Objective measurement of knee extension force based on computer adaptive testing

1. Introduction 

The clinical assessment of joint torque includes, among other factors, evaluation of maximal muscle strength exerted by the tested subject, often referred to as the maximal voluntary contraction (MVC) of the actuating muscle group [1]. This test, however, heavily depends on the examinee’s cooperation level. Hence, the accuracy by which the clinical test reflects real muscle capability is questionable in cases where subject cooperation is low or non-existent. Furthermore, there are cases of false impairment, where the examinee will either unintentionally or deliberately attempt to put an artificial upper limit on his/her force, in which case his true capacity cannot be disclosed in a straight forward measurement.

Various methods have been proposed to improve the reliability of clinically measured muscle capacity. Most methods rely on the extent of reproducibility of multiple tasks achieved by the examinee while performing the MVC. Alternatively, evaluation of reliability can be assessed by the comparison of the MVC results accomplished separately by different modes of activation, such as concentric versus eccentric contraction of the muscle group [3].

We hypothesized in this study that a more objective and reliable result can be achieved by developing a computer adaptive testing (CAT) protocol, whereby the tested subject is requested to fulfil series of isometric tasks, as displayed on a monitor placed in front of him/her. Both the degree of difficulty and the scale of the displayed force are varied by the testing algorithm in an un-anticipated manner. In this way, while the examinee is concentrated on performing the changing tasks, his/her attention is being distracted from the self-imposed force upper limit. Mind distraction is occasionally practiced by clinicians, e.g., in the process of differentiation between pathological and non-pathological causes of spine pain [12]. The underlying logic in this case is based on the assumption that the examinee is responding to various manoeuvres, aimed at indirectly provoking spine pain, while being unaware of their real purposes. The comparison of his/her responses to direct and indirect tests might yield the differentiation of true impairment from a false one. It should be noted, though, that incorrect conclusions are suspected if the tests are not adapted to the physical and mental capacities of each individual. Adaptation with the patient abilities becomes therefore essential in the validation of examinees’ individual performances [5].

Computer adaptive testing (CAT), known from cognitive testing, is aimed at matching the level of the tested item with the examinee’s ability to respond [6]. The CAT model yields a precise, comparable, measure for all examinees’ levels, including the less and the more competent ones [9]. The CAT method further enables the examiner to readjust the degree of difficulty of a test according to the examinee’s performances in multi-step interactive tasks in order to disclose the examinee’s real potential [2], [4], [7], [10], [11]. It should be noted that, to the best knowledge of the present authors, the CAT method has not been used as yet for physical testing.

In this study we expand the use of the CAT method for the assessment of the physical capacity of tested subjects. We hypothesized that, by using CAT principles, it is possible to direct subjects into generating a greater sub-maximal force than they intended. During the tests, the seated examinees were requested to exert assigned isometric tasks by forceful applications of the knee extensors. While fulfilling these tasks, they were asked to take care not to exceed a self-selected upper force limit that they were previously trained to memorize. An algorithm for CAT and consisting of testing cycles, each containing a series of tasks of differing task intensities, was developed to divert the examinee from his/her attempts not to exceed the memorized sub-maximal limit force. Visual feedback, displaying the applied force exertions, was provided to the tested subjects but was modified by re-scaling the display during the course of testing in an un-anticipated manner. The purpose of combining the CAT method with visual feedback was to lead to a statistically significant increase in the force applied by the subjects.

2. Subjects and methods 

2.2. Apparatus 

A system was designed to measure the torque during isometric extension efforts of the examinee’s right knee. The system, similar to a previously used apparatus [8], consisted of an adjustable chair with three restraints on which the volunteer subjects were seated during testing (Fig. 1). Isometric knee extension torque was produced by the knee extensors and measured by the counterbalancing force at the ankle level by means of a load cell. It was assumed that, under isometric conditions, the force applied at the ankle level by the foot was proportional to the force at the activated knee extensor muscles. The knee angle was fixed at 90° throughout the test. Data acquisition was made by sampling the force from the transducer at 200Hz into an A/D acquisition card and a Lab-View interface (National Instruments Corporation, Austin, TX). The testing procedure was based on converted-scale real-time feedback. Two computer screens were used: one was placed in front of the examinee and one in front of the operator, hidden from the examinee’s eyes.

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Fig. 1. Schematic description of the measuring system. The system includes an adjustable chair (with three restrainers), adjustable frame shown at the lower part of the figure, force (Fr) measuring load cell, a digital to analogue acquisition card, converted feedback screen for the tested subject (right), real-scale screen for the operator (left).

