Letter to the editor: Deriving transfer function analysis metrics from driven methods

Abstract

Driven and spontaneous methods have been used to quantify the cerebral pressure-flow relationship via transfer function analysis (TFA). Commonly, TFA derived estimates are assessed using band averages within the very-low (0.02–0.07 Hz) and low (0.07–0.20 Hz) frequency during spontaneous oscillations but are quantified at frequencies of interest where blood pressure oscillations are driven (e.g., 0.05 and/or 0.10 Hz). Driven estimates more closely resemble the autoregulatory challenges individuals experience on a daily basis, while also eliciting higher levels of reliability. While driven estimates with point-estimates are not feasible for all clinical populations, these approaches increase the ability to understand pathophysiological changes.

Transfer functional analysis (TFA) has been a widely used approach to quantify dynamic cerebral autoregulation (dCA) through both spontaneous and driven techniques. ¹ The former consists of quantifying the relationship between arterial blood pressure and cerebral blood velocity (CBv) during quiet sitting/standing positions, where band averages are used in the very-low-frequency (0.02–0.07 Hz) and low-frequency (0.07–0.20 Hz) to derive phase, gain, and normalized gain estimates.^2,3 Conversely, driven techniques produce ephemeral blood pressure changes at a given frequency, where point-estimates (e.g., 0.05 Hz, 0.10 Hz) or narrow-band (e.g., 0.04–0.06 Hz, 0.09–0.11 Hz) averages are used to derive TFA parameters around these frequencies. ⁴ Compared to spontaneous metrics with band averages, the reliability of TFA metrics produced from point estimates at a driven frequency is substantially augmented. For example, papers by Smirl et al., ⁴ and Burma et al., ⁵ highlight the between-day coefficient of variation for spontaneous metrics was ∼60–80% on average, while those assessed via squat-stand maneuvers were <20%. The bottom panel in Figure 1 demonstrates the between-day reliability between point-estimates, narrow band-estimates, and typical band-estimates from driven and spontaneous measures. The reproducibility of TFA estimates is largely influenced by physiological variability,^{3 –5} which reduces the direct linearity between arterial blood pressure and cerebral blood velocity (i.e., cerebral autoregulation). However, employing driven approaches minimizes the physiological variability in the cerebral pressure-flow relationship by augmenting the linearity, as quantified as a coherence value approaching 1.00.^{3 –5} This is achieved by driven methods augmenting the blood pressure power spectral densities from ∼5–10 mmHg²/Hz under spontaneous methods^{3 –5} to ∼500–2000 mmHg²/Hz during oscillatory lower body negative pressure ⁴ and 10000–20000 mmHg²/Hz during squat-stand maneuvers protocols.^{3 –5} While slightly lower, the cerebral blood velocity power spectral density values will have a similar relative increase.^{3 –5} The augmented power spectral densities will allow for a comparison of the cerebral pressure-flow relationship that is less influenced by other physiological variables such as respiratory parameters (Figure 1). Most importantly, it should be noted that despite the large blood pressure oscillations occurring (∼30–50 mmHg), this does not diminish/overwhelm the regulatory function of the cerebrovasculature. ⁶

Figure 1.

(a) Blood pressure and cerebral blood velocity power spectral densities obtained during squat-stand maneuvers (SSMs) at 0.05 (blue) and 0.10 (red) Hz and from spontaneous standing (black) conditions in one participant. Data are displayed across the cardiac cycle with blood pressure and cerebral blood velocity measured in (mmHg)²/Hz and (cm/s)²/Hz, respectively. Point-estimates from driven techniques are derived from at 0.05 and/or 0.10 Hz, while spontaneous metrics are computed from band averages in very low frequency (VLF; 0.02–0.07 Hz) and the low frequency (LF; 0.07–0.20 Hz) bands and (b) The between-day reliability of mean transfer function analysis estimates drawn from 10 healthy individuals during squat-stand maneuvers (SSMs) and from spontaneous approaches. The reliability was assessed as point-estimate (0.05 and 0.10 Hz) and narrow-band averages (0.04–0.06 and 0.09–0.11 Hz) for the SSMs. Spontaneous measures were calculated as band averages in the VLF (0.02–0.07 Hz) and the LF (0.07–0.20 Hz) ranges, as well as narrow band averages (0.04–0.06 and 0.09–0.11 Hz) to compare it to those obtained from the SSMs.

This has important ramifications for studies seeking to identify physiological differences between healthy and clinical populations, as well as those completing longitudinal assessments. For example, if comparing a concussion population to healthy controls, having inter-individual differences of 60–80% may abolish any true group differences, increasing the likelihood of making a Type II error. This would be especially important if employing a longitudinal study design to identify the extent autoregulatory deficits emerge during disease progression (e.g., Alzheimer’s, cognitive impairment), as highly variable point estimates would impede the ability to accurately demarcate disease projection. In addition to TFA, utilizing approaches that produce sufficient arterial blood pressure oscillations, allows researchers to also quantify the directional sensitivity of the cerebral pressure-flow relationship. ⁷ For more information, a review by Brassard et al., ⁸ further discusses the notion of directional sensitivity and the current state of the literature. Additionally, cardiac cycle differences in dCA are known to exist, which are more pronounced when driven measures are used. ⁵ As the brain is confined within the skull, the cerebrovasculature can only expand to a certain degree to ensure intracranial pressure does not increase (i.e., Monro-Kellie Doctrine). ⁹ This results in systolic measures displaying lower gain and higher phase values, indicative of better regulation. However, these cardiac cycle differences are only elicited when using sufficient arterial blood pressure oscillations. While driven approaches have their benefits, these are not practical for all clinical populations (e.g., acute stroke, severe traumatic brain injury). Nevertheless, these techniques, including sit-to-stand and squat-stand maneuvers, have been used across a wide variety of clinical patients. These are further detailed in the supplemental material. The advantages and limitations of driven and spontaneous techniques are additionally described in the supplemental material.

In conclusion, the authors agree with Liu, Simpson, and Panerai ¹⁰ in that a one-size-fits-all approach may not be dogmatic. The current letter to the editor focused primarily on deriving TFA estimates; however, a plethora of other techniques exist to quantify dCA. ⁸ The specific approach may differ depending on the analysis of interest (e.g., machine learning, time domain, wavelet coupling, etc.). Nonetheless, when selecting a methodological approach for a research design, ⁸ it is essential researchers do not sacrifice ease of implementation for more highly valid and reliable approaches.