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Estimation of grip force using the Grip-ball dynamometer
Medical Engineering & Physics 35 (2013) 1698–1702
Contents lists available at ScienceDirect
Medical Engineering & Physics journal homepage: www.elsevier.com/locate/medengphy
Technical note
Estimation of grip force using the Grip-ball dynamometer Aly Chkeir ∗ , Rana Jaber, David J. Hewson, Jacques Duchêne Institut Charles Delaunay, UMR CNRS 6279, Université de Technologie de Troyes, 12 rue Marie Curie, CS 42060, Troyes 10004, France
a r t i c l e
i n f o
Article history: Received 21 November 2012 Received in revised form 13 March 2013 Accepted 6 May 2013 Keywords: Grip-strength Dynamometer Grip-ball
a b s t r a c t The Grip-ball is an innovative device that has been designed to measure grip strength. The Grip-ball consists of an airtight ball that contains a pressure sensor and Bluetooth communication system. The Grip-ball can be inflated to different initial pressures, with data available continuously in real time. The aim of this study was to build a model to predict the force applied to the Grip-ball dynamometer based only on the pressure measured by the Grip-ball and its initial pressure. Forces ranging from 2 to 70 kg were applied to a hybrid version of the device for 10 different initial pressures, ranging from atmospheric pressure of 100 kPa through to 190 kPa. A model was constructed to predict applied force, with force as a function of the initial pressure and the pressure measured. The error of the model was calculated as 1.29 kg across all initial pressures and forces applied. The results of the study are comparable with the errors observed for the gold standard in grip force measurement, the Jamar dynamometer. The best results for force prediction were obtained over the range in which frailty is typically detected. The Grip-ball will now be tested using a large population in order to establish clinical norms. © 2013 IPEM. Published by Elsevier Ltd. All rights reserved.
1. Introduction Measurement of grip strength is an important component of many different evaluations. For instance, grip strength can be used to assess the effectiveness of a surgical or a therapeutical procedure as well as the effect of a rehabilitation programme [1–3]. Grip strength has also been used as a measure of general strength in order to determine work capacity [4] and provide insight into patients’ nutritional status [5]. Weak grip strength is also one of the five criteria of frailty identified by Fried et al. [6]. Grip strength is typically measured by means of a dynamometer, such as the Jamar (Sammons & Preston, Bolingbrook, IL, USA), the Lode (Lode dynamometer; Lode BV, Groningen, The Netherlands), and the Martin Vigorimeter (Martin Medizintechnik, Tuttlingen, Germany).The most widely used device is the Jamar, which is recommended by the American Society for Surgery of the Hand (ASSH) and the American Society of Hand Therapists (ASHT) [7]. The Jamar also has a series of published tables of normative data for a range of different populations [8]. Despite the widespread clinical use of the Jamar, the isometric nature of the device may lead to discomfort for some users [9,10]. For instance, conditions such as rheumatoid arthritis [11], lateral epicondylitis [12], and in particular recovery from carpal tunnel release (CTR) surgery [13], can all lead to lower
∗ Corresponding author. E-mail addresses: [email protected], [email protected] (A. Chkeir), [email protected] (R. Jaber), [email protected] (D.J. Hewson), [email protected] (J. Duchêne).
than expected grip-strength measurements with the Jamar. One of the alternatives to the Jamar is the Martin Vigorimeter, which consists of a bulb attached to a manometer via a tube, with the pressure applied to the bulb displayed on the manometer. The Vigorimeter is highly correlated with the Jamar [14], and is also comfortable to use [9]. Despite these positive points, the Vigorimeter does not actually measure force per se, meaning that it cannot be used to compare results to grip strength norms, for instance an evaluation of frailty using Fried’s criteria. An alternative dynamometer, the “Grip-ball”, was developed in 2008 [15]. This device consists of a supple ball in which pressure and temperature sensors, as well as a data acquisition and communication system have been placed. Communication is performed in real-time via Bluetooth, thus ensuring interoperability with other local devices that could store or transfer the data (computer, tablet, mobile phone, etc.). A comprehensive description of the device can be found in [16,17]. In addition to the digital acquisition system in the Grip-ball, the other main difference with the Vigorimeter is that the Grip-ball is airtight and is equipped with a valve, meaning that the pressure inside the Grip-ball can be modified. Any changes in the initial pressure inside lead to changes in the stiffness of the ball, thus modifying the corresponding dynamics of grip-strength measurement. In order for the Grip-ball to be used for grip-strength measurement, a model needs to be developed to predict the grip force applied based only on the pressure measured and the initial pressure inside the Grip-ball. It has already been shown that grip strength measured with the Jamar is highly correlated with the pressure recorded by the Vigorimeter. In the most comprehensive
1350-4533/$ – see front matter © 2013 IPEM. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.medengphy.2013.05.003
A. Chkeir et al. / Medical Engineering & Physics 35 (2013) 1698–1702
1699
Fig. 1. Experimental setup of the hybrid Grip-ball device and the Stentor.
