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The motion analysis system and the fingertip motion area
THE MOTION
ANALYSIS SYSTEM AND MOTION AREA
THE
FINGERTIP
Normal values in young adults H-Y. CHIU, F. C. SU and S-T. WANG
From the Section of Plastic Surgery, Department of Surgery, Institute of Biomedical Engineering and the Department of Public Health, National Cheng-Kung University, Tainan, Taiwan, Republic of China The reliability of the motion analysis system and the normal value of the fingertip motion area have been studied in young adults. The results indicate that the motion analysis system is a reliable tool for the evaluation of fingertip motion. It was found that the fingertip motion area in young adults has a linear correlation with the square of the finger length. Therefore, the normal value of the fingertip motion area can be calculated from the finger length.
Journal of Hand Surgery (British and European Volume, 1998) 23B." 1:53-56 The dynamic length of the finger should be measured to the base of the axis of rotation of the metacarpophalangeal joint. This measurement is difficult to do. In this study, the finger length was measured from a surface landmark. We marked the highest point of the knuckle of each finger when the hand was in the intrinsic-plus position with the fingers in the horizontal plane. The distance between this point and the corresponding fingertip was measured to give the length of each finger. The motion areas of the fingertips were evaluated by the ExpertVision motion analysis system (Motion Analysis Corporation, California, USA). This system consists of six CCD video cameras, two VP 320 video processors, a Sun 4/110 workstation and an IBM compatible personal computer which is capable of tracking the motion of reflecting markers in three dimensions with an accuracy within 0.1% error of the field of view. The calibration of the volume space in which the hand motion tasks were performed and the locations of the reflective markers on the hand were similar to those reported previously (Chiu and Su; )996). The subject was asked to adopt five postures when filmed by the video cameras (Chiu, 1995). Starting with all the finger joints in full extension, the subject was then instructed to make an intrinsic-plus posture, followed by flexion of the PIP joints while maintaining extension of the DIP joints. The subject was asked to make a fist, and then to extend the MP joints while maintaining flexion of the PIP and DIP joints (hook grip), and finally to return to the original posture. It took less than 5 seconds to complete such a cycle. The video system worked at 60 Hz during recording of the motion cycle and we recorded continuously for 10 seconds during each examination. The three-dimensional coordinates of the markers were registered and reconstructed using the motion analysis system software. Three markers on the dorsum of the hand were used to construct a local hand coordinate system. Through transformation between the laboratory coordinate system and the hand coordinate system, the marker on the fingertip was expressed in the hand coordinate system. Finally, a computer software system was developed for numerical integration to corn-
Computer-aided motion analysis instrumentation has been designed to provide objective spatial and temporal assessment of the movement of body segments. It has been primarily used for gait analysis. A video-based motion analysis system has been used to evaluate the upper-extremity performance in athletes and musicians (An and Bejjani, 1990). Harding et al (1993) have also used optoelectric motion analysis to measure finger movement during piano playing. Recently, the motion analysis system has been used to evaluate fingertip motion in hand injury patients (Chiu and Su, 1996). By using this technique, the finger function of patients can be assessed along with coexisting dysfunctions and deformities. The curve derived from the motion analysis system and the area calculated from it can be compared in serial examinations. However, the fingertip motion area in normal individuals has not yet been described. Therefore, the present study was done to assess the normal value of the fingertip motion area measured by the motion analysis system in young adults. SUBJECTS AND METHODS Subjects who had congenital anomalies or scars caused by previous injury in the hand were excluded. Thirty-two young volunteers (18 women and 14 men) were involved in this study. Their ages ranged from 18 to 26 years, with a mean of 22.3 years. Ten volunteers (four women and six men) were involved in the first part of the study to assess the reliability of the measurement of the fingertip motion area by the motion analysis system. In this part of the study, the fingertip motion area of the left long finger of each volunteer was studied three times with a 1-week interval between each study. The remaining 22 volunteers (14 women and eight men) were studied to assess the normal value of fingertip motion area in young adults. Since the length of the finger influences the fingertip motion area, the length of each finger studied was measured before the motion analysis study. The finger length and the fingertip motion area were measured in all the fingers of both hands in these volunteers. 53
54
THE JOURNAL OF HAND SURGERY VOL. 23B No. 1 FEBRUARY 1998
pute the area of the moving trajectory of the fingertip based on the vectors formed by the markers and data generated by the video tracking system.
