Feasibility of Hidden Markov Models for the Description of Time-Varying Physiologic State After Severe Traumatic Brain Injury.

OBJECTIVES: Continuous assessment of physiology after traumatic brain injury is essential to prevent secondary brain insults. The present work aims at the development of a method for detecting physiologic states associated with the outcome from time-series physiologic measurements using a hidden Markov model. DESIGN: Unsupervised clustering of hourly values of intracranial pressure/cerebral perfusion pressure, the compensatory reserve index, and autoregulation status was attempted using a hidden Markov model. A ternary state variable was learned to classify the patient's physiologic state at any point in time into three categories ("good," "intermediate," or "poor") and determined the physiologic parameters associated with each state. SETTING: The proposed hidden Markov model was trained and applied on a large dataset (28,939 hr of data) using a stratified 20-fold cross-validation. PATIENTS: The data were collected from 379 traumatic brain injury patients admitted to Addenbrooke's Hospital, Cambridge between 2002 and 2016. INTERVENTIONS: Retrospective observational analysis. MEASUREMENTS AND MAIN RESULTS: Unsupervised training of the hidden Markov model yielded states characterized by intracranial pressure, cerebral perfusion pressure, compensatory reserve index, and autoregulation status that were physiologically plausible. The resulting classifier retained a dose-dependent prognostic ability. Dynamic analysis suggested that the hidden Markov model was stable over short periods of time consistent with typical timescales for traumatic brain injury pathogenesis. CONCLUSIONS: To our knowledge, this is the first application of unsupervised learning to multidimensional time-series traumatic brain injury physiology. We demonstrated that clustering using a hidden Markov model can reduce a complex set of physiologic variables to a simple sequence of clinically plausible time-sensitive physiologic states while retaining prognostic information in a dose-dependent manner. Such states may provide a more natural and parsimonious basis for triggering intervention decisions

Critical Closing Pressure During Controlled Increase in Intracranial Pressure - Comparison of Three Methods

Critical closing pressure (CrCP) is the arterial blood pressure (ABP) threshold, below which small arterial vessels collapse and cerebral blood flow ceases. Here we aim to compare three methods for CrCPestimation in scenario of a controlled increase in intracranial pressure (ICP), induced by infusion tests performed in patients with suspected normal pressure hydrocephalus (NPH). METHODS: Computer recordings of directly-measured ICP, ABP and transcranial Doppler cerebral blood flow velocity (CBFV), from 37 NPH patients undergoing infusion tests, were retrospectively analyzed. The CrCP was calculated with three methods: one with the first harmonics ratio of the pulse waveforms of ABP and CBFV (CrCPA) and two methods based on a model of cerebrovascular impedance, as functions of both cerebral perfusion pressure (CrCPinv), and of ABP (CrCPninv). CONCLUSION: All methods give similar results in response to ICP changes. In the case of individual CrCP measurements for each patient, CrCPA may provide negative, non-physiological values. Invasive critical closing pressure is most sensitive to variations in ICP and CPP and can be used as an indicator of the cerebrospinal and the cerebrovascular system status during infusion tests.This study was partially supported by the statutory fund of the Mossakowski Medical Research Centre Polish Academy of Sciences and Institute of Electronic Systems, Warsaw University of Technology. Katarzyna Kaczmarska was also supported by the European Union in the framework of the European Social Fund through the Warsaw University of Technology Development Programme

Can interhemispheric desynchronization of cerebral blood flow anticipate upcoming vasospasm in aneurysmal subarachnoid haemorrhage patients?

