Non-linear multivariate modeling of cerebral hemodynamics with autoregressive Support Vector Machines

Time-domain methods for quantifying dynamic cerebral blood flow autoregulation: Review and recommendations. A white paper from the Cerebrovascular Research Network (CARNet)

Cerebral Autoregulation (CA) is an important physiological mechanism stabilizing cerebral blood flow (CBF) in response to changes in cerebral perfusion pressure (CPP). By maintaining an adequate, relatively constant supply of blood flow, CA plays a critical role in brain function. Quantifying CA under different physiological and pathological states is crucial for understanding its implications. This knowledge may serve as a foundation for informed clinical decision-making, particularly in cases where CA may become impaired. The quantification of CA functionality typically involves constructing models that capture the relationship between CPP (or arterial blood pressure) and experimental measures of CBF. Besides describing normal CA function, these models provide a means to detect possible deviations from the latter. In this context, a recent white paper from the Cerebrovascular Research Network focused on Transfer Function Analysis (TFA), which obtains frequency domain estimates of dynamic CA. In the present paper, we consider the use of time-domain techniques as an alternative approach. Due to their increased flexibility, time-domain methods enable the mitigation of measurement/physiological noise and the incorporation of nonlinearities and time variations in CA dynamics. Here, we provide practical recommendations and guidelines to support researchers and clinicians in effectively utilizing these techniques to study CA.

A multi-objective optimisation approach for the linear modelling of cerebral autoregulation system

OBJECTIVE

Dynamic cerebral autoregulation (dCA) has been addressed through different approaches for discriminating between normal and impaired conditions based on spontaneous fluctuations in arterial blood pressure (ABP) and cerebral blood flow (CF). This work presents a novel multi-objective optimisation (MO) approach for finding good configurations of a cerebrovascular resistance-compliance model.

METHODS

Data from twenty-nine subjects under normo and hypercapnic (5% CO2 in air) conditions was used. Cerebrovascular resistance and vessel compliance models with ABP as input and CF velocity as output were fitted using a MO approach, considering fitting Pearson's correlation and error.

RESULTS

MO approach finds better model configurations than the single-objective (SO) approach, especially for hypercapnic conditions. In addition, the Pareto-optimal front from the multi-objective approach enables new information on dCA, reflecting a higher contribution of myogenic mechanism for explaining dCA impairment.

Time-Series Modeling and Forecasting of Cerebral Pressure-Flow Physiology: A Scoping Systematic Review of the Human and Animal Literature

The modeling and forecasting of cerebral pressure-flow dynamics in the time-frequency domain have promising implications for veterinary and human life sciences research, enhancing clinical care by predicting cerebral blood flow (CBF)/perfusion, nutrient delivery, and intracranial pressure (ICP)/compliance behavior in advance. Despite its potential, the literature lacks coherence regarding the optimal model type, structure, data streams, and performance. This systematic scoping review comprehensively examines the current landscape of cerebral physiological time-series modeling and forecasting. It focuses on temporally resolved cerebral pressure-flow and oxygen delivery data streams obtained from invasive/non-invasive cerebral sensors. A thorough search of databases identified 88 studies for evaluation, covering diverse cerebral physiologic signals from healthy volunteers, patients with various conditions, and animal subjects. Methodologies range from traditional statistical time-series analysis to innovative machine learning algorithms. A total of 30 studies in healthy cohorts and 23 studies in patient cohorts with traumatic brain injury (TBI) concentrated on modeling CBFv and predicting ICP, respectively. Animal studies exclusively analyzed CBF/CBFv. Of the 88 studies, 65 predominantly used traditional statistical time-series analysis, with transfer function analysis (TFA), wavelet analysis, and autoregressive (AR) models being prominent. Among machine learning algorithms, support vector machine (SVM) was widely utilized, and decision trees showed promise, especially in ICP prediction. Nonlinear models and multi-input models were prevalent, emphasizing the significance of multivariate modeling and forecasting. This review clarifies knowledge gaps and sets the stage for future research to advance cerebral physiologic signal analysis, benefiting neurocritical care applications.

Can Alterations in Cerebrovascular CO2 Reactivity Be Identified Using Transfer Function Analysis without the Requirement for Carbon Dioxide Inhalation?

