Spastic hemiplegia gait characterization using support vector machines: Contralateral lower limb

RICARDO JOSÉ BRAVO ¹, OSBERTH CRISTHIAN DE CASTRO ², ANTONIO JOSÉ SALAZAR ²

¹ Universidad Simón Bolívar, Dpto. de Tecnología Industrial, Valle de Sartenejas, Edo. Miranda 1080, Venezuela.

² Universidad Simón Bolívar, Dpto. de Electrónica y Circuitos, Valle de Sartenejas, Edo. Miranda 1080, Venezuela.

ABSTRACT

Spastic Hemiplegia (SH) is a brain motor dysfunction with neuromuscular implications on one side of the body which leads to gait disorders. The gait of such dysfunction has been described and classified in terms of its affected side lower limb (known as ipsilateral limb) measurements using manual analytical methods. It has been assumed that the unaffected side limb (known as contralateral limb) compensates gait deviations due to the abnormal pattern of the ipsilateral limb. But in gait, the behavior of both limbs is highly correlated so analysis of the contralateral side should prove useful, although there are a lack of studies regarding contralateral limbs. This study is part of an ongoing effort to analyze the SH gait pathology in terms of limbs of both sides and it begins with the relationship between ipsilateral SH gait pattern classification versus contralateral limb compensating pattern. In this work, the focus has been on the kinematics of the unaffected contralateral limb of the disorder taking advantage of high profile statistical learning computational methods, such as Support Vector Machines (SVM) models. Results showed that consistent types of SH kinematics patterns can be found, described and also characterized using a SVM model. Further improvements in the accuracy of SH classification and characterization are under way.

Keywords: Gait, Kinematics, Hemiplegia, Learning, Pattern Recognition, Support Vector Machines.

CARACTERIZACIÓN DE LA MARCHA DE HEMIPLEJÍA ESPÁSTICA UTILIZANDO MÁQUINAS DE VECTORES DE SOPORTE: MIEMBRO INFERIOR CONTRALATERAL

RESUMEN

La Hemiplejía Espástica (HE) es una disfunción motora cerebral con implicaciones neuro-musculares en un lado del cuerpo las cuales llevan a alteraciones en marcha. La marcha en dicha disfunción ha sido descrita y clasificada en base a mediciones en el lado del miembro inferior afectado (conocido como miembro ipsilateral), utilizando métodos manuales de análisis. Se asume que el lado del miembro no afectado (conocido como miembro contralateral) compensa las desviaciones de la marcha debidas al patrón anormal del miembro ipsilateral. Pero en marcha, el comportamiento de ambos miembros es altamente correlacionado, de modo que el análisis del miembro contralateral podría demostrar ser útil en el estudio de la marcha, sin embargo en la literatura de especialidad no existen estudios que considere el miembro contralateral como objeto de estudio. Este trabajo es parte de un esfuerzo por estudiar la marcha patológica secuela de HE en términos de ambos miembros, y éste comienza con la relación entre la clasificación del patrón de marcha del miembro ipsilateral versus el patrón compensatorio del miembro contralateral. En este trabajo, el enfoque ha sido el estudio de la cinemática del miembro contralateral no afectado en esta patología de marcha aprovechando las ventajas de los métodos computacionales de aprendizaje estadístico de alto perfil, como los modelos basados en Máquinas de Vectores de Soporte (MVS). Los resultados muestran que se pueden encontrar tipos de patrones de cinemática consistentes de HE, descritos y también caracterizados utilizando modelos de MVS. Mejoras en la certeza de la clasificación y caracterización de HE se esperan en el futuro.

Palabras Claves: Marcha, Cinemática, Hemiplejía, Reconocimiento de Patrones, Maquinas de Vectores de Soporte.

INTRODUCTION

Clinical gait analysis record interpretation is a valuable instrument in the study and comprehension of the effects of neuro-muscular-skeletal pathologies in human gait. Kinematics (angles and rotations), kinetics (joint moment and power) and physiological records, such as electromyograms (EMG) and energy consumption, can be used to give a complete parametric description of the gait process of a patient; for further insight in normal and pathological gait refer to (Gage 1991) and (Perry 1992). Normal gait can be verified when certain prerequisites are accomplished, such as performance within normal gait patterns, high energetic consumption efficiency, etc. The compensation that occurs as a response to gait pathology has the goal of achieving a viable gait, and minimizing then deviation with respect to the normal pattern and the consumption of metabolic energy, which increases dramatically in pathological gait (Gage 1991).

