2.1 Data acquisition and preparation

In previous research, Marc Bächlin and colleagues developed an assistant for PD patients that detects FoG by analyzing frequency components inherent in the body movements. They used measurements from acceleration sensors worn on the body (Bächlin et al., 2010). Their detection algorithm was based on the principle illustrated by Moore et al. (2008) that introduced a freeze index (FI) to evaluate the gait condition of PD patients. The FI is a ratio defined as the power in the “freeze” band [3–8 Hz] divided by the power in the “locomotor” band [0.5–3 Hz]. The FoG detection is performed by defining a freeze threshold, where values above it are considered as FoG events.

To confirm and improve this approach, a multisensor device has been proposed in our previous work (Saad et al., 2014). This device acquires heterogeneous signals (i.e., from different types of sensors). The integrated sensors in the device are the goniometer, the telemeter, and the accelerometer. The variation of the step distance is measured using the telemeter sensor. From the PD expert’s point of view, this measurement defines the FoG phenomenon, since during a FoG episode, the patient’s step distance decreases significantly while maintaining movement. From the signals of the sensors, new features that are related to FoG were introduced to the FoG domain. Designing a system that is able to detect and diagnose a patient’s FoG episodes accurately would lead to discovering the actions that must be taken to overcome and correct each FoG episode.

The approach has been tested with simulation data that are generated by imitating the behavior of PD patients in normal walking and during FoG. The scenario is to wear the multisensor device, then walk with normal short steps for 10 s, and then simulating FoG for 5 s, and finally another 5 s of normal short steps. The short steps simulated the normal gait of PD patients. The mentioned scenario is repeated 10 times in order to extract the optimal features where abrupt changes in signals occur during FoG. Figure 26.1 shows signals from all sensors during one run of the abovementioned scenario.

Figure 26.2a shows a significant increasing of the mean frequency for the goniometer when an episode of FoG occurred. As for FI, one should notice that all previous studies applied this feature only with acceleration sensors. But our results show that this feature can be used to detect FoG using the goniometer as well. Signals of both upper and lower telemeter sensors showed a significant change of their mean during FoG episodes (Figure 26.2b). This result is very advantageous, especially in order to design a system for online detection of FoG, since the mean of the telemeter signal, which is a time domain feature, needs less computational time. Thus, an online detection system can be implemented with a minimal latency period. For the shin acceleration data, the features that allow to detect FoG in both the x- and y-axis are the standard deviation (time domain), power spectral density (PSD) power, and FI (frequency domain). It is worth mentioning that FI has the most significant change during FoG when compared to the other two indicators (Figure 26.2c). On the other hand, the z-axis of the shin accelerometer shows less significance than the other two axes. With respect to the foot accelerometer (Figure 26.2d), FI is the best indicator that can be used to detect FoG. Furthermore, standard deviation and PSD power can be considered, but they have much less significance. The changes of all three indicators in the foot accelerometer during FoG are less than those in the shin accelerometer. Positioning the accelerometer on the shin is better than placing it on the foot. Table 26.1 summarizes the best indicators for each sensor that can be used to detect FoG.

To conclude, this study confirms that the FI is a relevant feature for FoG detection. It also highlights the benefit to introduce simple features as the mean frequency of the goniometer for real-time detection. Finally, it shows that the multisensor device can be used to improve detection of FoG episodes. Referring to the data obtained by Bächlin et al. (2010) from 10 PD patients with FI, we incorporated these values into our probabilistic model in an attempt to predict upcoming FoG episodes.

2.2 Causality and methodology

Inferring the causal structure of a set of random variables is a challenging task. In the causality domain, the variables of interest are not just statistically associated with each other, and yet there is a causal relationship between them. The famous slogan “correlation does not imply causation” is recognized and seems approved by researchers in empirical and theoretical sciences. Formerly, Spirtes et al., 1990 stated that “one of the common aims of empirical research in social sciences is to determine the causal relations among a set of variables, and to estimate the relative importance of various causal factors.” Recently, the philosophical wisdom of this quote is broadly discussed, specifically in the medical and health fields, more precisely in the context of symptoms/disease episodes (Russo and Williamson, 2007; Frumkin, 2006; Lagiou, Adam, and Trichopoulos, 2005; Thagard, 1998).

In particular, Lagiou et al. (2005) stated: “A factor is a cause of a certain disease when alterations in the frequency or intensity of this factor, without concomitant alterations in any other factor, are followed by changes in the frequency of occurrence of the disease, after the passage of a certain time period (incubation, latency, or induction period.” In order to highlight the causal trends of our FoG problem, and from an epidemiological point of view, we will explicitly illustrate the FoG model (Figure 26.3) by applying the Hills Criteria of Causation (Hill, 1956). Hill’s work was recently validated by Kundi (2006) as a valuable tool, since both mechanistic and probabilistic aspects were considered. The first step for examining our causal proposal was to test if our study is consistent with Hill’s criteria. Table 26.2 summarizes the nine criteria defined by Hill and the observations when applying it to the FoG case with respect to FI. It can be clearly observed that not all of the criteria hold in our case, where criteria 4 and 9 did not apply.