The present study aimed to examine the validity of a novel method to assess cerebrovascular carbon dioxide (CO₂) reactivity (CVR) that does not require a CO₂ inhalation challenge, e.g., for use in patients with respiratory disease or the elderly, etc. In twenty-one healthy participants, CVR responses to orthostatic stress (50° head-up tilt, HUT) were assessed using two methods: (1) the traditional CO₂ inhalation method, and (2) transfer function analysis (TFA) between middle cerebral artery blood velocity (MCA V) and predicted arterial partial pressure of CO₂ (PaCO₂) during spontaneous respiration. During HUT, MCA V steady-state (i.e., magnitude) and MCA V onset (i.e., time constant) responses to CO₂ inhalation were decreased (p < 0.001) and increased (p = 0.001), respectively, indicative of attenuated CVR. In contrast, TFA gain in the very low-frequency range (VLF, 0.005-0.024 Hz) was unchanged, while the TFA phase in the VLF approached zero during HUT (-0.38 ± 0.59 vs. 0.31 ± 0.78 radians, supine vs. HUT; p = 0.003), indicative of a shorter time (i.e., improved) response of CVR. These findings indicate that CVR metrics determined by TFA without a CO₂ inhalation do not track HUT-evoked reductions in CVR identified using CO₂ inhalation, suggesting that enhanced cerebral blood flow response to a change in CO₂ using CO₂ inhalation is necessary to assess CVR adequately.

Machine Learning Models and Statistical Complexity to Analyze the Effects of Posture on Cerebral Hemodynamics

The mechanism of cerebral blood flow autoregulation can be of great importance in diagnosing and controlling a diversity of cerebrovascular pathologies such as vascular dementia, brain injury, and neurodegenerative diseases. To assess it, there are several methods that use changing postures, such as sit-stand or squat-stand maneuvers. However, the evaluation of the dynamic cerebral blood flow autoregulation (dCA) in these postures has not been adequately studied using more complex models, such as non-linear ones. Moreover, dCA can be considered part of a more complex mechanism called cerebral hemodynamics, where others (CO2 reactivity and neurovascular-coupling) that affect cerebral blood flow (BF) are included. In this work, we analyzed postural influences using non-linear machine learning models of dCA and studied characteristics of cerebral hemodynamics under statistical complexity using eighteen young adult subjects, aged 27 ± 6.29 years, who took the systemic or arterial blood pressure (BP) and cerebral blood flow velocity (BFV) for five minutes in three different postures: stand, sit, and lay. With models of a Support Vector Machine (SVM) through time, we used an AutoRegulatory Index (ARI) to compare the dCA in different postures. Using wavelet entropy, we estimated the statistical complexity of BFV for three postures. Repeated measures ANOVA showed that only the complexity of lay-sit had significant differences.

The INfoMATAS project: Methods for assessing cerebral autoregulation in stroke

Cerebral autoregulation refers to the physiological mechanism that aims to maintain blood flow to the brain approximately constant when blood pressure changes. Impairment of this protective mechanism has been linked to a number of serious clinical conditions, including carotid stenosis, head trauma, subarachnoid haemorrhage and stroke. While the concept and experimental evidence is well established, methods for the assessment of autoregulation in individual patients remains an open challenge, with no gold-standard having emerged. In the current review paper, we will outline some of the basic concepts of autoregulation, as a foundation for experimental protocols and signal analysis methods used to extract indexes of cerebral autoregulation. Measurement methods for blood flow and pressure are discussed, followed by an outline of signal pre-processing steps. An outline of the data analysis methods is then provided, linking the different approaches through their underlying principles and rationale. The methods cover correlation based approaches (e.g. Mx) through Transfer Function Analysis to non-linear, multivariate and time-variant approaches. Challenges in choosing which method may be 'best' and some directions for ongoing and future research conclude this work.

Superior fitting of arterial resistance and compliance parameters with genetic algorithms in models of dynamic cerebral autoregulation

OBJECTIVE

The capacity of discriminating between normal and impaired dynamic cerebral autoregulation (dCA), based on spontaneous fluctuations in arterial blood pressure (ABP) and cerebral blood flow (CBF), has considerable clinical relevance. This study aimed to quantify the separate contributions of vascular resistance and compliance as parameters that could reflect myogenic and metabolic mechanisms to dCA.

METHODS

Forty-five subjects were studied under normo and hypercapnic conditions induced by breathing a mixture of 5% carbon dioxide in air. Dynamic cerebrovascular resistance and compliance models with ABP as input and CBFV as output were fitted using Genetic Algorithms to identify parameter values for each subject, and respiratory condition.

RESULTS

The efficiency of dCA was assessed from the models generated CBFV response to an ABP step change, corresponding to an autoregulation index of 5.561.57 in normocapnia and 2.381.73 in hypercapnia, with an area under the ROC curve (AUC) of 0.9 between both conditions. Vascular compliance increased from 0.750.7 ml/mmHg in normocapnia to 5.8212.0 ml/mmHg during hypercapnia, with an AUC of 0.88.