comparison, Desrosiers et al. reported a linear relationship between the measurements obtained from the two devices, with a correlation of r = 0.89 [14]. Given the linear relationship reported by Desrosiers, it was hypothesised in the present study that a similar linear relationship would exist between the force applied to the Grip-ball and the pressure measured by the device. In respect to the effect of the initial pressure in the Grip-ball, a linear relationship would be expected for all pressures, but the slope of this relationship would vary as a function of the initial pressure. The appropriate model would be expected to take the form: F = aPA where F is the force applied, PA is the pressure applied by the user (the pressure measured by the sensor minus the initial pressure inside the ball), and a is the slope of the relationship that depends on the initial pressure. The aim of the present study, therefore, was to build a unique model to predict the force applied to the Grip-ball based only on the pressure measured by the Grip-ball and its initial pressure. 2. Methodology 2.1. Experimental protocol The Grip-ball is currently undergoing a final development to miniaturise the electronic components. During this development stage, the Grip-ball was evaluated using a hybrid device, partway between a Grip-ball and a Vigorimeter, in which the manometer of the Vigorimeter was replaced by the electronics of the Gripball. The device was rendered air-tight, but was able to be inflated to different pressures [17]. The hybrid device has previously been tested, with an excellent correlation obtained between the pressure measured by the Vigorimeter manometer and the Grip-ball sensor (r = 0.997, p < 0.05) [17]. In addition, the device has been shown to be extremely reliable across a range of internal pressures, with an average ICC value of 0.97 [18].
The force applied to the Grip-ball was quantified by means of a Stentor II 1000 (Andilog technologies, Boulogne-Billancourt, France). This device can exert a force from 0 to 100 kg, with an accuracy of 0.5% and a resolution of 1/10,000, which equates to 9 g for the Stentor used. The force range chosen for the present study was from 0 to 70 kg, corresponding to the range of force naturally produced by the human hand during power gripping [1,19]. The Stentor is equipped with a force transducer, which measures the instantaneous force applied. This force value was sampled at 100 Hz via a standard RS232 connection. Although the SI unit for force is the Newton, the commonly used unit for grip force measurement in clinical practice is kg or lb. Accordingly, all results in the present article are expressed in kg. The rubber bulb of the hybrid device was placed between two identical plastic blocks, as shown in Fig. 1. The position of the bulb was kept constant for all tests. The hybrid device was evaluated for 10 different initial pressures (PI ), ranging from 100 to 190 kPa. Pressure was increased in increments of approximately 10 kPa as the inflation system was not precise enough to enable exact 10 kPa changes to be made. For each PI , the Stentor applied a force from 0 to 70 kg, in 2-kg increments, with pressure values inside the bulb sampled at 15 Hz and wirelessly transmitted via the Bluetooth module included in the Grip-ball. The pressure values recorded corresponded to the absolute pressure inside the bulb, which is the sum of the initial pressure and the increased pressure resulting from the force applied by the Stentor. A five-min pause was observed between each change in PI in order to ensure there were no changes in elasticity as a result of the previous series of measurements.
2.2. Data analysis For all subsequent analyses, force and pressure values were taken to be the average of the last second of recording, corresponding to 100 data points for force (100 Hz) and 15 data points for pressure (15 Hz).
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A. Chkeir et al. / Medical Engineering & Physics 35 (2013) 1698–1702 80
80
70
70
60
Force (kg)
60
Force (kg)
50
50
Pi = 99.5 kPa
40
Pi = 131.4 kPa Pi = 155.5 kPa
30
40
Pi = 186.3 kPa
20 30 10 20
0
0
20
40
60
0
80
100
120
140
160
Pressure (kPa)
10
0
20
40
60
80
100
120
140
160
Fig. 3. Experimental data for four of the initial pressures (99.5, 131.4, 155.5, and 186.3 kPa). The dashed lines are best-fit linear regressions.
Pressure (kPa) Fig. 2. Comparison of the force–pressure relationship between the Grip-ball/Stentor and the Jamar/Vigorimeter (data from Desrosiers). All points displayed are for the Jamar/Vigorimeter. The straight line is the best-fit regression line for the Jamar/Vigorimeter. The regression line of the Grip-ball (- - -) is overlaid.