Numerous reasons can cause the gait pattern of an individual to deviate from normal, including temporary, permanent and/ or chronic pathologies, illnesses and/or accidents; this article focuses in one of such reasons: Spastic Hemiplegia (SH), a subtype of Cerebral Palsy (CP) motor dysfunction. SH consists of a motor compromise of the upper and lower limbs of one side of the body, due to the lack of neurological control, accompanied by muscular stiffness due to abnormal muscle tone increase. The affected limb is referred to as the ipsilateral limb, and the non-affected limb is called contralateral limb. Since one of the lower limbs is affected, SH therefore affects the gait pattern of the patient. Focusing on Spastic Hemiplegia (SH) pathology, this paper propose  he study of the behavior and kinematics gait patterns of the contralateral limb based on computational pattern classification.

In order to apply either surgical or rehabilitation treatments for the improvement of the gait pattern of a subject, specialists interpret the information extracted from a clinical gait analysis (kinematics, kinetics, electromyography and energetic consumption) from which they establish correlations based in the coherence of the results. Data from the lower limbs can be contrasted with pre-established normal patterns, serving as a base for diagnosis and treatment recommendation. This method is widely applied to children with neuromuscular diseases, mainly with CP, specifically in the case of SH, mielomeningocele, etc. (Gage 1991, Perry 1992, Davis 1997). Through the use of gait analysis and kinematics graphs of the ipsilateral limb, six distinct types of SH can be recognized (Gage 1991) (referred to in this article by roman numerals, Types I to VI). The first four types (I, II, III, and IV) are determined exclusively based only in kinematics data, while the remaining two types (V and VI) need complementary parameters obtained from kinetics plots studies. Each of these types has a particular movement pattern and a specific group of related treatments; surgical and non-surgical (Gage 1991). Although the mentioned classification scheme has contributed, up to now, in the specification of treatments for the different types of SH, a continuous search for improving its effectives is in place.

Previous research pursued the characterization of SH through the analysis in the temporal and frequency domain (Abondano 2001 & Viloria 2003) of electromyographic gait signals of the affected limb (Abondano 2001, Viloria 2003 & Viloria and Others 2003) while other approaches use kinetics data as a basis that contributes to improve classification of SH. However, gait dynamics and followups of patients with SH, that underwent treatment; suggest that there might exist factors which have not been taken into consideration in the current classification, therefore affecting the post-operatory outcome. Such factors could stem from the functional compensation of the contralateral limb.

Although signals topologies originating from kinematics and kinetics gait records seem suitable for analytical methods processing, the intra/inter patient variability and the physician’s learning/experience process in the interpretation of the signals and categories, makes the application of statistical learning methods desirable for the model synthesizing, such as neural network and support vector machines (SVM). The use of SVM has extended to pattern recognition application, such as face recognition in an image, with data with similar variability as the one present in gait patterns.

The main focus of this research is the analysis of the kinematics patterns of the contralateral limb in patients with SH, in order to verify the presence or not of differentiating patterns from the normal one due to compensating responses. SH types I through IV are considered within this research; statistical analysis was performed through the use of the Support Vector Machines (SVM) learning based model.

This article is the first in a series regarding the impact of the study of the contralateral limb behaviour and the contributions that it could bring to gait analysis. The results and techniques obtained from these studies will server as a basis for comparison with future methods and procedures.

Support Vector Machines: Model for Statistical Learning and Data Mining.

In the last ten years, SVM has become a practical pattern recognition model for learning from examples, such as the case of gait patterns. SVM has become a very useful tool for feature extraction, capable of finding subtle or diffuse patterns in complex problems with a minimum set of ad hoc parameters. Based on the Structural Risk Minimization Principle and Vapnik-Chervonenkis Theory (better known as the VC Theory) (Vapnik 1995), the model focuses on finding the optimal decision surface in terms of the linear function (1) or its modified version (2).

