Real-Time Analysis of Intracranial Pressure Waveform Morphology (Bioengineering in Neurological Disorders) Part 1

Introduction

The cranial vault is composed of four fundamental components: arterial blood, venous blood, cerebrospinal fluid (CSF), and brain parenchyma. Intracranial pressure (ICP) represents the pressure within the brain parenchyma and cerebrospinal fluid (CSF). The environment within the cranial vault is unique compared to other organ systems; it is enclosed within a rigid skull and thus small volumetric changes in any of the four elements lead to significant changes in ICP. One example of this, is the periodic influx of arterial blood over the cardiac cycle; this change causes the ICP pulse pressure waveform. The pulse pressure waveform has three characteristic peaks hypothesized to correspond to different physiologic components. Early work [1] demonstrated the relationship between pulsations in the choroid plexus and the pulse pressure waveform. Moreover, other studies [2] compared the right atrium (venous) and the aortic (arterial) pressures to the intracranial waveform in the cistern magna and showed that although the cranial pulse pressure is related to arterial pulsations, there is also a venous component. The results of these studies support the current theories for the etiology of the characteristic peaks in the ICP pulse pressure waveform. The majority of the literature indicates that P1, the percussion wave, corresponds with the pulsation of the choroid plexus and/or large intracranial conductive vessels [3-5]. The rebound of the percussion wave is thought to contribute to P2, which has also been related to cerebral compliance [5]. Finally, the dicrotic wave, or P3, is thought to be venous in origin [2, 4, 6].

ICP monitoring is fundamental to the management of numerous intracranial pathologies, including the management of traumatic brain injury (TBI), subarachnoid hemorrhage (SAH), hydrocephalous, and any other conditions where pathological changes in intracranial volume (ICV) may occur. Maintaining an ICP within normal limits is vital for adequate perfusion of the brain. An increase in ICP (intracranial hypertension) reduces arterial blood flow into the cranial vault, while decreased ICP (intracranial hypotension) results in severe headaches. Although the importance of monitoring ICP is well established, only recently has ICP pulse pressure waveform morphology yielded promising results due to advancing technology. However, the importance of ICP pulse pressure waveform morphology has been known for years; special interest should be focused not only on the height of mean ICP, but also on the pressure pulse curve, because the configuration and pulse amplitude of the CSF pulsations can be regarded to a certain extent as an index of the state of intracranial elastance or cerebral bulk compliance [6].

Methods for monitoring ICP include: epidural, subarachnoid, intraventricular, and intraparenchymal pressure probes. For the investigation of ICP morphology, a continuous measurement of ICP must be achieved. There have been several recent advances by various groups to analyze continuous ICP waveform morphology. An analysis method [7] that utilizes 6-sec time windows to extract average amplitude and latency information for the given window was developed. Our group has recently developed a time-domain analysis toolbox for intracranial waveform morphology known as Morphological Clustering and Analysis of Continuous Intracranial Pulse (MOCAIP)[8]. The details of this algorithm will be presented in the subsequent topic. Several groups have successfully utilized pulse pressure waveform morphology analysis in the diagnosis and management of various conditions. For example, pulse pressure amplitude has been linked to several conditions with promising results in normal pressure hydrocephalus (NPH) for predicting shunt responsiveness [9, 10]. Work has also been done in chronic headaches; again, showing the usefulness of pulse pressure amplitude. Furthermore, our group has investigated several conditions using ICP morphological metrics including: detection of cerebral hyoperfusion [11], prediction of ICP hypertension [12], segmentation of ICP slow waves [13], changes in vasoreactivity (vasodilatation) [14]. ICP monitoring has been fundamental for the diagnosis and management of several conditions for decades. In this topic, we present a few of the recent advances in the analysis of ICP pulse pressure waveforms and its applications as described above.

Automatic analysis of ICP morphology

As previously described, the ICP pulse pressure signal contains three characteristic peaks [5]. From those peaks, it is possible to describe in a parametric way the amplitude and timing information of the pulse for further examination. While several studies have focused on the offline analysis of the ICP waveform [15-17] and the extraction of its morphological features, processing ICP signals to extract the three peaks in a continuous way is challenging because the signal is commonly affected by various types of noise and artifacts. MOCAIP algorithm [18, 19] was developed by our group to address these issues. MOCAIP is capable of extracting morphological features of ICP pulses in real-time by recognizing legitimate ICP pulses, and by detecting the three peaks from average waveforms computed from segments of ICP.

Recently, two main extensions have been developed from the original framework. MOCAIP + + (Section 2.1) is a generalization of MOCAIP that allows different peak recognition techniques to be used and uses intermediate features to make the peak detection more robust to the variations observed in the clinical conditions. The latest extension of MOCAIP is presented in Section 2.2 and poses the peak detection problem in terms of Bayesian inference.

MOCAIP++

MOCAIP + + [20] generalizes MOCAIP in two ways. First, it proposes a unifying framework where different peak recognition techniques can be integrated. Second, it allows the algorithm to take advantage of additional ICP features to improve the peak recognition. A summary of the algorithm is described in the following subsections.

ICP Segmentation: The continuous raw ICP signal is segmented into a series of individual ICP pulses using a pulse extraction technique [21] combined with the ECG QRS detection [17, 22] that locates each ECG beat. Because ICP recordings are subject to various noise and artifacts during the acquisition process, an average pulse is extracted from a series of consecutive ICP pulses using hierarchical clustering [23].