Linear regression equations were calculated for each PI for the pressure/force relationship. In all regression equations the intercept was forced to pass through zero. The slopes ˛ of all the regression equations were plotted against PI with the resulting linear regression used to predict ˛ as a function of PI : ˛ = ˇPI + where ˇ is the slope of the regression equation and is the error term. The final model was then created using the slope estimation and the pressure applied as: F = (ˇPI + )PA
or
F = ˛PA
The standard error of the estimate was used as a measure of the error of the model:
PI
(j)
PI =PI
(j)
=
(FMES − FEST )2 N−1
where PI
(j)
is the standard error for an initial pressure j, FMES is the
measured force value, FEST is the estimated force value predicted by the model, and N is the number of observations. The standard error of overall model was taken as:
TOT =
∀PI (FMES − FEST )
2
NTOT − 1
where TOT is the standard error across all initial pressures and NTOT is the total number of observations. 3. Results A best-fit linear regression equation for PI of 100 kPa (atmospheric pressure) between the force applied and the change in pressure inside the ball was: F = 0.4753PA with PA expressed in kPa and F in kg, and R2 = 0.99. This equation was then overlaid onto the data obtained from the most highly cited comparison between the Jamar and the Martin
Vigorimeter, those of the paper of Desrosiers et al. [14] (Fig. 2). The regression equation obtained for the Desrosiers data was: F = 0.4926PA which corresponds to a relative difference in the slopes of the regression equations of 3.51%. Data for the force–pressure relationship for the Grip-ball for a selection of PI are shown in Fig. 3. It can be verified that the slope for the best-fit linear regression lines increases as PI increases. The slopes of the regression equations and the goodness of fit, as calculated by the standard error of the estimate, are shown in Table 1. The relationship between PI and the slope of the best-fit regression lines for each force–pressure relationship was linear, with a regression equation computed from all 10 slopes of: = 4.855 × 10−3 PI − 2.020 × 10−2 The goodness of fit of the equation was excellent (R2 = 0.991). In the hypothesised relationship between force and pressure, the only parameter required is the slope of the linear equation that depends on the initial pressure. Replacing ˛ by its model given above, the equation becomes: F = (4.855 × 10−3 PI − 2.020 × 10−2 )PA with force expressed in kg and pressure expressed in kPa. In order to assess the accuracy of the model, standard errors were calculated for the overall model, as well as for each initial pressure (Table 1). The error of the model across all 10 models was 1.29 kg, which equates to a 3.7% error for the median force of 35 kg. A comparison of the errors of the model for each PI is shown (Fig. 4). The lowest error was observed for a PI of 131.4 kPa. The error for PI = 131.4 kPa was significantly different from the errors Table 1 Slopes and goodness-of-fit for linear regression equations for different initial pressures. Initial pressure (kPa)
Slope of linear regression equation
Standard error of the estimate (kg)
99.5 109.3 121.3 131.4 140.3 150.1 155.5 167.2 176.0 186.3
0.4752 0.4975 0.5802 0.6127 0.6540 0.7009 0.7482 0.7904 0.8087 0.9095
1.47 1.54 1.70 0.71 0.85 0.94 1.12 1.20 1.40 2.01
A. Chkeir et al. / Medical Engineering & Physics 35 (2013) 1698–1702
Fig. 4. Error of the model across all initial pressures. Error bars are 95% confidence intervals. *Significant difference from PI = 131 kPa (p < 0.05).
for the three lowest initial pressures and for the two highest initial pressures (p < 0.05), but did not significantly differ from other pressures. These results were used to create three groups, according to the initial pressure. Those PI that did not differ significantly from the PI with the lowest error (PI = 131.4, 140.3, 150.1, 155.5, and 167.2) were grouped as “Medium Pressure”, while the other PI were grouped as “Low Pressure” (PI = 99.5, 109.3, and 121.4) and “High Pressure” (PI = 176.0 and 186.3). The errors of the predictive model for these three groups were then compared for both low force (2–36 kg) and high force (38–70 kg) (Fig. 5). There were no significant differences in the performance of the model for the low force across the three pressure groups. However, in respect to the high force levels, the low pressure group was significantly less accurate than the medium pressure group (Fig. 5; p < 0.05). 4. Discussion The aim of the present study was to build a model for the Gripball in order to predict the force applied to the ball using only the pressure recorded. Previous publications using the Grip-ball had provided a technical description [16], a validation compared to the Martin Vigorimeter [17], and a reliability study for different initial pressures [17]. In respect to the relationship between grip force and the pressure inside an object being squeezed, Desrosiers et al. had shown grip force, as measured by the gold standard Jamar dynamometer, to be highly correlated to the pressure recorded during grip strength contractions, as measured by the Vigorimeter [14]. In the study of Desrosiers, 360 healthy elderly subjects (181 men and 179 women) were tested, with a
Fig. 5. Error of the model across for low, medium, and high initial pressure groups. Error bars are 95% confidence intervals. *Significant difference from medium initial pressure (p < 0.05).