2.3. Testing procedure 

During the tests, the seated examinees were requested to exert assigned tasks of isometric extension force at the ankle level caused by forceful applications of the knee extensors. Preliminary tests indicated that 3s of force application were sufficient for the subjects in this study to reach a steady force response at the required displayed level (see later Fig. 3, Fig. 4). With the 200Hz sampling frequency, the sweep time of 3s, gave a total of 600 samples. The task intensity was indicated on the examinee screen by means of a horizontal target line. To allow for possible inaccuracies and instabilities in the force application, a double-target line was preferred to a single-target line display of the task (Fig. 2). The examinee had to aim and maintain the trace of his applied force within the narrow area between these two lines.

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Fig. 2. Schematic presentation of the different tasks as they appear to the subject on his monitor, in one testing cycle. In parenthesis, is the product of the scale factor (SF) and task factor (TF), which gives an indication to what extent the task is seen differently to the subject with comparison to the baseline force Fbl. (Fbl=maximum force (in real scale) achieved from the previous testing cycles. In the first cycle Fbl was set arbitrarily at an easy enough task to be performed by the examinee without difficulty; SF=ratio between displayed force on examinee’s monitor and real force; TF=ratio of the task force to Fbl.)

An additional instruction was given to the subjects: while fulfilling the above task they should take care not to exceed a self-selected upper sub-maximal force limit (Fssl) (expressed as a percentage of their own initially measured maximal voluntary contraction MVCi of the extensor muscles, see Section 2.3.1), that they were previously trained to memorize. Given this set of instructions, a developed computer adaptive testing (CAT) algorithm was intended to cause the participants to deliver a higher quadriceps force than the self-selected force limit they were requested to observe.

The testing protocol was divided into two phases: the pre-test and the test phase.

2.3.1. Pre-test 

The pre-test phase consisted of two parts: one for calibration and, one for training the examinee’s knee joint to memorize the Fssl.

In the first part the examinee was asked to exert the highest knee extension force, denoted as the initial maximal voluntary contraction (MVCi). This was repeated three times with an interval time of 10min and the average was taken to represent the actual MVCi. It was assumed that, since the subjects were cooperative, the measured MVCi was the true initial maximal voluntary contraction. Thus, except for adjustment due to possible existence of fatigue (see later Section 2.3.4), MVCi could be used as a reliable measure for force normalization. In the second part, the tested subject was trained to set and memorize a specific force limit Fssl (usually near 20–50% of the subject’s MVCi). The training process was made with real-scale feedback, as displayed on the examinee’s monitor and was not limited in time. Training was terminated when the examinee felt confident in being able to memorize her Fssl, which usually corresponded to force reproducibility of better than 5% of the selected Fssl.

2.3.2. Test 

The algorithm developed for the CAT consisted of testing cycles, each containing a series of tasks of differing intensities. The objective of this algorithm was to distract the examinee from her attempts not to exceed the memorized sub-maximal Fssl, i.e., to cause her to (unintentionally) exert a higher force than her own Fssl. For this purpose, two different scales were used for displaying the force. While on the operator monitor a real-scale force was displayed (presented in % of the MVCi), on the examinee’s monitor a factored-scale was used with a scaling factor (SF), defined as the ratio between displayed and real force. Depending on SF, the following representative values could be obtained on the examinee’s screen for the exerted force: real force value (SF=1), 50% (SF=0.5), and 150% (SF=1.5) of the real force.

In addition, the difficulty level of the task was changed as follows. For each cycle we set, a baseline force (Fbl) , defined as the maximum force (in real scale) achieved from the previous testing cycles. In the first cycle Fbl was set arbitrarily at an easy enough task to be performed by the examinee without difficulty. The difficulty level of each task (task factor, TF) was thus expressed as the ratio of the task force (real scale) to Fbl. Sample values for TF are 0.5, 1 or 1.5, reflecting a 50% easier, similar, or 50% more difficult task, respectively.

On the examinee’s screen the task force was thus represented as the product of the following 3 quantities: Fbl, SF and TF. On the operator screen, the real-scale force was displayed. Once again, the examinee was instructed to perform the assigned tasks while remaining aware not to exceed her self selected limit force Fssl. The latter was not displayed on her screen and had to be referred to from memory only.