Statistical analysis The repeated fingertip motion areas of the ten normal subjects were analysed by one-way (random-effect) analysis of variance (ANOVA) to determine the reliability of the measurements derived from the motion analysis system (Fleiss, 1986), and interval estimation on the reliability was made accordingly based on the results. The relationship between the fingertip motion area and the finger length was modelled by a parabola of the form (i) Area = bl x length
+
b 2 × (length) 2
where b I and b 2 are the regression parameters for the first- and second-degree terms, respectively. An intercept term was not included in the above equation because of the constraint that area = 0 when length = 0. Following a suggestion by Kv~tlseth (1985), caution was taken in the estimation of squared multiple correlation coefficient (so-called R 2) of such a fit without intercept. The hypothesis that b 1 = 0 and/or b 2 = 0 were tested statistically. A simpler model of (i) was applied to the data if either of them was found to be zero.
ues of fingertip motion area. In nine examinations there was some disturbance of reflection which as a consequence affected the reconstruction of the motion area. These invalid data were excluded from the assessment of normal values. The disturbance occurred most frequently (six cases) when assessing the motion area of the little finger. The reason was probably that the little finger is the shortest finger and the detection of the reflected signal from the fingertip is often affected by other fingers. The data of the remaining 167 fingers showed that the finger length ranged from 5.8 cm to 11.9 cm, and the maximal fingertip motion area ranged from 16.1 cm 2 to 119.3 cm 2. The mean and standard deviation of measured finger length and fingertip motion area for each finger are summarized in Table 2. The results from a multiple regression analysis of the data between the fingertip motion area and the finger length using the model (i) are presented in Table 3. The first-degree term was not statistically significant (b 1 = -0.454, P = 0.552), but the second term was (b 2 = 0.723, P < 0.0001). A simpler model of (i) including the second-degree term only was then applied to fit the data. A scatterplot of the area versus square of the finger length and the fitted linear function is shown in Figure 2. The square of the finger length clearly has a linear relationship with the area of fingertip motion described by the equation: Motion area (cm z) = 0.677 x (Finger length) 2 when R 2 is 0.972 (Kvgtlseth, 1985: equation 7).
RESULTS The three repeated measurements of the fingertip motion area in the ten normal subjects are shown in Table 1. A graphic display of the repeated measurements in one case is shown in Figure 1. The reliability was calculated as 0.94 (Fleiss, 1986: equation (1.16)), and the 95% confidence limits of the reliability was 0.86-1.00 (Fleiss, 1986: equation (1.20)). This assessment reveals that the motion analysis system is a reliable tool for the evaluation of fingertip motion. One hundred and seventy-six fingers from both hands of the volunteers were studied to assess the normal val-
DISCUSSION Traditionally, evaluation of finger motion has been mainly based on the measurement of the active range of motion of each joint of the finger (Strickland, 1985; Swanson et al, 1987) but these evaluations fail to express the actual multi-articular motion of the finger. We reported a new technique to measure the fifigertip motion area in a two-dimensional plane by motion analysis system (Chiu and Su, 1996), although the motion analysis system can also measure the finger movement in threedimensional space. However, the movement of the finger
Table 1--The repeated measurements of fingertip motion area (cm2) in ten normal subjects Case no.
1st
2nd
3rd
1 2 3 4 5 6 7 8 9 10
86.12 67.99 65.70 86.72 86.81 55.14 76.23 80.13 66.17 100.73
91.94 63.38 67.55 95.36 82.09 54.66 72.41 78.59 55.55 98.23
89.15 70.14 59.09 95.01 80.66 58.24 74.74 77.73 68.62 103.60
Mean (SD)
77.17 (13.55)
75.98 (15.93)
77.70 (14.84)
MOTIONANALYSISSYSTEM
55
Table 2--Data of the measured finger length (era) and fingertip motion area (era2) in 22 normal subjects. Mean (SD).
