2000 Mathematics Subject Classification: 62P10, 92C20Gait analysis is one of the methods used for estimation of the degree of restoration of motor recovery after stroke. The purpose of the present study was to examine the diagnostic value of the footprint parameters and their relationship with the functional ambulation profile (FAP) scores provided automatically by the pressure sensor walkway system for gait examination. The patterns of walking were studied in a group of 23 patients with chronic unilateral stroke and 72 healthy subjects. Among the measured gait variables the peak times of the footprints were found as most informative parameters. Their predictive value was compared with some other gait indicators
for motor recovery after stroke

Mateev, Plamen S.

Tarkka, Ina M.

Titianova, Ekaterina B.

Bulgarian Digital Mathematics Library at IMI-BAS

Pliska Stud. Math. Bulgar. 16 (2004), 121-128STUDIA MATHEMATICABULGARICAGAIT MEASUREMENTS AND MOTOR RECOVERY AFTERSTROKEPlamen S. Mateev, Ina M. Tarkka, Ekaterina B. TitianovaGait analysis is one of the methods used for estimation of the degree ofrestoration of motor recovery after stroke. The purpose of the present studywas to examine the diagnostic value of the footprint parameters and theirrelationship with the functional ambulation profile (FAP) scores providedautomatically by the pressure sensor walkway system for gait examination.The patterns of walking were studied in a group of 23 patients with chronicunilateral stroke and 72 healthy subjects. Among the measured gait vari-ables the peak times of the footprints were found as most informative param-eters. Their predictive value was compared with some other gait indicatorsfor motor recovery after stroke.1. IntroductionGait abnormalities after chronic unilateral stroke have been clinically evaluatedand described by a number of investigators using different methods [1],[3],[6],[7].Most of the techniques however are time consuming or otherwise insufficient forcollecting reliable data. Recent technology has resulted in flexible and portablewalkways with embedded pressure sensitive sensors. The pressure sensor systemrecords the location of activated sensors and the time of their activation anddeactivation. It provides the spatial and temporal variables of gait along with adynamic pressure mapping of each footprint during walking [4],[5]. The clinicalapplicability of this technique is under investigation.2000 Mathematics Subject Classification: 62P10, 92C20Key words: gait analysis, recovery after stroke122 P. Mateev, I. Tarkka, E. TitianovaThe purpose of the present study was to examine the diagnostic value of thepressure sensor system GAITRite for distinguish gait abnormalities after strokeusing the estimation of footprint parameters and functional ambulation profile(FAP) scores provided automatically by the equipment.2. Gait Equipment and RecordingsAll gait measurements were performed with a portable GAITRite system (MAP/CIR Inc., Havertown, PA). This system consists of an electronic walkway of 4.57m with an active area of 3.66 × 0.61 m, where the sensor pads are encapsulated.13,824 sensors, each 1 cm in diameter, are arranged in a 48 × 288 grid pattern.Detail information about the methodology is given in [8]. The system continu-ously scans the sensors, provides information about the geometry of the footprintsin 2-D space and gives a dynamic pressure mapping during walking by recordingthe location of activated sensors and the time of sensor activation/deactivation.At least one complete stride for each side inside the walkway is required to com-plete the computation. Measurements of the spatial and temporal gait variablesare based on the geometric centers of heels for each of the 3 consecutive footprints(Figure 1). The subjects were asked to walk twice across the walkway withoutshoes. The average of both trials was analyzed. The walking distance (cm) andthe ambulation time (s) were obtained from the heel centers of the first and lastfootprints.Figure 1: The series of three footprints.Each footprint is divided into 12 trapezoids. Points A, D and G are thegeometric centers of the heel for each footprint [2].Gait Measurements and Motor Recovery after Stroke 123The Functional Ambulation Profile (FAP) scores are calculated by the systemas a general indicator for the tested patient. The algorithm of FAP calculationincludes following steps [2]:1) For each limb the step length (measured electronically by the walkway) isdivided by the leg length (measured manually) to produce the Step Length/LegLength ratio (SL/LL), at the patient’s preferred velocity. The velocity, collectedover the 3.66 meters of the GAITRite active area is divided by the patient’s meanleg length to produce the mean normalized velocity expressed in Leg Lengths persecond (LL/sec).2) For each limb, the SL/LL ratio, the step time and the mean normalized velocityare then compared on a model of regression lines to determine their deviationsfrom the normal. This constitutes 44% of the total score, or 22% for each limb’sperformance.3) The degree of asymmetry is calculated