In designing a typical cycle for the CAT algorithm, various strategies can be attempted. The one used in this study and shown schematically in Fig. 2, consisted of 6 tasks. The baseline reference task Fbl shown in the center of the figure is denoted as task 1. Moving in a clockwise direction shows the sequence of the tasks presented, with different scaling factors SF and task factors TF. In task number 2 the examinee is shown a mission which, to her, seems to have a similar magnitude as that of task 1. However, the required force is actually easier than expected. Tasks 3 and 4, although of the same difficulty as task 2, are shown to appear easier than task 2. Task 4, which is scaled down on the examinee monitor by 0.5 appears to be particularly easy. The same scaling down of 0.5 is used in tasks 5 and 6. In task 5, however, although the force required is the same as that the baseline task 1, it appears on the examinee monitor to be an easier task. Furthermore, task 6 requires an application of a 50% higher force than the initial task and still appears easier to the examinee. The maximum force (in real scale) achieved from this cycle was used as the baseline force Fbl for the next cycle and the procedure hereby described was repeated.

Termination of the test (last testing cycle) was set when, in a given testing cycle, the real-scale force reached was not higher than in its preceding cycle. Following the principles of CAT, this highest result achieved by an examinee constitutes a better representation of her capacity compared to her initial intent.

2.3.3. Evaluation measures 

Fig. 3 shows the force output from a typical task output. The task force is indicated by the horizontal double-line and the actual force output is shown by the trace. From the force outputs two evaluation measures were defined, as follows: (a) Average force rate to maximum, shown by the slope of the incline (Fig. 3), i.e., by dividing the highest force level reached by the time elapsed from the onset of force to maximum. (b) Task score, defined as the average of the highest 5% samples of the task, and located within the double-target line. An additional measure was used for the complete test: CAT score, defined as the Fmax of all tasks of a complete given test.

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Fig. 3. Output in typical task. The required task is indicated by the horizontal double-line and the force output is shown by the trace. The average force rate to maximum (FRTM) is defined as the slope of the straight incline line.

2.3.4. Adjustment for muscle fatigue 

After completion of the CAT, the maximal voluntary contraction was measured again to verify whether the muscle had undergone fatigue during the test (final, MVCf). This was repeated three times and the average was taken to represent the actual MVCf. Thus, the true final maximal voluntary contraction MVCf, provided a correction for MVCi due to the possible development of muscle fatigue during the test. The values of MVCf and MVC i were used to linearly interpolate MVCtask, corresponding to each actual task and to which the force values were normalized during the test (Eq. (1)).

(1)

where k denotes the task number of the given task (from the beginning of testing) and n is the total number of tasks.

2.3.5. Joint memory repeatability 

Repeatability of joint memory was tested one week after the CAT. Its purpose was to confirm the subject’s ability to remember her Fssl. The ability to successfully retain joint memory several days after the CAT should provide a confirmation as to whether the CAT succeeds in overcoming the examinee’s intention to avoid exerting higher forces than her memorized Fssl. Similar number of cycles and testing durations as in the CAT were used in the repeatability tests.

2.3.6. Statistical analysis 

The Wilcoxon non-parametric test was used to compare the differences between the results observed in the CAT and the repeatability tests. The Wilcoxon test was found suitable due to the relatively small number of subjects taking part in the study (n=11).

3. Results 

Fig. 4 demonstrates a typical 6-task testing-cycle of one of the subjects, as displayed on the operator’s (left) and on the examinee’s (right) screens. The task sequence is as described in Fig. 2. The initial baseline force Fbl (Task 1) in this case was approximately 50% of the subject’s MVCi. It can be noticed that in the second task the examinee expects a mission of the same magnitude as in task 1. However, in her tracking attempt an overshoot results until the examinee finds out that the task turns out to be easier than expected and she eventually converges to the task force. In the subsequent missions (3–5) the task does not exceed Fbl and tracking performance is satisfactory. In the sixth task the examinee gets a seemingly easy task (SF=0.5), despite the fact that the task force is 50% higher than the baseline force Fbl (and, in fact the highest in that cycle); thus an initial undershoot results with subsequent correction. It is noted that on that sixth task, the examinee exerted the highest force magnitude of the test (higher than the initial Fbl). The baseline force for the next cycle is readjusted in accordance with the force thus achieved in that last task.