N Length Area
Index finger
Long finger
Ring finger
Little finger
43 9.4 (0.7) 58.2 (10.7)
42 10.3 (0.8) 74.8 (13.5)
44 9.8 (0.8) 66.9 (15.3)
38 7.7 (0.7) 37.7 (11.8)
140 Area = 0.677*(Finger Length)2
120
©
100 o
80 60
40 20
0
•
0 -20
Fig 1
-15
-10
-5
0
5
,
,
20
40
is mainly in a two-dimensional plane parallel to the long axis of each finger. This was confirmed by the results of the previous study which showed that after reconstruction of a three-dimensional motion track, the area of fingertip motion was concentrated in one plane with minimal motion in the remaining two planes (Chiu and Su, 1996). The examined finger moves along a fixed motion track in a two-dimensional plane, and the assessment of the volume covered by the moving track in three-dimensional space would be very complicated. There are some disadvantages in applying this method of evaluation (Chiu, 1995). It is more complicated than the conventional angular measurement. It requires more active participation by the patient. Also the passive range of motion cannot be evaluated. Howevel, it has several advantages. Firstly, it is not an angular measurement, it is a two-dimensional figure in which the fingertip cannot move from this fixed plane (as shown in Fig 1). Secondly, the postures made in constructing the motion track figure are governed by various combinations of flexion and extension of the MP, PIP and D I P joints along with contraction and relaxation of the flexor and extensor muscles. Therefore, this method can be used on fingers with functional abnormalities or deformities. Thirdly, the figure derived from the study can easily be compared in serial examinations. The first part of this study was conducted to assess the reliability of data derived from the motion analysis
80
100
,
.
120
,
140
.
160
Square o f Finger Length
10
Graphic display of the three repeated measured areas of fingertip motion in one subject. Measurements in cm.
.
60
Fig 2
The scatterplot of the fingertip motion area versus square of finger length and associated regression line.
system. Repeated studies of the same finger for three times at 1-week intervals showed a high statistical reliability for the method. The data derived is reproducible. The length of the finger certainly influences the motion area. Therefore, in addition to the fingertip motion area, finger length has been measured to allow standardization of the data for fingertip motion area obtained in this study. After statistical analysis, the results have shown that there is a linear correlation between the motion area and the square of finger length. From the regression equation, the normal value of fingertip motion area can easily be calculated from the measured finger length for comparison. The square of the finger length multiplied by 0.677 would equal the predicted fingertip motion area in a normal subject. Acknowledgement
This workwas supportedby grant NSC 85-2331-B-006-097,fromthe National ScienceCouncilof the Republicof China. Table 3--Multiple regression analysis of the relationship between area and length
Variable
Coeff
SE
T
P-value
Length (Length)2
-0.454 0.723
0.762 0.78
-0.592 9.245
0.552 <0.0001
Coeff,coefficient;SE, standarderror
56
References An K-N, Bejjani F J (1990). Analysis of upper-extremity performance in athletes and musicians. H a n d Clinics, 6: 3 9 3 4 0 3 . Chiu H-Y (1995). A method of two-dimensional measurement for evaluating finger motion impairment: A description of the method and comparison with angular measurement. Journal of H a n d Surgery, 20B: 691 695. Chiu H-Y, Su F C (1996). The motion analysis system and the maximal area of fingertip motion. Journal of H a n d Surgery, 21B: 604 608. Fleiss J L. The design and analysis of clinical experiments. New York, John Wiley & Sons, 1986: 8-12. Harding D C, Brand K D, Hillberry B M (1993). Finger joint force minimization in pianists using optimization techniques. Journal of Biomechanics, 26: 1403 1412.
THE J O U R N A L OF H A N D SURGERY VOL. 23B No. 1 FEBRUARY 1998 KvSlseth T O (1985). Cautionary note about R ~'. The American Statistician, 39: 279-285. Strickland J W (1985). Results of flexor tendon surgery in Zone II. H a n d Clinics, 1: 167-179. Swanson A B, Goran-Hagert C, de Groot Swanson G (1987). Evaluation of impairment in the upper extremity. Journal of H a n d Surgery, 12A: 896426. Received: 24 April 1997 Accepted after revision: 3 September 1997 H-Y Chiu MD, Section of Plastic Surgery, Department of Surgery, National Cheng-Kung University, 138 Shengli Road, Tainan, Taiwan, Republic of China. ~©1997The British Society for Surgery of the Hand
ANALYSIS SYSTEM AND MOTION AREA
THE
FINGERTIP
Normal values in young adults H-Y. CHIU, F. C. SU and S-T. WANG
From the Section of Plastic Surgery, Department of Surgery, Institute of Biomedical Engineering and the Department of Public Health, National Cheng-Kung University, Tainan, Taiwan, Republic of China The reliability of the motion analysis system and the normal value of the fingertip motion area have been studied in young adults. The results indicate that the motion analysis system is a reliable tool for the evaluation of fingertip motion. It was found that the fingertip motion area in young adults has a linear correlation with the square of the finger length. Therefore, the normal value of the fingertip motion area can be calculated from the finger length.