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correlation of r = 0.89 observed. The initial pressure inside the Martin Vigorimeter is also atmospheric pressure, which is typically around 100 kPa. When the results of the Desrosiers study were compared to those of the present study for an initial pressure corresponding to atmospheric pressure (PI = 99.5 kPa), the regression equations for the two sets of data were comparable. The slope of the Jamar–Vigorimeter relationship was 0.49, compared to a slope of 0.48 for the Force–Grip-ball relationship. The similarity of the two slopes, which differed only by only 2%, implies that the Grip-ball should be able to accurately predict grip force. It should be noted that the method used in the present study to apply force to the Grip-ball differs from the way in which a human hand applies force to the Vigorimeter or to the Grip-ball, particularly in respect to the surface area in contact with the ball. In the present study the contact was applied by two plates above and below the ball, whereas the human hand encloses the ball and applies force across a less uniform contact surface regardless of the force applied. In addition, the human hand does not apply force in a uniform fashion due to differences in the force applied by the fingers. In contrast to the human hand, the surface area of the two plates in contact with the Grip-ball slightly increases as a function of both the force applied and the initial pressure of the Grip-ball. Increases in the surface area of the Grip-ball in contact with the Stentor plate were logically observed for lower initial pressures and for higher force levels. However, such changes in the surface area did not have a marked effect on the pressure measured inside the Grip-ball. For instance, when a 30 kg force was applied successively using circular surfaces of 6 cm2 and 26 cm2 , despite the increase in surface area of 333%, only a two percent decrease in pressure was observed (from 51 to 50 kPa). This finding suggests that any differences in contact area would be unlikely to have a marked influence on the accuracy of the model. Despite the differences in the contact surface between a flat plate and a human hand, it should be noted that the average contact surface in the present study was around 95 cm2 , which corresponds to a typical surface in contact surface with an adult human hand during grip-strength contractions [20]. However, in respect to a use by children, it would be necessary to use a smaller ball to take account of hand morphology. A final commentary on the question of surface area is that, despite the differences between squeezing a ball in a hand and squashing a ball between two plates, the relationship observed for an initial pressure of 100 kPa was almost identical to that obtained from the data of Desrosiers and colleagues. In respect to the model itself, the initial hypothesis was that a linear relationship would exist between applied force and measured pressure irrespective of the initial pressure of the Grip-ball. In addition, it was hypothesised that the slope of this linear relationship would increase as initial pressure increased. The results of the experimentation confirmed these hypotheses, with linear relationships between force and pressure observed for all initial pressures. In addition, the relationship between the slopes of the force–pressure regression equations was also linear in respect to the initial pressures. Given this finding, the model chosen to predict grip force, based on the pressure measured, was able to accurately predict force based only on initial pressure and the pressure applied. The results of the model were highly satisfactory, with an overall error of 1.29 kg in respect to the force applied. Such an error compares favourably with the variability reported in measurements with the Jamar, which are of the order of 1.4 kg [21]. The error of the model varied according to the initial pressure of the ball. The most accurate results for the model were obtained for initial pressures in the middle of the range studied, corresponding to 130–170 kPa. When the error of the model was calculated only for these initial pressures, the estimation error dropped to 0.96 kg, with the
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A. Chkeir et al. / Medical Engineering & Physics 35 (2013) 1698–1702
lowest error reported for the 131.4 kPa initial pressure of 0.71 kg. The decreased accuracy of the model at low initial pressure studied was dependent on the force applied, with a decreased accuracy observed only at high force levels. When the errors were compared for two force ranges (2–36 kg and 38–70 kg), no differences were found for the lower force level. In respect to the decrease in the performance of the model for high forces at low initial pressure, the decrease in accuracy was due to an underestimation of the actual force applied. However, when this error was considered as a percentage of the force applied, there were no differences between the model predictions at high and low force levels. Given the satisfactory results of the model, the Gripball should offer a viable alternative to isometric dynamometers that can be uncomfortable to use. 5. Conclusion The model developed was able to accurately estimate force based only on the pressure applied, irrespective of the initial pressure inside the Grip-ball. Such a result ensures that the pressure inside the Grip-ball can be regulated according to the stiffness required by the clinician, without adversely affecting the quality of the measurement of grip-force. In respect of the future use of the Grip-ball, it is encouraging that the model works best over the force range that is of the most interest in frailty detection. The Fried criteria for frailty have cut-offs for grip strength that vary according to the sex and the weight of the person being tested. The cut-offs for women vary from 17 to 21 kg, while those for men vary from 29 to 32 kg [6]. The next step in the validation of the Grip-ball will be to obtain data from a large population, ranging from young to elderly, in order to ensure that the results of the current study hold true across population trials. Funding None. Ethical approval Not required. Acknowledgements This work was supported by the Champagne-Ardenne Regional Council (CRCA) and the European Regional Development Fund under the Collaborative Research Program (Domo-Grip Project, grant reference numbers CRCA E201012437 and FEDER E201013375).