BACKGROUND: Asymmetry of cerebral autoregulation (CA) was demonstrated in patients after aneurysmal subarachnoid haemorrhage (aSAH). A classical method for CA assessment requires simultaneous measurement of both arterial blood pressure (ABP) and cerebral blood flow velocity (CBFV). In this study, we have proposed a cerebral blood flow asymmetry index based only on CBFV and analysed its association with the occurrence of vasospasm after aSAH. NEW METHOD: The phase shifts (PS) between slow oscillations in left and right CBFV (side-to-side PS) and between ABP and CBFV (CBFV-ABP PS) were estimated using multichannel matching pursuit (MMP) and cross-spectral analysis. RESULTS: We retrospectively analysed data collected from 45 aSAH patients (26 with vasospasm). Data were analysed up to 7th day after aSAH unless the vasospasm was detected earlier. A progressive asymmetry, manifested by a gradual increase in side-to-side PS on consecutive days after aSAH, was observed in patients who developed vasospasm (Radj2 = 0.14, p = 0.009). In these patients, early side-to-side PS was more positive than in patients without vasospasm (2.8° ± 5.6° vs -1.7° ± 5.7°, p = 0.011). No such a difference was found in CBFV-ABP PS. Patients with positive side-to-side PS were more likely to develop vasospasm than patients with negative side-to-side PS (21/7 vs 5/12, p = 0.0047). COMPARISON WITH EXISTING METHOD: MMP, in contrast to the spectral approach, accounts for non-stationarity of analysed signals. MMP applied to the PS estimation reflects the cerebral blood flow asymmetry in aSAH better than the spectral analysis. CONCLUSIONS: Changes in side-to-side PS might be helpful to identify patients who are at risk of vasospasm

A comparison of the time constant of the cerebral arterial bed using invasive and non-invasive arterial blood pressure measurements

Abstract: Objective: The time constant of the cerebral arterial bed (τ), which is an index of brain haemodynamics, can be estimated in patients using continuous monitoring of arterial blood pressure (ABP), transcranial Doppler cerebral blood flow velocity (CBFV) and intracranial pressure (ICP) if these measures are available. But, in some clinical scenarios invasive measurement of ABP is not feasible. Therefore, in this study we aimed to investigate whether invasive ABP can be replaced with non-invasive ABP, monitored using the Finapres photoplethysmograph (fABP). Approach: Forty-six recordings of ICP, ABP, fABP, and CBFV in the right and left middle cerebral arteries were performed daily for approximately 30 min in 10 head injury patients. Two modelling approaches (constant flow forward [CFF, pulsatile blood inflow and steady blood outflow] and pulsatile flow forward [PFF, where both blood inflow and outflow are pulsatile]) were applied to estimate τ using either invasive ABP (τCFF, τPFF) or non-invasive ABP (fτCFF, fτPFF). Main results: Bland–Altman analysis showed quite poor agreement between the fτ and τ methods of estimation. The fτ method produced significantly higher values than the τ method when calculated using both the CFF and PFF models (p < .001 for both). The correlation between fτCFF and τCFF was moderately high (r s = 0.63; p < .001), whereas that between fτPFF and τPFF was weaker (r s = 0.40; p = .009). Significance: Our results suggest that using non-invasive ABP for estimation of τ is inaccurate in head injury patients

Relationship Between Baroreflex and Cerebral Autoregulation in Patients With Cerebral Vasospasm After Aneurysmal Subarachnoid Hemorrhage.

Introduction: Common consequences following aneurysmal subarachnoid hemorrhage (aSAH) are cerebral vasospasm (CV), impaired cerebral autoregulation (CA), and disturbance in the autonomic nervous system, as indicated by lower baroreflex sensitivity (BRS). The compensatory interaction between BRS and CA has been shown in healthy volunteers and stable pathological conditions such as carotid atherosclerosis. The aim of this study was to investigate whether the inverse correlation between BRS and CA would be lost in patients after aSAH during vasospasm. A secondary objective was to analyze the time-trend of BRS after aSAH. Materials and Methods: Retrospective analysis of prospectively collected data was performed at the Neuro-Critical Care Unit of Addenbrooke's Hospital (Cambridge, UK) between June 2010 and January 2012. The cerebral blood flow velocity (CBFV) was measured in the middle cerebral artery using transcranial Doppler ultrasonography (TCD). The arterial blood pressure (ABP) was monitored invasively through an arterial line. CA was quantified by the correlation coefficient (Mxa) between slow oscillations in ABP and CBFV. BRS was calculated using the sequential cross-correlation method using the ABP signal. Results: A total of 73 patients with aSAH were included. The age [median (lower-upper quartile)] was 58 (50-67). WFNS scale was 2 (1-4) and the modified Fisher scale was 3 (1-3). In the total group, 31 patients (42%) had a CV and 42 (58%) had no CV. ABP and CBFV were higher in patients with CV during vasospasm compared to patients without CV (p = 0.001 and p < 0.001). There was no significant correlation between Mxa and BRS in patients with CV, neither during nor before vasospasm. In patients without CV, a significant, although moderate correlation was found between BRS and Mxa (rS = 0.31; p = 0.040), with higher BRS being associated with worse CA. Multiple linear regression analysis showed a significant worsening of BRS after aSAH in patients with CV (R p = -0.42; p < 0.001). Conclusions: Inverse compensatory correlation between BRS and CA was lost in patients who developed CV after aSAH, both before and during vasospasm. The impact of these findings on the prognosis of aSAH should be investigated in larger studies