Journal of Hand Surgery (British and European Volume, 1998) 23B." 1:53-56 The dynamic length of the finger should be measured to the base of the axis of rotation of the metacarpophalangeal joint. This measurement is difficult to do. In this study, the finger length was measured from a surface landmark. We marked the highest point of the knuckle of each finger when the hand was in the intrinsic-plus position with the fingers in the horizontal plane. The distance between this point and the corresponding fingertip was measured to give the length of each finger. The motion areas of the fingertips were evaluated by the ExpertVision motion analysis system (Motion Analysis Corporation, California, USA). This system consists of six CCD video cameras, two VP 320 video processors, a Sun 4/110 workstation and an IBM compatible personal computer which is capable of tracking the motion of reflecting markers in three dimensions with an accuracy within 0.1% error of the field of view. The calibration of the volume space in which the hand motion tasks were performed and the locations of the reflective markers on the hand were similar to those reported previously (Chiu and Su; )996). The subject was asked to adopt five postures when filmed by the video cameras (Chiu, 1995). Starting with all the finger joints in full extension, the subject was then instructed to make an intrinsic-plus posture, followed by flexion of the PIP joints while maintaining extension of the DIP joints. The subject was asked to make a fist, and then to extend the MP joints while maintaining flexion of the PIP and DIP joints (hook grip), and finally to return to the original posture. It took less than 5 seconds to complete such a cycle. The video system worked at 60 Hz during recording of the motion cycle and we recorded continuously for 10 seconds during each examination. The three-dimensional coordinates of the markers were registered and reconstructed using the motion analysis system software. Three markers on the dorsum of the hand were used to construct a local hand coordinate system. Through transformation between the laboratory coordinate system and the hand coordinate system, the marker on the fingertip was expressed in the hand coordinate system. Finally, a computer software system was developed for numerical integration to corn-
Computer-aided motion analysis instrumentation has been designed to provide objective spatial and temporal assessment of the movement of body segments. It has been primarily used for gait analysis. A video-based motion analysis system has been used to evaluate the upper-extremity performance in athletes and musicians (An and Bejjani, 1990). Harding et al (1993) have also used optoelectric motion analysis to measure finger movement during piano playing. Recently, the motion analysis system has been used to evaluate fingertip motion in hand injury patients (Chiu and Su, 1996). By using this technique, the finger function of patients can be assessed along with coexisting dysfunctions and deformities. The curve derived from the motion analysis system and the area calculated from it can be compared in serial examinations. However, the fingertip motion area in normal individuals has not yet been described. Therefore, the present study was done to assess the normal value of the fingertip motion area measured by the motion analysis system in young adults. SUBJECTS AND METHODS Subjects who had congenital anomalies or scars caused by previous injury in the hand were excluded. Thirty-two young volunteers (18 women and 14 men) were involved in this study. Their ages ranged from 18 to 26 years, with a mean of 22.3 years. Ten volunteers (four women and six men) were involved in the first part of the study to assess the reliability of the measurement of the fingertip motion area by the motion analysis system. In this part of the study, the fingertip motion area of the left long finger of each volunteer was studied three times with a 1-week interval between each study. The remaining 22 volunteers (14 women and eight men) were studied to assess the normal value of fingertip motion area in young adults. Since the length of the finger influences the fingertip motion area, the length of each finger studied was measured before the motion analysis study. The finger length and the fingertip motion area were measured in all the fingers of both hands in these volunteers. 53
54
THE JOURNAL OF HAND SURGERY VOL. 23B No. 1 FEBRUARY 1998
pute the area of the moving trajectory of the fingertip based on the vectors formed by the markers and data generated by the video tracking system.