Conflict of interest None declared. References [1] Mathiowetz V, Weber K, Volland G, Kashman N. Reliability and validity of grip and pinch strength evaluations. J Hand Surg Am 1984;9:222–6. [2] Mathiowetz V. Effects of three trials on grip and pinch strength measurements. J Hand Ther 1990;3:195–8. [3] Incel NA, Ceceli E, Durukan PB, Erdem HR, Yorgancioglu ZR. Grip strength: effect of hand dominance. Singapore Med J 2002;43:234–7. [4] Cooper R, Kuh D, Hardy R. Objectively measured physical capability levels and mortality: systematic review and meta-analysis. Brit Med J 2010;341: 4467–79. [5] Norman K, Stobaus N, Gonzalez MC, Schulzke JD, Pirlich M. Hand grip strength: outcome predictor and marker of nutritional status. Clin Nutr 2011;30: 135–42. [6] Fried LP, Tangen CM, Walston J, Newman AB, Hirsch C, Gottdiener J, et al. Frailty in older adults: evidence for a phenotype. J Gerontol A Biol Sci Med Sci 2001;56:146–57. [7] Fess EE. Grip strength. In: Casanova JS, editor. Clinical assessment recommendations. 2nd ed American Society of Hand Therapists; 1992. p. 41–5. [8] Mathiowetz V, Kashman N, Volland G, Weber K, Dowe M, Rogers S. Grip and pinch strength: normative data for adults. Arch Phys Med Rehabil 1985;66:69–74. [9] Fike ML, Rousseau F. Measurement of adult hand strength: a comparison of two instruments. Occup Ther J Res 1982;2:43–9. [10] Richards L, Palmiter-Thomas P. Grip strength measurement: a critical review of tools, methods, and clinical utility. Crit Rev Phys Rehabil Med 1996;8:87–109. [11] Shmerling RH, Parker JA, Johns WD, Trentham DE. Measurement of joint inflammation in rheumatoid arthritis with indium-111 chloride. Ann Rheum Dis 1990;49:88–92. [12] Lundeberg T, Abrahamsson P, Haker E. A comparative study of continuous ultrasound, placebo ultrasound and rest in epicondylalgia. Scand J Rehabil Med 1988;20:99–101. [13] Gellman H, Kan D, Gee V, Kuschner SH, Botte MJ. Analysis of pinch and grip strength after carpal tunnel release. J Hand Surg Am 1989;14: 863–4. [14] Desrosiers J, Hebert R, Bravo G, Dutil E. Comparison of the Jamar dynamometer and the Martin vigorimeter for grip strength measurements in a healthy elderly population. Scand J Rehabil Med 1995;27:137–43. [15] Hogrel JY, Duchêne J. Device for evaluating and/or reinforcing gripping strength. Patent # FR08/05193; 2008. [16] Hewson D, Li K, Frerejean A, Hogrel JY, Duchene J. Domo-Grip: functional evaluation and rehabilitation using grip force. Conf Proc IEEE Eng Med Biol Soc 2010:1308–11. [17] Jaber R, Hewson D, Duchêne J. Design and validation of the Grip-ball for measurement of hand grip strength. Med Eng Phys 2012;34:1356–61. [18] Chkeir A, Jaber R, Hewson D, Duchêne J. Reliability and validity of the Grip-Ball dynamometer for grip-strength measurement. Conf Proc IEEE Eng Med Biol Soc 2012:1996–9. [19] Wimer B, Dong RG, Welcome DE, Warren C, McDowell TW. Development of a new dynamometer for measuring grip strength applied on a cylindrical handle. Med Eng Phys 2009;31:695–704. [20] Seo NJ, Armstrong TJ. Investigation of grip force, normal force, contact area, hand size, and handle size for cylindrical handles. Hum Factors 2008;50:734–44. [21] Harkonen R, Harju R, Alaranta H. Accuracy of the Jamar dynamometer. J Hand Ther 1993;6:259–62.
Contents lists available at ScienceDirect
Medical Engineering & Physics journal homepage: www.elsevier.com/locate/medengphy
Technical note
Estimation of grip force using the Grip-ball dynamometer Aly Chkeir ∗ , Rana Jaber, David J. Hewson, Jacques Duchêne Institut Charles Delaunay, UMR CNRS 6279, Université de Technologie de Troyes, 12 rue Marie Curie, CS 42060, Troyes 10004, France
a r t i c l e
i n f o
Article history: Received 21 November 2012 Received in revised form 13 March 2013 Accepted 6 May 2013 Keywords: Grip-strength Dynamometer Grip-ball
a b s t r a c t The Grip-ball is an innovative device that has been designed to measure grip strength. The Grip-ball consists of an airtight ball that contains a pressure sensor and Bluetooth communication system. The Grip-ball can be inflated to different initial pressures, with data available continuously in real time. The aim of this study was to build a model to predict the force applied to the Grip-ball dynamometer based only on the pressure measured by the Grip-ball and its initial pressure. Forces ranging from 2 to 70 kg were applied to a hybrid version of the device for 10 different initial pressures, ranging from atmospheric pressure of 100 kPa through to 190 kPa. A model was constructed to predict applied force, with force as a function of the initial pressure and the pressure measured. The error of the model was calculated as 1.29 kg across all initial pressures and forces applied. The results of the study are comparable with the errors observed for the gold standard in grip force measurement, the Jamar dynamometer. The best results for force prediction were obtained over the range in which frailty is typically detected. The Grip-ball will now be tested using a large population in order to establish clinical norms. © 2013 IPEM. Published by Elsevier Ltd. All rights reserved.
1. Introduction Measurement of grip strength is an important component of many different evaluations. For instance, grip strength can be used to assess the effectiveness of a surgical or a therapeutical procedure as well as the effect of a rehabilitation programme [1–3]. Grip strength has also been used as a measure of general strength in order to determine work capacity [4] and provide insight into patients’ nutritional status [5]. Weak grip strength is also one of the five criteria of frailty identified by Fried et al. [6]. Grip strength is typically measured by means of a dynamometer, such as the Jamar (Sammons & Preston, Bolingbrook, IL, USA), the Lode (Lode dynamometer; Lode BV, Groningen, The Netherlands), and the Martin Vigorimeter (Martin Medizintechnik, Tuttlingen, Germany).The most widely used device is the Jamar, which is recommended by the American Society for Surgery of the Hand (ASSH) and the American Society of Hand Therapists (ASHT) [7]. The Jamar also has a series of published tables of normative data for a range of different populations [8]. Despite the widespread clinical use of the Jamar, the isometric nature of the device may lead to discomfort for some users [9,10]. For instance, conditions such as rheumatoid arthritis [11], lateral epicondylitis [12], and in particular recovery from carpal tunnel release (CTR) surgery [13], can all lead to lower
∗ Corresponding author. E-mail addresses: [email protected], [email protected] (A. Chkeir), [email protected] (R. Jaber), [email protected] (D.J. Hewson), [email protected] (J. Duchêne).