In Equation 1 and 2 «si» represents the support vectors, «y_i” the associated label of the support vectors (1 or -1, positive or negative vector), the “á_i» represents the coefficients of the support vectors and b is the associated threshold. The “ái» are positive real coefficients with an upper bound for the non-separable case defined by a constant C. These coefficients are fine-tuned at the SVM training phase and reach their natural stable value during optimization when the data is separable. When the data is inseparable these coefficients tend to infinite values during optimization, for this reason a tolerance parameter is introduced, represented by C, which is the upper-bound for the “á_i» and it is established arbitrarily. The kernel function, K(x,y) that appears in (2), maps the decision function into a high dimensional «feature space» in which the function becomes linear (See Figure 1). For example, K can convert f(x) into a polynomial classifier using,

Figure 1. A qualitative example of a SVM transformation of a function in a feature space where it becomes linear.

or a Radial Basis Learning Machine using a Gaussian form, or a Multilayer Neural Network using a Sigmoidal K(x,y) in (2). In (3) N represents the smoothing factor and «p» is the order of the polynomial. Each of these kernel functions are used under restricted conditions. The more intuitive condition is

where Φ is a non linear map to some inner product space in which the hyper plane exist when the non linear function is on input space (Figure 1),

The usual approach for finding the optimal f (x) with SVM is to solve a quadratic optimization problem with linear constrains by finding the hyper plane in «feature space», which maximizes the distance between the class boundary in the separable case. The non-separable case is solved by including error penalty variables which translate in the formulation by creating an upper bound on the quadratic optimization variables.

SVM has become a very useful tool for feature extraction, finding subtle or diffuse patterns in complex problems with a minimum set of ad hoc parameters. In order to solve multiclass problems using SVM the usual approach is to generate several binary classifiers between the classes or between one class and the rest of them, in order to construct the final set of classifiers (Platt 2000). Figure 2 shows SVM diagrams for SVM for Pattern Recognition for SH Classification used in (Salazar 2004). In Figure 2, (a) shows a vector sample constructed with SH information and (b) illustrates a classifier surface for a SH classification task. Figure 2 (a) illustrates how kinematics variables are organized as a vector, there is a lack of details in axis labels due to the scale; the vertical axes labels refers to pelvis attitude and joint angles in degrees, and horizontal axis represents gait cycle samples for those kinematics variables.

Figure 2. SVM in SH classification (a) A qualitative SH task Input Vector for SVM. (b) SVM classifier surface for Hemiplegia Classification.

METHODOLOGY

The data groups, SVM classification tool and pattern characterization procedure is explained as follows:

Experimental Datasets: SH and Non-SH Groups.

Data records obtained from the Gait Laboratory Unit database at «Hospital Ortopédico Infantil» (Caracas, Venezuela), were recorded with a Vicon 370 Motion System using 5 HiRes, 60Hz IR cameras, and calibration residuals d» 2mm. The marker set used follows the model described by Kadaba (Kadaba 1990) using a Knee Alignment Device (KAD) at the static trial. KAD is a device used by biomechanical model reconstruction algorithms in order calculate certain critical angles, instead of manual input. In this way the hip center was estimated based on the distance between antero-superior iliac spines. Kinematics and kinetics data were generated with VCM 1.34 Software (Vicon Clinical Manager, Oxford Metric LTD).

A number of 933 records were divided into two groups: ‘hemiplegic patients’ and ‘other patterns’ groups. Records from SH patients group included subjects with SH Types I, II, III and IV, according to (Gage 1991) (Labeled as Subgroups 1, 2, 3, 4. See Table 1). Several features of these samples are: age 8.3±3.5 years (range 3 – 25 years), size  1.26±0.17 meters (range 0.93-1.79 meters) and weight 28.4±12.8kg (range 12-90.3 kg). Other patterns group records (Labeled as Group 5, Table 1) included: normal subjects, a variety of hip disorders (arthrodesis, Perthes disease), mielodisplasia (at several levels) and the affected ipsilateral limb of the Types I to IV SH.

Table 1. CLASS DATA DISTRIBUTION

For this study, only sagittal plane kinematics variables were used: pelvic tilt, hip flexion-extension, knee flexion extension and ankle dorsi-plantar flexion, in order to have a match with the traditional kinematics criteria used in the classical classification (Gage 1991). A guide for this angle definition is shown in Figure 3.