Statistical analysis The repeated fingertip motion areas of the ten normal subjects were analysed by one-way (random-effect) analysis of variance (ANOVA) to determine the reliability of the measurements derived from the motion analysis system (Fleiss, 1986), and interval estimation on the reliability was made accordingly based on the results. The relationship between the fingertip motion area and the finger length was modelled by a parabola of the form (i) Area = bl x length
+
b 2 × (length) 2
where b I and b 2 are the regression parameters for the first- and second-degree terms, respectively. An intercept term was not included in the above equation because of the constraint that area = 0 when length = 0. Following a suggestion by Kv~tlseth (1985), caution was taken in the estimation of squared multiple correlation coefficient (so-called R 2) of such a fit without intercept. The hypothesis that b 1 = 0 and/or b 2 = 0 were tested statistically. A simpler model of (i) was applied to the data if either of them was found to be zero.
ues of fingertip motion area. In nine examinations there was some disturbance of reflection which as a consequence affected the reconstruction of the motion area. These invalid data were excluded from the assessment of normal values. The disturbance occurred most frequently (six cases) when assessing the motion area of the little finger. The reason was probably that the little finger is the shortest finger and the detection of the reflected signal from the fingertip is often affected by other fingers. The data of the remaining 167 fingers showed that the finger length ranged from 5.8 cm to 11.9 cm, and the maximal fingertip motion area ranged from 16.1 cm 2 to 119.3 cm 2. The mean and standard deviation of measured finger length and fingertip motion area for each finger are summarized in Table 2. The results from a multiple regression analysis of the data between the fingertip motion area and the finger length using the model (i) are presented in Table 3. The first-degree term was not statistically significant (b 1 = -0.454, P = 0.552), but the second term was (b 2 = 0.723, P < 0.0001). A simpler model of (i) including the second-degree term only was then applied to fit the data. A scatterplot of the area versus square of the finger length and the fitted linear function is shown in Figure 2. The square of the finger length clearly has a linear relationship with the area of fingertip motion described by the equation: Motion area (cm z) = 0.677 x (Finger length) 2 when R 2 is 0.972 (Kvgtlseth, 1985: equation 7).
RESULTS The three repeated measurements of the fingertip motion area in the ten normal subjects are shown in Table 1. A graphic display of the repeated measurements in one case is shown in Figure 1. The reliability was calculated as 0.94 (Fleiss, 1986: equation (1.16)), and the 95% confidence limits of the reliability was 0.86-1.00 (Fleiss, 1986: equation (1.20)). This assessment reveals that the motion analysis system is a reliable tool for the evaluation of fingertip motion. One hundred and seventy-six fingers from both hands of the volunteers were studied to assess the normal val-
DISCUSSION Traditionally, evaluation of finger motion has been mainly based on the measurement of the active range of motion of each joint of the finger (Strickland, 1985; Swanson et al, 1987) but these evaluations fail to express the actual multi-articular motion of the finger. We reported a new technique to measure the fifigertip motion area in a two-dimensional plane by motion analysis system (Chiu and Su, 1996), although the motion analysis system can also measure the finger movement in threedimensional space. However, the movement of the finger
Table 1--The repeated measurements of fingertip motion area (cm2) in ten normal subjects Case no.
1st
2nd
3rd
1 2 3 4 5 6 7 8 9 10
86.12 67.99 65.70 86.72 86.81 55.14 76.23 80.13 66.17 100.73
91.94 63.38 67.55 95.36 82.09 54.66 72.41 78.59 55.55 98.23
89.15 70.14 59.09 95.01 80.66 58.24 74.74 77.73 68.62 103.60
Mean (SD)
77.17 (13.55)
75.98 (15.93)
77.70 (14.84)
MOTIONANALYSISSYSTEM
55
Table 2--Data of the measured finger length (era) and fingertip motion area (era2) in 22 normal subjects. Mean (SD).