2.3 Modeling with BNCs

The first step of our learning protocol is to divide the acceleration data into learning (nine data sets for each different patient) and the rest for testing. Each data set consists of nine signals: the x, y, and z components from the ankle accelerometer, the x, y, and z components from the knee accelerometer, and the x, y, and z components from the hip accelerometer. For each component, FI is calculated. Thus, we built nine BNC models for nine different patients. For this purpose, nine belief network graphs were constructed (Figure 26.4), where the class node (FoG) was the parent of the three FI nodes (FI nodes represented the magnitude of the FI components for each acceleration sensor). Although the data intended to learn each BNC model was divided into 70% learning data and 30% testing data. Continuous variables were discretized based on Akaike’s criterion (Song et al., 2011) before learning the BNC structure. The learning experiments were conducted with a random ten fold validation; each fold takes a random 70% from the data set for learning and the remaining 30% for testing.

After learning each fold, a classical confusion matrix was calculated (Table 26.3) using the test data. This table represents the true positives (TP), false positives (FP), false negatives (FN), and true negative (TN). From the confusion matrix, we evaluated three important values: FoG-precision, NoFoG-precision, and Accuracy.

After calculating these values for each fold, we choose the learning that holds the highest three values based on the priority of each value (FoG-precision was the highest priority, followed by NoFoG-precision, and finally Accuracy). After choosing the nine BNC models for nine different patients, the other data sets was introduced to each BNC model as testing data sets for the purpose of testing the degree of generalization of our models.

2.4 Results and discussion

Following the learning and testing protocol, data sets were represented by S<patient number>R<test or run number >. It is seen when testing S01R01 (patient 1, first run) that the FoG precision value was apparently high in all nine classifiers. We can see that the best results were for the data sets S01R02 (FoG-precision = 70.67% and NoFoG-precision = 84.74%) and S03R01 (FoG-precision = 73.68% and NoFoG-precision = 79.13%); the first data set was for the same patient but on a different run, while the second data set was for another patient. This finding shows that both patients may be correlated in freezing behavior. As for data set S02R02, some results had low FoG-precision; this may be due to the different walking behavior of patients, knowing that S02R01 (same patient, but different run) showed an acceptable result for NoFoG-precision and a very high result for FoG-precision (92.85%). Table 26.4 presents the average accuracy, FoG-precision, and noFoG-precision for different data sets.

3.1 Experimental protocol

A total of 10 subjects diagnosed with PD were recruited. Using a digitizer tablet, each patient was asked to write four traces: (1) the letter l written in cursive manner with one stroke (Figure 26.5, left), (2) the number 8, (3) the infinity symbol (∞), and (4) the sentence “the killing bullet is fast” (Figure 26.5, right). The extracted kinematic parameters that fit to the characteristics of different handwriting traces are the mean velocity, fluidity, fluency, mean pressure, pause in duration, and the number of strokes.

The acoustic feature measurements of the PDPs were done by quantifying several vocal phonations. Using a noise-canceling microphone, they were asked to emit a sustained vowel a and a short sentence in Arabic. The use of sustained vowel phonations was to assess the degree of vocal symptoms in the acquired voice. We applied the Praat software package, which has been widely and recently used (Rusz et al. 2011; Little et al., 2009) as a speech feature extractor, and specifically as a PD speech diagnosis. Features extracted from the vowel included the maximum phonation time (MPT), frequency perturbation (jitter), intensity perturbation (shimmer), and harmonic/noise ratio (HNR). While the standard deviation of the intensity (STD intensity) and the voice breaks were extracted from the phrase.

3.2 Clustering with BBNs

Currently, attractive requests of graphical models, particularly in the form of BBN classifiers, can be found in many disciplines, such as finance (risk evaluation and stress test) (Rebonato, 2010; Meucci, 2008), network diagnosis (Khanafar et al., 2008), and for medical applications (Intan and Yuliana, 2011; Sacha, Goodenday, and Cios, 2002; Gong, Zhang and Gao, 2009). BBNs are high-level representation of probability distributions over a set of variables that are used for building a model of the problem domain. It provides a compact and natural representation, an effective inference, and efficient learning (Friedman, 1997; Borgelt, Steinbrecher, and Krus, 2009). Based on BBN framework models—more specifically, the Hierarchical Latent Class (HLC) models anticipated in Zhang and Kocka (2004a), Wang and Zhang (2004), and Zhang (2004) and used in Zaarour et al. (2004a, 2005, 2010)— we modeled our problem with HLC. Those are tree-structured BBNs where leaf nodes are observed while internal nodes are hidden. We represented the physiological brain structure (i.e., PPN²) by a hidden variable that influences both handwriting and speech measuring variables. Continuous variables have been discretized based on Akaike’s criterion (Song et al., 2011) before learning the BBN structures.