Baroreflex sensitivity and heart rate variability are predictors of mortality in patients with aneurysmal subarachnoid haemorrhage.

OBJECT: We aimed to investigate the link between the autonomic nervous system (ANS) impairment, assessed using baroreflex sensitivity (BRS) and heart rate variability (HRV) indices, and mortality after aneurysmal subarachnoid haemorrhage (aSAH). METHODS: A total of 57 patients (56 ± 18 years) diagnosed with aSAH were retrospectively enrolled in the study, where 25% of patients died in the hospital. BRS was calculated using a modified cross-correlation method. Time- and frequency-domain HRV indices were calculated from a time-series of systolic peak intervals of arterial blood pressure signals. Additionally, cerebral autoregulation (CA) was assessed using the mean velocity index (Mxa), where Mxa > 0 indicates impaired CA. RESULTS: Both BRS and HRV indices were lower in non-survivors than in survivors. The patients with disturbed BRS and HRV had more extensive haemorrhage in the H-H scale (p = .040) and were more likely to die (p = .013) when compared to patients with the intact ANS. The logistic regression model for mortality included: the APACHE II score (p = .002; OR 0.794) and the normalised high frequency power of the HRV (p < <.001; OR 0.636). A positive relationship was found between the Mxa and BRS (R = 0.48, p = .003), which suggests that increasing BRS is moderately strongly associated with worsening CA. CONCLUSION: Our results indicated that lower values of HRV indices and BRS correlate with mortality and that there is a link between cerebral dysautoregulation and the analysed estimates of the ANS in aSAH patients

Analysis of relative changes in pulse shapes of intracranial pressure and cerebral blood flow velocity.

Objective.Analysis of relative changes in the shapes of pulse waveforms of intracranial pressure (ICP) and transcranial Doppler cerebral blood flow velocity (CBFV) may provide information on intracranial compliance. We tested this hypothesis, introducing an index named the ratio of pulse slopes (RPS) that is based on inclinations of the ascending parts of the ICP and CBFV pulse waveforms. It has hypothetically a simple interpretation: a value of 1 indicates good compliance and a value less than 1, reduced compliance. Here, we investigated the usefulness of RPS for assessment of intracranial compliance.Approach.ICP and CBFV signals recorded simultaneously in 30 normal-pressure hydrocephalus patients during infusion tests were retrospectively analysed. CBFV was measured in the middle cerebral artery. Changes in RPS during the test were compared with changes in the height ratio of the first and second peak of the ICP pulse (P1/P2) and the shape of the ICP pulse was classified from normal (1) to pathological (4). Values are medians (lower, upper quartiles).Main results.There was a significant correlation between baseline RPS and intracranial elasticity (R = -0.55,p = 0.0018). During the infusion tests, both RPS and P1/P2 decreased with rising ICP [RPS, 0.80 (0.56, 0.92) versus 0.63 (0.44, 0.80),p = 0.00015; P1/P2, 0.58 (0.50, 0.91) versus 0.52 (0.36, 0.71),p = 0.00009] while the ICP pulses became more pathological in shape [class: 3 (2, 3) versus 3 (3, 4),p = 0.04]. The magnitude of the decrease in RPS during infusion was inversely correlated with baseline P1/P2 (R = -0.40,p < 0.03).Significance.During infusion, the slopes of the ascending parts of ICP and CBFV pulses become increasingly divergent with a shift in opposite directions. RPS seems to be a promising methodological tool for monitoring intracranial compliance with no additional volumetric manipulation required

Intracranial pulse pressure waveform analysis using the higher harmonics centroid.