by subtracting the SL/LL ratios of eachlimb and then compared to normal, representing 8% of the total score.4) The dynamic base of support, measured by the GAITRite walkway is alsocompared to normal, representing 8% of the total score.5) Use of assisting devices such as orthoses, splints etc. represent 5% of the totalscore. Ambulatory aids such as canes, crutches, or walkers represent 5% of thetotal score.The final score is derived subtracting points from a maximum score of 100.The maximum score of 100 is obtained at ordinary speed when step extremityratios and step times are symmetrical and a dynamic base of support is less than10 cm (see [5], [8]).So defined FAP score is not sufficiently convincing and manual operationsare necessarily. Our hypothesis is that among measured parameters exist moreinformative ones.According the recording system, the footprint was divided into 12 trapezoids,6 for the lateral part and 6 for the medial part. Each trapezoid, includes a spe-cific number of sensors and the order for assigning sensor activation is heel-to-toe.The following parameters were evaluated for each trapezoid: segmental integratedpressure over time (P*t) (expressed as a percent of the overall integrated pres-sure over time), peak time (s) (first time point of each trapezoid when one ormore sensors within a segment is at the maximum switching level), active area(expressed as a percent of the sum of the active sensors within one segment) andpeak pressure (the maximum switching level expressed as a percent of the overallmaximum switching level at the peak time in a segment). Detailed explanationof technology of the footprint measurements is given in [9].124 P. Mateev, I. Tarkka, E. TitianovaAll mentioned variables were tested as predictors in models for degree ofmotor recovery.3. The SampleFor the purpose of the study 3 experimental groups were measured:The first group (A) consisted from 23 patients (16 men and 7 women, meanage 54.8± 6.9 years, range 38-65 years; mean height 170.8± 8.8 cm, mean weight82.8 ± 18.9 kg) with residual hemiparesis due to stroke. Some patients had sur-vived unilateral cerebral infarction in the middle cerebral artery territory andothers had a unilateral cerebral hemorrhage. They walked with a preferred ordi-nary speed.The second group (B) included 62 clinically healthy subjects (21 men and41 women, mean age 41.41 ± 11.0 years, range 21-61 years, mean height 1.70 ±10.09 m, mean weight 71.61±11.6 kg).They were non homogeneous set of peoplewithout explicit illness and walked with a preferred ordinary speed.In the third group (C) were enrolled 10 clinically healthy subjects (5 men and5 women, mean age 50.9 ± 4.4 years, range 46-58 years, mean height 1.69± 0.09m, mean weight 77.6 ± 23.4kg). Fifty measurements were taken at 5 differentspeeds (from very slow to very fast). The velocity performance was divided into5 categories: < 40 cm/s, 40-70 cm/s, 70-100 cm/s, 100-130 cm/s and > 160 cm/s.All patients and healthy subjects were engaged in a small training session andthey gave an informed consent prior to the study.4. Results and discussionThe description of the algorithm calculating the FAP score is not enough to bereproduced. Nevertheless it is clear that the value of the FAP score depends onthe velocity of the tested person. The scatter plot of Velocity and FAP scoreof patients of group (A) and volunteers in group (C) illustrate our suspicions(Figure 2.The FAP score falls when velocity is small as well higher than 160 cm/s.Decreasing the velocity is not sufficient to distinguish the ailing from healthypersons.Most of the reported gait measurements are unidimensional (velocity, ca-dence, FAP scores etc.) or bidimensional (left and right stance time, swing time,step length, etc.) averaged characteristics. The latter are commonly used toindicate some gait asymmetry.As shown earlier, there were four indicators, reported by the system for everyone of the twelve trapezoids of each footprint. We chose one of them, namelyGait Measurements and Motor Recovery after Stroke 125Figure 2: Scatter plot of Velocity versus FAP score points. The dependencefollows a nonlinear function . The FAP scores fall when velocity were smallerthan 80 cm/s and higher than 160 cm/s.”Peak-time”, as more informative for some deviations of the manner of the steps.Our choice was based on numerical experiments with correlation matrix of thosefour sets of parameters evaluated on the three experimental groups and theircombinations. As an example, for the peak time using the homogenous group(C) we found that the first principal component explains 85% of total variance.Another control group (B) is more variable and only 45% are explained fromfirst two principal components. The combination of the groups (A) and (C) gives81% explained variation for two factors (principal components). The scatter plot(Figure 3) of that two groups ((A) and (C)) over the two factors suggests thatthe two groups may be distinguished using peak-time characteristics.Adding group (A) to group (C) increased the number of factors in the analysisfrom one (when only (C) was