than expected grip-strength measurements with the Jamar. One of the alternatives to the Jamar is the Martin Vigorimeter, which consists of a bulb attached to a manometer via a tube, with the pressure applied to the bulb displayed on the manometer. The Vigorimeter is highly correlated with the Jamar [14], and is also comfortable to use [9]. Despite these positive points, the Vigorimeter does not actually measure force per se, meaning that it cannot be used to compare results to grip strength norms, for instance an evaluation of frailty using Fried’s criteria. An alternative dynamometer, the “Grip-ball”, was developed in 2008 [15]. This device consists of a supple ball in which pressure and temperature sensors, as well as a data acquisition and communication system have been placed. Communication is performed in real-time via Bluetooth, thus ensuring interoperability with other local devices that could store or transfer the data (computer, tablet, mobile phone, etc.). A comprehensive description of the device can be found in [16,17]. In addition to the digital acquisition system in the Grip-ball, the other main difference with the Vigorimeter is that the Grip-ball is airtight and is equipped with a valve, meaning that the pressure inside the Grip-ball can be modified. Any changes in the initial pressure inside lead to changes in the stiffness of the ball, thus modifying the corresponding dynamics of grip-strength measurement. In order for the Grip-ball to be used for grip-strength measurement, a model needs to be developed to predict the grip force applied based only on the pressure measured and the initial pressure inside the Grip-ball. It has already been shown that grip strength measured with the Jamar is highly correlated with the pressure recorded by the Vigorimeter. In the most comprehensive
1350-4533/$ – see front matter © 2013 IPEM. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.medengphy.2013.05.003
A. Chkeir et al. / Medical Engineering & Physics 35 (2013) 1698–1702
1699
Fig. 1. Experimental setup of the hybrid Grip-ball device and the Stentor.
comparison, Desrosiers et al. reported a linear relationship between the measurements obtained from the two devices, with a correlation of r = 0.89 [14]. Given the linear relationship reported by Desrosiers, it was hypothesised in the present study that a similar linear relationship would exist between the force applied to the Grip-ball and the pressure measured by the device. In respect to the effect of the initial pressure in the Grip-ball, a linear relationship would be expected for all pressures, but the slope of this relationship would vary as a function of the initial pressure. The appropriate model would be expected to take the form: F = aPA where F is the force applied, PA is the pressure applied by the user (the pressure measured by the sensor minus the initial pressure inside the ball), and a is the slope of the relationship that depends on the initial pressure. The aim of the present study, therefore, was to build a unique model to predict the force applied to the Grip-ball based only on the pressure measured by the Grip-ball and its initial pressure. 2. Methodology 2.1. Experimental protocol The Grip-ball is currently undergoing a final development to miniaturise the electronic components. During this development stage, the Grip-ball was evaluated using a hybrid device, partway between a Grip-ball and a Vigorimeter, in which the manometer of the Vigorimeter was replaced by the electronics of the Gripball. The device was rendered air-tight, but was able to be inflated to different pressures [17]. The hybrid device has previously been tested, with an excellent correlation obtained between the pressure measured by the Vigorimeter manometer and the Grip-ball sensor (r = 0.997, p < 0.05) [17]. In addition, the device has been shown to be extremely reliable across a range of internal pressures, with an average ICC value of 0.97 [18].
The force applied to the Grip-ball was quantified by means of a Stentor II 1000 (Andilog technologies, Boulogne-Billancourt, France). This device can exert a force from 0 to 100 kg, with an accuracy of 0.5% and a resolution of 1/10,000, which equates to 9 g for the Stentor used. The force range chosen for the present study was from 0 to 70 kg, corresponding to the range of force naturally produced by the human hand during power gripping [1,19]. The Stentor is equipped with a force transducer, which measures the instantaneous force applied. This force value was sampled at 100 Hz via a standard RS232 connection. Although the SI unit for force is the Newton, the commonly used unit for grip force measurement in clinical practice is kg or lb. Accordingly, all results in the present article are expressed in kg. The rubber bulb of the hybrid device was placed between two identical plastic blocks, as shown in Fig. 1. The position of the bulb was kept constant for all tests. The hybrid device was evaluated for 10 different initial pressures (PI ), ranging from 100 to 190 kPa. Pressure was increased in increments of approximately 10 kPa as the inflation system was not precise enough to enable exact 10 kPa changes to be made. For each PI , the Stentor applied a force from 0 to 70 kg, in 2-kg increments, with pressure values inside the bulb sampled at 15 Hz and wirelessly transmitted via the Bluetooth module included in the Grip-ball. The pressure values recorded corresponded to the absolute pressure inside the bulb, which is the sum of the initial pressure and the increased pressure resulting from the force applied by the Stentor. A five-min pause was observed between each change in PI in order to ensure there were no changes in elasticity as a result of the previous series of measurements.
2.2. Data analysis For all subsequent analyses, force and pressure values were taken to be the average of the last second of recording, corresponding to 100 data points for force (100 Hz) and 15 data points for pressure (15 Hz).