CONCLUSION

we demonstrated that Genetic Algorithms are a powerful tool to provide accurate identification of model parameters expressing the performance of human CA Significance: Further work is needed to validate this approach in clinical applications where individualised model parameters could provide relevant diagnostic and prognostic information about dCA impairment Index Terms arterial compliance, autoregulation impairment, cerebral blood flow, Genetic Algorithms, hypercapnia.

Determinants of cerebral blood flow velocity change during squat-stand maneuvers

The large changes in mean arterial blood pressure (MABP) and cerebral blood flow velocity (CBFV) induced by squat-stand maneuvers (SSM) make this approach particularly suited for studying dynamic cerebral autoregulation (CA). However, the role of other systemic determinants of CBFV has not been described and could provide alternative physiological interpretations of SSM results. In 32 healthy subjects (16 female), continuous recordings of MABP (Finometer), bilateral CBFV (transcranial Doppler, MCA), end-tidal CO₂ (EtCO₂; capnography), and heart rate (HR; electrocardiogram) were performed for 5 min standing at rest, and during 15 SSM at the frequency of 0.05 Hz. A time-domain, multivariate dynamic model estimated the CBFV variance explained by different inputs, corresponding to significant contributions from MABP (P < 0.00001), EtCO₂ (P < 0.0001), and HR (P = 0.041). The autoregulation index (ARI; range 0-9) was estimated from the CBFV response to a step change in MABP. At rest, ARI values (typically 5.7) were independent of the number of model inputs, but during SSM, ARI was reduced compared with baseline (P < 0.0001), and the three input model yielded lower values for the right and left MCA (3.4 ± 1.2, 3.1 ± 1.3) when compared with the single-input MABP-CBFV model (4.1 ± 1.1, 3.9 ± 1.0; P < 0.0001). The high coherence of the MABP-CBFV transfer function at 0.05 Hz (typically 0.98) was considerably reduced (around 0.71-0.73; P < 0.0001) when the contribution of CBFV covariates was taken into account. Not taking into consideration other determinants of CBFV, in addition to MABP, could be misleading and introduce biases in physiological and clinical studies.

Alternative representation of neural activation in multivariate models of neurovascular coupling in humans

Neural stimulation leads to increases in cerebral blood flow (CBF), but simultaneous changes in covariates, such as arterial blood pressure (BP) and [Formula: see text], rule out the use of CBF changes as a reliable marker of neurovascular coupling (NVC) integrity. Healthy subjects performed repetitive (1 Hz) passive elbow flexion with their dominant arm for 60 s. CBF velocity (CBFV) was recorded bilaterally in the middle cerebral artery with transcranial Doppler, BP with the Finometer device, and end-tidal CO2 (EtCO2) with capnography. The simultaneous effects of neural stimulation, BP, and [Formula: see text] on CBFV were expressed with a dynamic multivariate model, using BP, EtCO2, and stimulation [ s( t)] as inputs. Two versions of s( t) were considered: a gate function [ sG( t)] or an orthogonal decomposition [ sO( t)] function. A separate CBFV step response was extracted from the model for each of the three inputs, providing estimates of dynamic cerebral autoregulation [CA; autoregulation index (ARI)], CO2 reactivity [vasomotor reactivity step response (VMRSR)], and NVC [stimulus step response (STIMSR)]. In 56 subjects, 224 model implementations produced excellent predictive CBFV correlation (median r = 0.995). Model-generated sO( t), for both dominant (DH) and nondominant (NDH) hemispheres, was highly significant during stimulation (<10−5) and was correlated with the CBFV change ( r = 0.73, P = 0.0001). The sO( t) explained a greater fraction of CBFV variance (~50%) than sG( t) (44%, P = 0.002). Most CBFV step responses to the three inputs were physiologically plausible, with better agreement for the CBFV-BP step response yielding ARI values of 7.3 for both DH and NDH for sG( t), and 6.9 and 7.4 for sO( t), respectively. No differences between DH and NDH were observed for VMRSR or STIMSR. A new procedure is proposed to represent the contribution from other aspects of CBF regulation than BP and CO2 in response to sensorimotor stimulation, as a tool for integrated, noninvasive, assessment of the multiple influences of dynamic CA, CO2 reactivity, and NVC in humans.