Figure 3. Kinematics angles definition

Analysis Method and Experiments.

The analysis procedure goal was to find a kinematics’ pattern for the unaffected contralateral limb of the patients in Types I to IV groups. Evaluation of the existence of consistent patterns in each type category was performed using a Support Vector pattern recognition model, in order to generate a statistical classification rule between one SH type pattern versus the remaining classes.

Classification Tool: The Support Vector Machine Model.

The aforementioned kinematics variables: pelvic tilt, hip flexion-extension, knee flexion extension and ankle dorsiplantar flexion, associated to the groups previously described were arranged as input vectors of a SVM-based classification tool. Such was achieved by connecting the data of the aforementioned variables in a singular string (in the same manner data from an image is arrange for pattern recognition), using the order generally utilize by medical experts (research of the impact of variable order in the input vector effectiveness for revealing patterns is part of ongoing efforts); in Figure 3 an example of an input vector can be observed. The SVM scheme used was developed for gait kinematics studies (Salazar 2004). The training set consisted of 75% of the records from each group (those records were at the same time used for the pattern definition), while the remaining 25% was used as a validation set; both sets were taken randomly. SVM parameters C and N were tuned manually, in order to obtain their best classification performance. The determination of C by analytical methods does not apply when working with SVM in feature spaces (high number of dimensions spaces) and when the separability of data is too complicated to be analyzed; generally for these cases a trial and error approach is utilized. N is determined in the same manner and for similar reasons as C; a p = 3 surface was chosen as an initial separation surface of the data which in Equation 3 implies that determining N would not be complicated.

Sensibility, specificity, negative predictive and positive predictive values were calculated for each case.

Kinematics Patterns.

To obtain the representative patterns for each group, the data of the kinematics variables (51 samples of the gait cycle, 2% of gait cycle each) of the correct classified vectors from the training set were point to point averaged, excluding the support vectors. In addition, the point to point standard deviation was calculated; the resulting datasets was arranged and plotted in a average ± std dev. style using the gait analysis report format (Bravo 1999). The support vectors represent the boundary and/or misclassification cases, they were averaged in the same way as mentioned before; to obtain the kinematics pattern were the classification failed.

RESULTS & DISCUSSION

Classification and SVM procedures

Tables 2 and 3 summarize the results of the experiments using the statistical learning tool selected following the protocols described in (Salazar 2004):

Table 2. SVM MODEL FINAL PARAMETERS

Table 3. EXPERIMENTAL RESULTS ON TESTING SET

Although these sensibilities and specificities are less than the values obtained for the affected side in (Salazar 2004), they are still sufficiently high (all of them greater than 75%) in order to allow us to accept the type groups classification and their corresponding records as a source of a kinematics pattern characterization.

Kinematics Pattern Description Plots

Plots from the obtained patterns for the unaffected contralateral limb for SH type I, II, III and IV are shown in Figure 4, 5, 6 and 7 respectively.

Figure 4. Averaged kinematics pattern for unaffected contralateral limb Type I SH. a) Pelvic tilt, b) Hip flexion-extension, c) Knee flexion-extension, d) Ankle dorsi-plantar flexion.

Figure 5. Averaged kinematics pattern for unaffected contralateral limb Type II SH. a) Pelvic tilt, b) Hip flexion-extension, c) Knee flexion extension, d) Ankle dorsi-plantar flexion.

Figure 6. Averaged kinematics patterns for unaffected contralateral limb Type III SH. a) Pelvic tilt, b) Hip flexion-extension, c) Knee flexion extension, d) Ankle dorsi-plantar flexion.

Figure 7. Averaged kinematics patterns for unaffected contralateral limb type IV SH. a) Pelvic tilt, b) Hip flexion-extension, c) Knee flexion-extension, d) Ankle dorsi-plantar flexion.