Funder: National Health Research Institutes; doi: http://dx.doi.org/10.13039/501100004737BACKGROUND: The pulse waveform of intracranial pressure (ICP) is its distinctive feature almost always present in the clinical recordings. In most cases, it changes proportionally to rising ICP, and observation of these changes may be clinically useful. We introduce the higher harmonics centroid (HHC) which can be defined as the center of mass of harmonics of the ICP pulse waveform from the 2nd to 10th, where mass corresponds to amplitudes of these harmonics. We investigate the changes in HHC during ICP monitoring, including isolated episodes of ICP plateau waves. MATERIAL AND METHODS: Recordings from 325 patients treated between 2002 and 2010 were reviewed. Twenty-six patients with ICP plateau waves were identified. In the first step, the correlation between HHC and ICP was examined for the entire monitoring period. In the second step, the above relation was calculated separately for periods of elevated ICP during plateau wave and the baseline. RESULTS: For the values averaged over the whole monitoring period, ICP (22.3 ± 6.9 mm Hg) correlates significantly (R = 0.45, p = 0.022) with HHC (3.64 ± 0.46). During the ICP plateau waves (ICP increased from 20.9 ± 6.0 to 53.7 ± 9.7 mm Hg, p < 10-16), we found a significant decrease in HHC (from 3.65 ± 0.48 to 3.21 ± 0.33, p = 10-5). CONCLUSIONS: The good correlation between HHC and ICP supports the clinical application of pressure waveform analysis in addition to the recording of ICP number only. Mean ICP may be distorted by a zero drift, but HHC remains immune to this error. Further research is required to test whether a decline in HHC with elevated ICP can be an early warning sign of intracranial hypertension, whether individual breakpoints of correlation between ICP and its centroid are of clinical importance

Exactly solvable Richardson–Gaudin models and their applications

3 pages, 1 table, 1 figure.--PACS nrs.: 21.60.Cs, 21.60.Fw, 02.30.Ik.--Arxiv pre-print available at: http://arxiv.org/abs/math-ph/0609022v1We first show that the quantum pairing problem can be mapped exactly on to a classical electrostatic problem in two dimensions and then use this analogy to obtain a pictorial representation of how superconductivity arises in a finite fermionic system. Specific application to the nuclei 114−116Sn suggests some new insight into the evolution of pairing correlations in a quantum system with few active particles. We also summarize other recent work on exactly solvable pairing models, including their applications in a wide variety of strongly correlated quantum systems.The work reported herein was supported in part by the US National Science Foundation under grant no PHY-0140036 and in part by the Spanish DGI under grant no BFM2003-05316-C02-02.Peer reviewe

Compliance of the cerebrospinal space: comparison of three methods

Abstract: Background: Cerebrospinal compliance describes the ability of the cerebrospinal space to buffer changes in volume. Diminished compliance is associated with increased risk of potentially threatening increases in intracranial pressure (ICP) when changes in cerebrospinal volume occur. However, despite various methods of estimation proposed so far, compliance is seldom used in clinical practice. This study aimed to compare three measures of cerebrospinal compliance. Methods: ICP recordings from 36 normal-pressure hydrocephalus patients who underwent infusion tests with parallel recording of transcranial Doppler blood flow velocity were retrospectively analysed. Three methods were used to calculate compliance estimates during changes in the mean ICP induced by infusion of fluid into the cerebrospinal fluid space: (a) based on Marmarou’s model of cerebrospinal fluid dynamics (CCSF), (b) based on the evaluation of changes in cerebral arterial blood volume (CCaBV), and (c) based on the amplitudes of peaks P1 and P2 of ICP pulse waveform (CP1/P2). Results: Increase in ICP caused a significant decrease in all compliance estimates (p < 0.0001). Time courses of compliance estimators were strongly positively correlated with each other (group-averaged Spearman correlation coefficients: 0.94 [0.88–0.97] for CCSF vs. CCaBV, 0.77 [0.63–0.91] for CCSF vs. CP1/P2, and 0.68 [0.48–0.91] for CCaBV vs. CP1/P2). Conclusions: Indirect methods, CCaBV and CP1/P2, allow for the assessment of relative changes in cerebrospinal compliance and produce results exhibiting good correlation with the direct method of volumetric manipulation. This opens the possibility of monitoring relative changes in compliance continuously