included in analysis) to two. There were not sucheffect combining the groups (A) and (B).Our hypothesis was confirmed in the next phase of the investigations, namelythe linear discriminant analysis. First we applied the procedure to the groups(A) and (C) as training sample. As a result (see table 1) we had 98% correctclassification of the group (C) and 82.6% correct classification in the group (A).The total correct classification was 93.15%. Posterior probabilities of the controlgroup (B) gave 59 right classifications of 62 examined persons or 95.16 %.A similar attempt was performed using groups (A) and (B) as training sam-ple. The classification of the both groups was a little bit better, but posteriorprobabilities on control group (C) now is extremely indicative(see table 2).126 P. Mateev, I. Tarkka, E. TitianovaFigure 3: The principal component analysis of the footprint peak times in patientsand controls. The projection of the all footprint peak time observations of thetwo common factors differentiated stroke gait from normal walking.Classified as good bad CorrectGroup walkers walkers classifications(A) (23 bad) 4 19 82.61%(C) (50 good) 49 1 98.00%Total 93.15%(B) (62 good) 59 3 95.16%Table 1: The classification table: the groups (A) and (C) as training sample.5. ConclusionsOur study reveals that a pressure sensor system GAITRite is a reliable screeninginstrument for detection of gait abnormalities after chronic unilateral stroke basedon the footprint peak time measurements. By testing the volunteers at differentwalking velocities as a training sample more reliable information for gait qualityis possible to obtain.There are optimistic conjectures that a better diagnostics are to be attained.First, using more flexible nonlinear algorhytm [10] for estimation of discriminationrule. Second, detailed information from the equipment including dynamics of thegait and higher order statistics.Gait Measurements and Motor Recovery after Stroke 127Classified as good bad CorrectGroup walkers walkers classifications(A) (23 bad) 3 20 86.96%(B) (62 good) 62 0 100.00%Total 96.47%(C) (5×10 good) 31 19 62.00%velocity categories:< 40 cm/s 0 10 0.00%40-70 cm/s 5 5 50.00%70-100 cm/s 7 3 70.00%100-130 cm/s 9 1 90.00%> 160 cm/s 10 0 100.00%Table 2: The classification table: groups (A) and (B) as training sample6. AcknowledgmentNeither an author nor any author’s institution has received any commercial finan-cial support related to this study. The company manufacturing this equipmentor the distributor were not involved in any way in this study. The authors thankMr. Paavo Kononen, MSc, and Mrs. Aila Keinanen, RN, for their help duringthe collection of the data. The Academy of Finland and Bulgarian Academyof Science and the Brain Research and Rehabilitation Center Neuron, Kuopio,Finland provided financial support for this work.REFERE NCES[1] T. P. Andriacchi, J. A. Ogle, J. O. Galante. Walking speed as a basisfor normal and abnormal gait measurements. Biomech. 10 (1977) 261–68.[2] GAITRite Operating manual. GAITRite portable gait analysis system.CIR/MAP Inc., 1625 East Darby Rd., Havertown, PA 19083, USA.[3] M. Marks, G. Hirschberg. Analysis of the hemiparetic gait. Ann NYAcad Sci. 74 (1958), 59–77.[4] A. L. McDonough, M. Batavia, F. C. Chen, et al. The validity andthe reliability of the GAITRite system’s measurements: a preliminary eval-uation. Arch Phys Med Rehabil 82 (2001), 419–425.128 P. Mateev, I. Tarkka, E. Titianova[5] A. J. Nelson, L. J. Certo, L. Lembo, et al. The functional ambula-tion performance of elderly fallers and non-fallers walking at their preferredvelocity. NeuroRehab 3 (1999), 141–146.[6] E. J. Roth, C. Merbitz, K. Mroczek , S. A. Dugan, W. W. Suh.Hemiplegic gait. Relationship between walking speed and other temporalparameters. Stroke. 76 (1997), 128–133.[7] E. B. Titianova, I.Tarkka. Asymmetry in walking performance and pos-tural sway in patients with chronic unilateral infarction. J. Rehabil Res Dev.32 (1995), 236–44.[8] E. B. Titianova, K. Pitkanen, J. Sivenius, I. M. Tarkka. Gait charac-teristics and functional ambulation profile in patients with chronic unilateralstroke. Am. J. Phys. Med .Rehabil. 82 (2003), 778–786.[9] E. B. Titianova, P. S. Mateev, I. M. Tarkka. Footprint analysis ofgait using a pressure sensor system. J EMG & Kinesiol. 14 (2) (2004),275–281.[10] D. Vandev. Interactive Discriminant Analysis in MATLAB, Proc. Seminaron Statistical Data Analysis SDA’2003, 21-28 June, Sozopol (2003) (in thisvolume).Plamen S. Mateev Ph.D.Institute of Mathematics and Informatics, Bulgarian Academy of Science,G.Bonchev Str. blok 8,BG -1113 Sofiae-mail: pmat@math.bas.bgIna M. Tarkka, Ph.D.Brain Research and Rehabilitation Center NeuronKortejokiFIN-71130 Kuopioemail:Ina.Tarkka@neuron.fiEkaterina B. Titianova, M.D.,Ph.D.,Specialized University Hospital of Neurology and Psychiatry St. Naum,BG - 1113 Sofiae-mail: titianova@yahoo.com

Gait Measurements and Motor Recovery after Stroke

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Gait Measurements and Motor Recovery after Stroke

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