NEW & NOTEWORTHY A new approach was proposed to identify the separate contributions of stimulation, arterial blood pressure (BP), and arterial CO2 ([Formula: see text]) to the cerebral blood flow (CBF) response observed in neurovascular coupling (NVC) studies in humans. Instead of adopting an empirical gate function to represent the stimulation input, a model-generated function is derived as part of the modeling process, providing a representation of the NVC response, independent of the contributions of BP or [Formula: see text]. This new marker of NVC, together with the model-predicted outputs for the contributions of BP, [Formula: see text] and stimulation, has considerable potential to both quantify and simultaneously integrate the separate mechanisms involved in CBF regulation, namely, cerebral autoregulation, CO2 reactivity and other contributions.

Non-linear models for the detection of impaired cerebral blood flow autoregulation

The ability to discriminate between normal and impaired dynamic cerebral autoregulation (CA), based on measurements of spontaneous fluctuations in arterial blood pressure (BP) and cerebral blood flow (CBF), has considerable clinical relevance. We studied 45 normal subjects at rest and under hypercapnia induced by breathing a mixture of carbon dioxide and air. Non-linear models with BP as input and CBF velocity (CBFV) as output, were implemented with support vector machines (SVM) using separate recordings for learning and validation. Dynamic SVM implementations used either moving average or autoregressive structures. The efficiency of dynamic CA was estimated from the model's derived CBFV response to a step change in BP as an autoregulation index for both linear and non-linear models. Non-linear models with recurrences (autoregressive) showed the best results, with CA indexes of 5.9 ± 1.5 in normocapnia, and 2.5 ± 1.2 for hypercapnia with an area under the receiver-operator curve of 0.955. The high performance achieved by non-linear SVM models to detect deterioration of dynamic CA should encourage further assessment of its applicability to clinical conditions where CA might be impaired.

Comparing Models of Spontaneous Variations, Maneuvers and Indexes to Assess Dynamic Cerebral Autoregulation

OBJECTIVE

We analyzed the performance of linear and nonlinear models to assess dynamic cerebral autoregulation (dCA) from spontaneous variations in healthy subjects and compared it with the use of two known maneuvers to abruptly change arterial blood pressure (BP): thigh cuffs and sit-to-stand.

MATERIALS AND METHODS

Cerebral blood flow velocity and BP were measured simultaneously at rest and while the maneuvers were performed in 20 healthy subjects. To analyze the spontaneous variations, we implemented two types of models using support vector machine (SVM): linear and nonlinear finite impulse response models. The classic autoregulation index (ARI) and the more recently proposed model-free ARI (mfARI) were used as measures of dCA. An ANOVA analysis was applied to compare the different methods and the coefficient of variation was calculated to evaluate their variability.

RESULTS

There are differences between indexes, but not between models and maneuvers. The mfARI index with the sit-to-stand maneuver shows the least variability.

CONCLUSIONS

Support vector machine modeling of spontaneous variation with the mfARI index could be used for the assessment of dCA as an alternative to maneuvers to introduce large BP fluctuations.

Applying time-frequency analysis to assess cerebral autoregulation during hypercapnia

OBJECTIVE

Classic methods for assessing cerebral autoregulation involve a transfer function analysis performed using the Fourier transform to quantify relationship between fluctuations in arterial blood pressure (ABP) and cerebral blood flow velocity (CBFV). This approach usually assumes the signals and the system to be stationary. Such an presumption is restrictive and may lead to unreliable results. The aim of this study is to present an alternative method that accounts for intrinsic non-stationarity of cerebral autoregulation and the signals used for its assessment.

METHODS

Continuous recording of CBFV, ABP, ECG, and end-tidal CO2 were performed in 50 young volunteers during normocapnia and hypercapnia. Hypercapnia served as a surrogate of the cerebral autoregulation impairment. Fluctuations in ABP, CBFV, and phase shift between them were tested for stationarity using sphericity based test. The Zhao-Atlas-Marks distribution was utilized to estimate the time-frequency coherence (TFCoh) and phase shift (TFPS) between ABP and CBFV in three frequency ranges: 0.02-0.07 Hz (VLF), 0.07-0.20 Hz (LF), and 0.20-0.35 Hz (HF). TFPS was estimated in regions locally validated by statistically justified value of TFCoh. The comparison of TFPS with spectral phase shift determined using transfer function approach was performed.

RESULTS

The hypothesis of stationarity for ABP and CBFV fluctuations and the phase shift was rejected. Reduced TFPS was associated with hypercapnia in the VLF and the LF but not in the HF. Spectral phase shift was also decreased during hypercapnia in the VLF and the LF but increased in the HF. Time-frequency method led to lower dispersion of phase estimates than the spectral method, mainly during normocapnia in the VLF and the LF.