Type I: There is an anterior pelvic tilt of about 15° along all the gait cycle. It produces an increase in the hip flexion between terminal swing (T-S) and the end of mid stance (M-S). The knee flexion plot result in a pattern that follows the morphology of the normal pattern, however, a hyperflexion of 20° respect to normal is verified from loading response (L-R) to almost all the M-S. The foot showed a pattern that is similar to the normal, but with a slight dorsiflexion, which is more evident in pre-swing (P-S) and initial swing (I-S). This may be due to a pelvic descends in order to compensates the other limb which is in stance at that time. The proportion between stance phase and swing phases are practically normal. The upper and lower standard deviation boundaries around the average pattern look very consistent and uniform along the gait cycle for all levels.

Type II: The pelvis shows an important anterior tilt of 10° except for P-S, which points to a forward lean in trunk. Another important increase, of 10°, can be found in the hip  lexion, mainly in T-S. The knee flexion pattern looks almost normal, however, a premature knee extension occurs before the half of M-S, and this extension is preceded by an increase in flexion since the initial heel contact (H-C), which has a 15° deviation of flexion. At the ankle, the initial H-C and LR are done in normal pattern. Along stance, the foot is practically neutral, and in swing, the plantar flexion is restricted only to 10°. The stance phase is enlarged in 10% of the gait cycle, which leads to a 70% - 30% of stance to swing proportion. Also, a good uniformity in standard deviations is shown for all levels, only a remark at the pelvis, where a uniform but wide band is observed (±8° therefore a 16° span).

Type III: Except for almost all the M-S, the pelvic tilt is maintained in the same order that is observed in Type I, around 5°. Also, hip flexion resembles that for Type I and is near the normal limits even though it is slightly increased from T-S to the end of M-S. The knee flexion is similar to
Type II, but in this case, the initial H-C is done in a normal way. Knee extension is more premature (half of M-S) and the flexion in swing is restricted in a few degrees. For this  ype of SH, a dorsal flexion is never reached: in L-R, the ankle is neutral and from second half of M-S to P-S there are almost 10° of plantar flexion. P-S and mid swing are in a plantar flexion of 20°, reaching neutral for T-S and final H-C. Swing phase is decreased (stance phase enlarged, in almost 15%) slightly more than Type II, in a 75% stance, 25% swing proportion. There is a great variability for all levels during the swing, but more specifically at pelvis, hip and knee. At the ankle, the major variability in observed between P-S and initial swing. High consistency (small standard deviation) for the knee and ankle during stance is observed.

Type IV: A remarkable lordosis is observed, in the M-S and in terminal swing it reaches 15o respect to normal. In terminal stance it is reduced until almost 7o which indicates a strong antero-posterior swinging of the trunk. The hip flexion is very augmented, which is expected, reaching an excess of 12o with respect to normal for initial heel contact (around 47o) and more than 15o with respect to normal in terminal swing. The raise in hip flexion is maintained almost to the end of the mid stance, then being hyper-extended slightly from the end of P-S to almost half of the M-S. After the half of M-S until P-S, a recurvatum can be observed, and it reaches a knee hyper-extension of 10o, then a delayed flexion between normal limits and finally, end the gait cycle with almost 10o in flexion. Ankle flexion is like normal until the middle of M-S, and between normal limits until P-S, however, the plantar flexion is restricted until the end of initial swing where it reaches only around 10o, and then returns to neutral or slightly dorsal in the rest of swing phase. As, in Type III, the duration of swing phase is shortened (in about 15o), and slightly more than Type II, in a 75% stance, 25% swing proportion. The pattern consistency is good for the ankle and for the pelvic tilt in swing and terminal stance. Another range of augmented variability is observed in hip flexion during the first two sub phases of stance, and in the knee in P-S and initial swing.

CONCLUSIONS

There is a consistent kinematics pattern for Types I to IV SH for the unaffected contralateral limb, and SVM models can be used successfully as a classifying tool in gait patterns. Support vectors form an important dataset to analyze, because they represent the kinematic pattern that makes the classification difficult and it could be related with the inconsistencies and critical points in SH characterization. The widening of standard deviation band could be due to variability either in amplitude or in the stride, stance and swing durations. It is recommended to increase the number of patients and records. For further studies, in the inclusion of all kinematics variables instead of just the sagittal plane should be considered.

ACKNOWLEDGMENT

All authors would like to give an acknowledgment to Danirida Urbano, P.T. from the Gait Laboratory of the «Hospital Ortopédico Infantil», Caracas, Venezuela.

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