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80
70
70
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Force (kg)
60
Force (kg)
50
50
Pi = 99.5 kPa
40
Pi = 131.4 kPa Pi = 155.5 kPa
30
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Pi = 186.3 kPa
20 30 10 20
0
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40
60
0
80
100
120
140
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Pressure (kPa)
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Fig. 3. Experimental data for four of the initial pressures (99.5, 131.4, 155.5, and 186.3 kPa). The dashed lines are best-fit linear regressions.
Pressure (kPa) Fig. 2. Comparison of the force–pressure relationship between the Grip-ball/Stentor and the Jamar/Vigorimeter (data from Desrosiers). All points displayed are for the Jamar/Vigorimeter. The straight line is the best-fit regression line for the Jamar/Vigorimeter. The regression line of the Grip-ball (- - -) is overlaid.
Linear regression equations were calculated for each PI for the pressure/force relationship. In all regression equations the intercept was forced to pass through zero. The slopes ˛ of all the regression equations were plotted against PI with the resulting linear regression used to predict ˛ as a function of PI : ˛ = ˇPI + where ˇ is the slope of the regression equation and is the error term. The final model was then created using the slope estimation and the pressure applied as: F = (ˇPI + )PA
or
F = ˛PA
The standard error of the estimate was used as a measure of the error of the model:
PI
(j)
PI =PI
(j)
=
(FMES − FEST )2 N−1
where PI
(j)
is the standard error for an initial pressure j, FMES is the
measured force value, FEST is the estimated force value predicted by the model, and N is the number of observations. The standard error of overall model was taken as:
TOT =
∀PI (FMES − FEST )
2
NTOT − 1
where TOT is the standard error across all initial pressures and NTOT is the total number of observations. 3. Results A best-fit linear regression equation for PI of 100 kPa (atmospheric pressure) between the force applied and the change in pressure inside the ball was: F = 0.4753PA with PA expressed in kPa and F in kg, and R2 = 0.99. This equation was then overlaid onto the data obtained from the most highly cited comparison between the Jamar and the Martin
Vigorimeter, those of the paper of Desrosiers et al. [14] (Fig. 2). The regression equation obtained for the Desrosiers data was: F = 0.4926PA which corresponds to a relative difference in the slopes of the regression equations of 3.51%. Data for the force–pressure relationship for the Grip-ball for a selection of PI are shown in Fig. 3. It can be verified that the slope for the best-fit linear regression lines increases as PI increases. The slopes of the regression equations and the goodness of fit, as calculated by the standard error of the estimate, are shown in Table 1. The relationship between PI and the slope of the best-fit regression lines for each force–pressure relationship was linear, with a regression equation computed from all 10 slopes of: = 4.855 × 10−3 PI − 2.020 × 10−2 The goodness of fit of the equation was excellent (R2 = 0.991). In the hypothesised relationship between force and pressure, the only parameter required is the slope of the linear equation that depends on the initial pressure. Replacing ˛ by its model given above, the equation becomes: F = (4.855 × 10−3 PI − 2.020 × 10−2 )PA with force expressed in kg and pressure expressed in kPa. In order to assess the accuracy of the model, standard errors were calculated for the overall model, as well as for each initial pressure (Table 1). The error of the model across all 10 models was 1.29 kg, which equates to a 3.7% error for the median force of 35 kg. A comparison of the errors of the model for each PI is shown (Fig. 4). The lowest error was observed for a PI of 131.4 kPa. The error for PI = 131.4 kPa was significantly different from the errors Table 1 Slopes and goodness-of-fit for linear regression equations for different initial pressures. Initial pressure (kPa)
Slope of linear regression equation
Standard error of the estimate (kg)
99.5 109.3 121.3 131.4 140.3 150.1 155.5 167.2 176.0 186.3
0.4752 0.4975 0.5802 0.6127 0.6540 0.7009 0.7482 0.7904 0.8087 0.9095
1.47 1.54 1.70 0.71 0.85 0.94 1.12 1.20 1.40 2.01
A. Chkeir et al. / Medical Engineering & Physics 35 (2013) 1698–1702
Fig. 4. Error of the model across all initial pressures. Error bars are 95% confidence intervals. *Significant difference from PI = 131 kPa (p < 0.05).
for the three lowest initial pressures and for the two highest initial pressures (p < 0.05), but did not significantly differ from other pressures. These results were used to create three groups, according to the initial pressure. Those PI that did not differ significantly from the PI with the lowest error (PI = 131.4, 140.3, 150.1, 155.5, and 167.2) were grouped as “Medium Pressure”, while the other PI were grouped as “Low Pressure” (PI = 99.5, 109.3, and 121.4) and “High Pressure” (PI = 176.0 and 186.3). The errors of the predictive model for these three groups were then compared for both low force (2–36 kg) and high force (38–70 kg) (Fig. 5). There were no significant differences in the performance of the model for the low force across the three pressure groups. However, in respect to the high force levels, the low pressure group was significantly less accurate than the medium pressure group (Fig. 5; p < 0.05). 4. Discussion The aim of the present study was to build a model for the Gripball in order to predict the force applied to the ball using only the pressure recorded. Previous publications using the Grip-ball had provided a technical description [16], a validation compared to the Martin Vigorimeter [17], and a reliability study for different initial pressures [17]. In respect to the relationship between grip force and the pressure inside an object being squeezed, Desrosiers et al. had shown grip force, as measured by the gold standard Jamar dynamometer, to be highly correlated to the pressure recorded during grip strength contractions, as measured by the Vigorimeter [14]. In the study of Desrosiers, 360 healthy elderly subjects (181 men and 179 women) were tested, with a
Fig. 5. Error of the model across for low, medium, and high initial pressure groups. Error bars are 95% confidence intervals. *Significant difference from medium initial pressure (p < 0.05).