Peak Candidates: Peak candidates, each being a potential match to one of the three peaks, are detected at curve inflections of the average ICP pulse using the second derivative of the signal.

Second-order ICP Features: We have shown in a recent study [20] that the first derivative of the ICP signal is very useful to discriminate between ICP peaks and therefore preoviding improve recognition. In our previous work, the first Lx demonstrated the best improvements in comparison with the second derivative and the curvature within MOCAIP + + framework. The derivative Lx is computed according to the smoothed version L of the ICP,

where the ICP signal I( x ) is first convolved with a Gaussian smoothing filterwith the standard deviationto generate

Peak Recognition: The peak recognition tasks consists in recognizing the three peaks among the set of candidate peaks detected within the pulse. Several techniques have been developed and can be used such as independent Gaussian models [18], Gaussian Mixture Models (GMM), and spectral regression (SR) analysis [19]. Depending on the technique, it can exploit the latency of the peak candidates, the raw ICP pulse, or different features extracted from the pulse.

Morphological metrics: Once the peaks have been detected in an ICP pulse, a set of metrics (Fig. 1) is used to describe the shape morphology in a parametric way. This allows to obtain a better understanding about the type of variations that take place.

Fig. 1. Illustration of morphological metrics extracted From ICP peaks (reproduced with permission from [14] and [66]).

Bayesian tracking of ICP morphology

In this section, we present a probabilistic framework [24] to track ICP peaks in real time. The tracking is posed as inference in a graphical model that associates a continuous random variable to the position of each of the three peaks, in terms of their latency within the pulse and pressure level. The model (Section 2.3) represents the dependencies between the peaks using a Kernel Density Estimation (KDE) from evidence collected from manually annotated pulses, while Nonparametric Belief Propagation (NBP) [25] is used during the detection process (Section 2.4).

We assume that the tracking framework is presented with a series of raw pulses extracted from the ICP signal. The model consists of three distinct statesat timeone for the position of each peak. A stateis two-dimensional that defines the latency, and the ICP elevationof the peak. To each stateis associated an observationdirectly extracted from the position of the peak within the current pulse.

Probabilistic tracking framework

The graphical model used in our tracking framework defines relations between pairs of nodes. Statesand observationsare represented in the graphical model and illustrated in Fig. 2 by white, and shaded nodes, respectively. Edges represent dependencies between states, and possibly observations, by two types of functions: observation potentials that are the equivalent of the likelihood partand compatibility potentialsthat embed the conditional partsof the Bayesian formulation and can be used by conditioning them in either directions during inference. By introducing compatibility potentials between states of the same peak at successive timesthat we name temporal potentials, the model becomes a dynamic Markov model.

Fig. 2. The graphical model represents the dependence through pairwise potentialsbetween hidden nodes, and likelihood functionsbetween hidden and observable nodesBy introducing temporal potentials between successive nodes (b), the graphical model becomes dynamic and allows for tracking ICP peaks in real time (reproduced from permission from [24]).

Observation model

An observationcorresponds to the position of thepeak, in terms of latency and ICP elevation, that was produced by a peak detector at time t. Our framework uses MOCAIP as peak detector but any other peak detection technique can be used within our model. Observationsare linked to their statethrough an observation potential Equation (3) formalizes the integration of the observation using a Gaussian model,

whereis a smoothing parameter, andis a constant factor that accounts for missing peaks by the detector.

Compatibility and Temporal potentials

Temporal potentialsdefine the relationship between two successive states of a peak. They are defined as a Gaussian difference between their arguments,

where the standard deviationof the model was previously estimated using maximum likelihood (ML) on training data. Compatibility potentialshowever, are not expected to follow a Gaussian distribution. Each potential is represented by a KDE [26] that is constructed by collecting co-occurring ICP peak positions across the training set.

Tracking ICP peaks using nonparametric bayesian inference

Detecting peaks in an ICP pulse at time t amounts to estimatingthe posterior belief associated with the statesgiven all observations

accumulated so far. Thus, peak detection is achieved through inference in our graphical model. One way to do this efficiently is to use Nonparametric Belief Propagation [25]. It is a message passing algorithm for graphical models that generalizes particle filtering and Belief Propagation (BP). Messages are repeatedly exchanged between nodes to perform inference. Following the notation of BP, a messagesent from node i to j is written 1,

whereis the set of neighbors of state i where j is excluded,is the pairwise potential between nodesι is the observation potential. Each

messageas well as each nodedistribution is represented through a multivariate KDE.

To compute an outgoing messageNBP requires the pairwise potential which represents the joint distribution between the nodes, to be conditioned on the source stateThis task is achieved by samplingfrom the potential.

After any iteration of message exchanges, each state can compute an approximationcalled belief, to the marginal distributionby combining the incoming messages with the local observation:

An example of inference is provided in Fig. 3 where the latency and the elevation of the three peaks is tracked simultaneously and in real-time on a pulse-by-pusle fashion.

Fig. 3. Peak latency (left) and ICP elevation (right) estimated on ICP sequences by NBP tracking algorithm. The predictions of the tracking are obtained in real-time and are robust to transient perturbations that frequently occur during the ICP signal recording.