke group, the BFVR and BPR phase diagrams were similar, suggesting that cerebral blood flow was entrained by systemic BP. In the stroke and hypertensive groups, BFV phases at the BFVR minimum and maximum were greater compared to the normotensive group. The BP-BFV phase shifts were smaller in the stroke and hypertensive group, compared to healthy controls.
Methods evaluating dynamic cerebral autoregulation that use the Fourier transform-based coherence and transfer functions assume a linear relationship between stationary signals. Coherence, phase and gain derived from the transfer function of spontaneous BP and BFV fluctuations have been used to assess autoregulation. These analyses have shown a significant phase lead of cerebral BFV with respect to systemic BP [4, 20, 21]. However, assumptions about signal stationarity and a linear flow/pressure relationship are not met for the short nonstationary time series from the VM, and therefore transfer function gain was not evaluated. The joint time-frequency distributions , such as the new MMPF developed here, that make no assumptions about signal characteristics and can reliably track simultaneous changes of spectral powers and frequencies, are better suited for these short nonstationary signals. The variable time delay between BP and BFV suggests that the relationship between the cerebral blood flow and systemic pressure is not linear.
Previous studies indicated bilateral impairment of the dynamics of pressure autoregulation after an acute [2, 3] and subacute ischemic stroke . Dynamic indices of autoregulation that were calculated from spontaneous BP and BFV fluctuations were altered, with no significant difference between autoregulatory indices in the affected and unaffected hemispheres. No significant differences were found in autoregulatory indices between large vessel anterior and posterior circulation infarcts and lacunar infarcts . In patients with large hemispheric strokes, head elevations from 0° to 45° induced reductions in arterial BP, BFV, intracranial and perfusion pressures . We have reported  that cerebral vasomotor responses to hypocapnia and hypercapnia were diminished following minor chronic infarctions. Baseline BFVs in the MCAs were similar between the stroke and the non-stroke groups, but differed during head-up tilt. BFV declined in the stroke side MCA during the head-up tilt. Side-to-side BFV differences were the most prominent in stroke-normotensive subjects with lower BP during head-up tilt compared to stroke-hypertensive subjects and non-stroke groups. The present study has confirmed bilateral impairment of autoregulation dynamics in stroke-normotensive and stroke-hypertensive subjects and also in a non-stroke hypertensive group. The BP-BFV phase relationships suggest that the autoregulatory responses were delayed in both hemispheres and that the BFV responses were dependent on perfusion pressure. About one third of stroke patients are hypertensive upon hospital admission. Hypertension and stroke may exert similar pathophysiological effects on vascular compliance, sympatho-vagal interactions  and blood pressure regulation [26, 27]. Increased vascular stiffness, impaired vasodilatation and shift of the autoregulatory responses toward higher BP values may also affect the timing of autoregulatory responses in both hemispheres.
There are several limitations of this study: 1) The MMPF method was implemented for the VM, which is widely used for clinical autonomic testing. The VM allows noninvasive evaluation of pressure autoregulation, and testing can be completed in less than 5 minutes. However, the VM requires active patient cooperation, and may not be advisable in acute stroke settings where change in intracranial pressure should be avoided. 2) This study evaluated a population of younger subjects with minor stroke. A larger cohort is needed to determine the effects of ischemic stroke subtypes on the dynamics of autoregulation. 3) Age was different between groups; however, it had no significant effect on BP-BFV relationship in our analysis. Aging and cardiovascular risk factors exert significant but distinct effects on regulation of cerebral blood flow. The vasomotor reactivity to hypercarbia declines with aging and hypertension, while the dynamics of pressure regulation can be preserved . This effect may be in part due to a shift of the autoregulatory range toward higher blood pressure values.