N Length Area
Index finger
Long finger
Ring finger
Little finger
43 9.4 (0.7) 58.2 (10.7)
42 10.3 (0.8) 74.8 (13.5)
44 9.8 (0.8) 66.9 (15.3)
38 7.7 (0.7) 37.7 (11.8)
140 Area = 0.677*(Finger Length)2
120
©
100 o
80 60
40 20
0
•
0 -20
Fig 1
-15
-10
-5
0
5
,
,
20
40
is mainly in a two-dimensional plane parallel to the long axis of each finger. This was confirmed by the results of the previous study which showed that after reconstruction of a three-dimensional motion track, the area of fingertip motion was concentrated in one plane with minimal motion in the remaining two planes (Chiu and Su, 1996). The examined finger moves along a fixed motion track in a two-dimensional plane, and the assessment of the volume covered by the moving track in three-dimensional space would be very complicated. There are some disadvantages in applying this method of evaluation (Chiu, 1995). It is more complicated than the conventional angular measurement. It requires more active participation by the patient. Also the passive range of motion cannot be evaluated. Howevel, it has several advantages. Firstly, it is not an angular measurement, it is a two-dimensional figure in which the fingertip cannot move from this fixed plane (as shown in Fig 1). Secondly, the postures made in constructing the motion track figure are governed by various combinations of flexion and extension of the MP, PIP and D I P joints along with contraction and relaxation of the flexor and extensor muscles. Therefore, this method can be used on fingers with functional abnormalities or deformities. Thirdly, the figure derived from the study can easily be compared in serial examinations. The first part of this study was conducted to assess the reliability of data derived from the motion analysis
80
100
,
.
120
,
140
.
160
Square o f Finger Length
10
Graphic display of the three repeated measured areas of fingertip motion in one subject. Measurements in cm.
.
60
Fig 2
The scatterplot of the fingertip motion area versus square of finger length and associated regression line.
system. Repeated studies of the same finger for three times at 1-week intervals showed a high statistical reliability for the method. The data derived is reproducible. The length of the finger certainly influences the motion area. Therefore, in addition to the fingertip motion area, finger length has been measured to allow standardization of the data for fingertip motion area obtained in this study. After statistical analysis, the results have shown that there is a linear correlation between the motion area and the square of finger length. From the regression equation, the normal value of fingertip motion area can easily be calculated from the measured finger length for comparison. The square of the finger length multiplied by 0.677 would equal the predicted fingertip motion area in a normal subject. Acknowledgement
This workwas supportedby grant NSC 85-2331-B-006-097,fromthe National ScienceCouncilof the Republicof China. Table 3--Multiple regression analysis of the relationship between area and length
Variable
Coeff
SE
T
P-value
Length (Length)2
-0.454 0.723
0.762 0.78
-0.592 9.245
0.552 <0.0001
Coeff,coefficient;SE, standarderror
56
References An K-N, Bejjani F J (1990). Analysis of upper-extremity performance in athletes and musicians. H a n d Clinics, 6: 3 9 3 4 0 3 . Chiu H-Y (1995). A method of two-dimensional measurement for evaluating finger motion impairment: A description of the method and comparison with angular measurement. Journal of H a n d Surgery, 20B: 691 695. Chiu H-Y, Su F C (1996). The motion analysis system and the maximal area of fingertip motion. Journal of H a n d Surgery, 21B: 604 608. Fleiss J L. The design and analysis of clinical experiments. New York, John Wiley & Sons, 1986: 8-12. Harding D C, Brand K D, Hillberry B M (1993). Finger joint force minimization in pianists using optimization techniques. Journal of Biomechanics, 26: 1403 1412.
THE J O U R N A L OF H A N D SURGERY VOL. 23B No. 1 FEBRUARY 1998 KvSlseth T O (1985). Cautionary note about R ~'. The American Statistician, 39: 279-285. Strickland J W (1985). Results of flexor tendon surgery in Zone II. H a n d Clinics, 1: 167-179. Swanson A B, Goran-Hagert C, de Groot Swanson G (1987). Evaluation of impairment in the upper extremity. Journal of H a n d Surgery, 12A: 896426. Received: 24 April 1997 Accepted after revision: 3 September 1997 H-Y Chiu MD, Section of Plastic Surgery, Department of Surgery, National Cheng-Kung University, 138 Shengli Road, Tainan, Taiwan, Republic of China. ~©1997The British Society for Surgery of the Hand