The fundamental hypothesis published by Zaarour et al. (2003, 2004b, p. 78, 2010) assumes that if features of writing (or speech) of a set of PD pupils are similar with respect to a given metric, then these pupils nearly share the same handwriting (or speech) pattern. Part of our work, therefore, aims at identifying and studying patterns by clustering PDPs according to their HSS. Thus, the discovered PD clusters can serve as a fundamental reference for future assistance, such as a motor diagnosis tool based on HSS. We used the EM algorithm, which is a broadly applicable approach to the iterative computation of maximum likelihood (ML) estimates, useful in a variety of incomplete-data problems (McLachlan and Ng, 2009; Han and Kamber, 2006). Typically, the bottom layer is the visible one, containing the observable data variables, and the top layer is the hidden one, representing latent variables.

There are no justified theoretical selection criteria for HLC models in particular and BBNs with latent nodes (Wang and Zhang, 2004; Zhang and Kocka, 2004b). The challenge is that both the BBN structure and the number of clusters partially depend on the neurologist expert knowledge, and the parameters (i.e., conditional probabilities between children and their parents) are estimated by the EM algorithm. The missing data in this challenge are hidden variables treated as a new unlabeled pattern in the outline of unsupervised learning (i.e., clustering). After clustering, we attempted to split the feature values into a set of nominal values based on a percentage scale. This methodology lead to more informative results interpretation for each discovered cluster (Zaarour, Labiche, and Meillier, 2010; Naim et al., 2008). Thus, using the scale shown in Figure 26.6, each feature value was categorized according to five levels.

The results of our voice diagnosis model classified patients according to their ability to control their voice, which is related to the extent that they utilize their voice in their daily activity. The results of the handwriting diagnosis models showed that traces l, 8, and ∞ clustered patients according to their ability of controlling the handwriting of each trace. Moreover, the trace phrase clustered patients with respect to their response ability to hand-motor physiotherapy. The result obtained from this trace reveals that clinical physiotherapy leads to more effective improvements for PD patients’ motor abilities than if it were done at home (Saad et al., 2012).

4.1 Handwriting and speech link

On the way of building our HLC model, we considered the obtained handwriting and speech patterns (local diagnosis models) as leaf nodes for a new latent class that is a source influencing and acting on both types of patterns (pattern of speech and writing). Each local prototype has its own particular motor abilities represented by hidden discrete variables. This model is conceptualized as a global diagnosis model that deals with each local diagnosis model (Figure 26.7). The only assumption we make is that these abilities are independent but conditionally dependent on a hidden global class, which is the missing data in this case. For this reason, we used the EM algorithm for calculating the conditional probabilities between local classes and the global class, knowing that the previously calculated conditional probabilities between features (handwriting or speech) and their corresponding class was predetermined for the global model.

4.2 Results and discussion

After the modeling and learning phase, the global BBNs were used as an inference tool. For instance, through inference, we can make tradeoffs between traces and voice parameters: What is the probability that a PDP has such difficulty in handwriting, knowing that this person has such a fixed pattern of speech? Our approach had resulted in classification into three groups, as shown in Figure 26.8.

In Table 26.5, the common feature characteristics of each cluster are summarized, where each feature was characterized according to resulting output measurements in the form of low (L), high (H), and medium (M) with respect to the percentage scale shown in Figure 26.6.

After tabulating these groups, it was recognized that C1 includes two patients (P3 and P8) (Figure 26.8). C1 includes patients with better acoustic features. On the other hand, patients were capable of controlling all their writing abilities while writing each trace test. Thus, we can conclude that the patients in C1 are capable of controlling their voice and handwriting motor abilities. Probably, based on demographic data of the patients, those results may be because the patients (P3 and P8) are in the early stages of the disease (3–4 years). As for C2 patients, they have low voice quality with respect to the extracted acoustic features. On the other hand, they showed little ability to control axiomatic traces (trace L). Also, they negatively responded to hand-motor physiotherapy (trace Phrase). Hence, C2 patients were not able to control their handwriting or acoustic abilities. This may be linked to their belated disease duration (11–15 years). Finally, the common feature characteristics of C3 patients are moderate kinematic features during hand-motor physiotherapy (trace Phrase) and moderate acoustic features acquired from the sustained vowel. In addition, we noticed that C3 patients have a disease duration of 2–6 years. Hence, our global methodology consists of diagnosing PD by clustering patients with respect to their behavior. The PD behavior is represented by a set of features. Each cluster will be simply labeled by experts in neurology and motor control domain using the classical percentage scale. In the case of handwriting and speech syndromes, characteristics are gathered in the same experiments. To expand this methodology to new PD syndromes, a new experimental protocol must be introduced concerning the new syndromes. For example, the FoG syndrome can be integrated into our methodology by acquiring handwriting and speech data from patients before, during, and after FoG episodes. Next, by constructing and learning our BBN, we can discover a specific prototype (or cluster) of handwriting and speech linked to the FoG episodes.