CONCLUSION

The time-frequency method performed no worse than the classic one and yet may offer benefits from lower dispersion of phase shift as well as a more in-depth insight into the dynamic nature of cerebral autoregulation.

Neurovascular coupling in humans: Physiology, methodological advances and clinical implications

Neurovascular coupling reflects the close temporal and regional linkage between neural activity and cerebral blood flow. Although providing mechanistic insight, our understanding of neurovascular coupling is largely limited to non-physiologicalex vivopreparations and non-human models using sedatives/anesthetics with confounding cerebrovascular implications. Herein, with particular focus on humans, we review the present mechanistic understanding of neurovascular coupling and highlight current approaches to assess these responses and the application in health and disease. Moreover, we present new guidelines for standardizing the assessment of neurovascular coupling in humans. To improve the reliability of measurement and related interpretation, the utility of new automated software for neurovascular coupling is demonstrated, which provides the capacity for coalescing repetitive trials and time intervals into single contours and extracting numerous metrics (e.g., conductance and pulsatility, critical closing pressure, etc.) according to patterns of interest (e.g., peak/minimum response, time of response, etc.). This versatile software also permits the normalization of neurovascular coupling metrics to dynamic changes in arterial blood gases, potentially influencing the hyperemic response. It is hoped that these guidelines, combined with the newly developed and openly available software, will help to propel the understanding of neurovascular coupling in humans and also lead to improved clinical management of this critical physiological function.

A new model-free index of dynamic cerebral blood flow autoregulation

The classic dynamic autoregulatory index (ARI), proposed by Aaslid and Tiecks, is one of the most widely used methods to assess the efficiency of dynamic cerebral autoregulation. Although this index is often used in clinical research and is also included in some commercial equipment, it exhibits considerable intra-subject variability, and has the tendency to produce false positive results in clinical applications. An alternative index of dynamic cerebral autoregulation is proposed, which overcomes most of the limitations of the classic method and also has the advantage of being model-free. This new index uses two parameters that are obtained directly from the response signal of the cerebral blood flow velocity to a transient decrease in arterial blood pressure provoked by the sudden release of bilateral thigh cuffs, and a third parameter measuring the difference in slope of this response and the change in arterial blood pressure achieved. With the values of these parameters, a corresponding classic autoregulatory index value could be calculated by using a linear regression model built from theoretical curves generated with the Aaslid-Tiecks model. In 16 healthy subjects who underwent repeated thigh-cuff manoeuvres, the model-free approach exhibited significantly lower intra-subject variability, as measured by the unbiased coefficient of variation, than the classic autoregulatory index (p = 0.032) and the Rate of Return (p<0.001), another measure of cerebral autoregulation used for this type of systemic pressure stimulus, from 39.23%±41.91% and 55.31%±31.27%, respectively, to 15.98%±7.75%.

Contribution of arterial blood pressure and PaCO2 to the cerebrovascular responses to motor stimulation

Motor stimulation induces a neurovascular response that can be detected by continuous measurement of cerebral blood flow (CBF). Simultaneous changes in arterial blood pressure (ABP) and PaCO2 have been reported, but their influence on the CBF response has not been quantified. Continuous bilateral recordings of CBF velocity (CBFV), ABP, and end-tidal CO2 (ETCO2) were obtained in 10 healthy middle-aged subjects at rest and during 60 s of repetitive, metronome-controlled (1 Hz) elbow flexion. A multivariate autoregressive-moving average model was adopted to quantify the relationship between beat-to-beat changes in ABP, breath-by-breath ETCO2, and the motor stimulus, represented by the metronome on-off signal (inputs), and the CBFV response to stimulation (output). All three inputs contributed to explain CBFV variance following stimulation. For the ipsi- and contralateral hemispheres, ABP explained 20.3 ± 17.3% ( P = 0.0007) and 19.5 ± 17.2% ( P = 0.01) of CBFV variance, respectively. Corresponding values for ETCO2 and metronome signals were 22.0 ± 24.2% ( P = 0.008), 24.0 ± 24.1% ( P = 0.037), 32.7 ± 22.5% ( P = 0.0015), and 43.2 ± 25.1% ( P = 0.013), respectively. Synchronized population averages suggest that the initial sudden change in CBFV was largely due to ABP, while the influence of ETCO2 was more erratic. The component due to elbow flexion showed a well-defined pattern, with rise time slower than the main CBFV change but reaching a stable plateau after 15 s of stimulation. Identifying and removing the influences of ABP and PaCO2 to motor-induced changes in CBF should lead to more robust estimates of neurovascular coupling and better understanding of its physiological covariates.