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correlation of r = 0.89 observed. The initial pressure inside the Martin Vigorimeter is also atmospheric pressure, which is typically around 100 kPa. When the results of the Desrosiers study were compared to those of the present study for an initial pressure corresponding to atmospheric pressure (PI = 99.5 kPa), the regression equations for the two sets of data were comparable. The slope of the Jamar–Vigorimeter relationship was 0.49, compared to a slope of 0.48 for the Force–Grip-ball relationship. The similarity of the two slopes, which differed only by only 2%, implies that the Grip-ball should be able to accurately predict grip force. It should be noted that the method used in the present study to apply force to the Grip-ball differs from the way in which a human hand applies force to the Vigorimeter or to the Grip-ball, particularly in respect to the surface area in contact with the ball. In the present study the contact was applied by two plates above and below the ball, whereas the human hand encloses the ball and applies force across a less uniform contact surface regardless of the force applied. In addition, the human hand does not apply force in a uniform fashion due to differences in the force applied by the fingers. In contrast to the human hand, the surface area of the two plates in contact with the Grip-ball slightly increases as a function of both the force applied and the initial pressure of the Grip-ball. Increases in the surface area of the Grip-ball in contact with the Stentor plate were logically observed for lower initial pressures and for higher force levels. However, such changes in the surface area did not have a marked effect on the pressure measured inside the Grip-ball. For instance, when a 30 kg force was applied successively using circular surfaces of 6 cm2 and 26 cm2 , despite the increase in surface area of 333%, only a two percent decrease in pressure was observed (from 51 to 50 kPa). This finding suggests that any differences in contact area would be unlikely to have a marked influence on the accuracy of the model. Despite the differences in the contact surface between a flat plate and a human hand, it should be noted that the average contact surface in the present study was around 95 cm2 , which corresponds to a typical surface in contact surface with an adult human hand during grip-strength contractions [20]. However, in respect to a use by children, it would be necessary to use a smaller ball to take account of hand morphology. A final commentary on the question of surface area is that, despite the differences between squeezing a ball in a hand and squashing a ball between two plates, the relationship observed for an initial pressure of 100 kPa was almost identical to that obtained from the data of Desrosiers and colleagues. In respect to the model itself, the initial hypothesis was that a linear relationship would exist between applied force and measured pressure irrespective of the initial pressure of the Grip-ball. In addition, it was hypothesised that the slope of this linear relationship would increase as initial pressure increased. The results of the experimentation confirmed these hypotheses, with linear relationships between force and pressure observed for all initial pressures. In addition, the relationship between the slopes of the force–pressure regression equations was also linear in respect to the initial pressures. Given this finding, the model chosen to predict grip force, based on the pressure measured, was able to accurately predict force based only on initial pressure and the pressure applied. The results of the model were highly satisfactory, with an overall error of 1.29 kg in respect to the force applied. Such an error compares favourably with the variability reported in measurements with the Jamar, which are of the order of 1.4 kg [21]. The error of the model varied according to the initial pressure of the ball. The most accurate results for the model were obtained for initial pressures in the middle of the range studied, corresponding to 130–170 kPa. When the error of the model was calculated only for these initial pressures, the estimation error dropped to 0.96 kg, with the
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lowest error reported for the 131.4 kPa initial pressure of 0.71 kg. The decreased accuracy of the model at low initial pressure studied was dependent on the force applied, with a decreased accuracy observed only at high force levels. When the errors were compared for two force ranges (2–36 kg and 38–70 kg), no differences were found for the lower force level. In respect to the decrease in the performance of the model for high forces at low initial pressure, the decrease in accuracy was due to an underestimation of the actual force applied. However, when this error was considered as a percentage of the force applied, there were no differences between the model predictions at high and low force levels. Given the satisfactory results of the model, the Gripball should offer a viable alternative to isometric dynamometers that can be uncomfortable to use. 5. Conclusion The model developed was able to accurately estimate force based only on the pressure applied, irrespective of the initial pressure inside the Grip-ball. Such a result ensures that the pressure inside the Grip-ball can be regulated according to the stiffness required by the clinician, without adversely affecting the quality of the measurement of grip-force. In respect of the future use of the Grip-ball, it is encouraging that the model works best over the force range that is of the most interest in frailty detection. The Fried criteria for frailty have cut-offs for grip strength that vary according to the sex and the weight of the person being tested. The cut-offs for women vary from 17 to 21 kg, while those for men vary from 29 to 32 kg [6]. The next step in the validation of the Grip-ball will be to obtain data from a large population, ranging from young to elderly, in order to ensure that the results of the current study hold true across population trials. Funding None. Ethical approval Not required. Acknowledgements This work was supported by the Champagne-Ardenne Regional Council (CRCA) and the European Regional Development Fund under the Collaborative Research Program (Domo-Grip Project, grant reference numbers CRCA E201012437 and FEDER E201013375).
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