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Fig. 4. Typical 6-task cycle of one of the subjects, as displayed on the operator’s (left) and on the examinee’s (right) screens. Vertical axis: force (in kg force units), the values are real on operator’s screen. Horizontal axis: number of samples. The double-horizontal lines designate the boundaries between which the task is to be accomplished, while the force actually exerted is shown by the trace. The task sequence is as described in Fig. 2. It is noted that in the sixth task the examinee exerted the highest force magnitude of the test (higher than the initial Fbl). Fbl=maximum force (in real scale) achieved from the previous testing cycles. In the first cycle Fbl was set arbitrarily at an easy enough task to be performed by the examinee without difficulty.

Table 1 presents the MVC force obtained for each of the tested subjects, before (MVCi) and after (MVCf) each of the CAT and repeatability tests. The results presented are averages of 3 trials (SD).

Table 1. Maximal voluntary contraction (MVC) force (kg) obtained for each of the tested subjects, before (MVCi) and after (MVCf) the CAT and repeatability tests

	Subject #	CAT		Repeatability test
		MVCi	MVCf	MVCi	MVCf
	1	49.0 (3.3)	46.5 (0.7)	58.2 (0.9)	57.5 (3.8)
	2	27.9 (2.4)	19.8 (1.3)	27.2 (2.0)	21.4 (0.3)
	3	19.7 (2.9)	11.5 (0.8)	14.2 (2.1)	13.7 (1.9)
	4	40.8 (1.3)	36.0 (1.3)	37.2 (1.7)	27.7 (1.6)
	5	25.7 (1.1)	21.5 (2.7)	33.0 (0.8)	29.6 (2.3)
	6	29.8 (2.5)	21.2 (1.0)	41.7 (0.6)	34.8 (2.1)
	7	55.3 (1.1)	51.1 (2.9)	49.7 (3.4)	41.1 (2.7)
	8	37.2 (2.8)	35.3 (1.6)	34.7 (1.0)	29.2 (0.8)
	9	31.5 (1.6)	29.6 (0.4)	30.3 (1.3)	28.3 (2.5)
	10	50.8 (0.6)	48.0 (0.9)	42.2 (4.2)	29.5 (2.7)
	11	48.8 (0.3)	35.6 (2.8)	55.0 (2.0)	48.9 (2.9)

The results presented are averages of three trials (SD).

Table 2 presents, for all the subjects, summary of the Fssl values (ranging between 20% and 50% MVCi, with mean of 36% and SD of 9.7%) and of the total number of cycles in the CAT (ranging between 4 and 9 cycles, with mean of 6.09 and SD of 1.56). A linear regression test showed that there was no correlation between the amount of fatigue, as expressed as percentage loss of MVC, and either the self-selected limit force Fssl, or the number of cycles till termination of the CAT.

Table 2. Summary, for all subjects, of: self-selected upper force limit (Fssl, in % MVCi); total number of cycles in the CAT; scores for the CAT and repeatability test; and correlation (r) between average force rate to maximum (FRTM) and the task score

	Subject #	Fssl (% MVCi)	Number of cycles in CAT	Score CAT	Score repeatability	r-Value (FRTM vs. Fmax)
	1	50	4	1.98	1.40	0.59
	2	25	7	2.09	1.18	0.50
	3	20	8	2.44	2.67	0.33
	4	50	5	0.96	0.95	0.31
	5	30	4	2.34	1.89	0.67
	6	40	7	1.38	1.15	0.37
	7	40	9	2.03	1.56	0.63
	8	30	7	3.19	1.74	0.49
	9	30	5	1.85	1.59	0.61
	10	40	6	2.46	1.67	0.32
	11	40	5	1.23	1.28	0.05
	Mean (SD)	36 (9.7)	6.09 (1.56)	1.99 (0.64)	1.55 (0.47)

Task score=average of highest 5% samples of the force trace at a given task; CAT score=highest force applied in a complete given CAT; repeatability score=highest force applied in a complete given repeatability test. Note that 10 out of the 11 subjects rendered a higher force than intended by their self imposed limit. It is also seen that, except in subjects 3, 4 and 11, the CAT algorithm caused a higher force than the repeatability test.

Fig. 5 demonstrates the force output for one examinee as obtained using the CAT in a complete test (top), as compared to the force output during the repeatability test. The force values at the initial and final ends of the test were normalized by using the respective MVC values. For any intermediate task, the MVC was interpolated as indicated in Eq. (1). In the CAT (upper panel) the examinee’s performance was characterized by oscillations of the exerted forces below and over Fssl. These oscillations were synchronized with the testing cycles, as can be noted by the arrows shown on the time axis in Fig. 5. The applied force eventually reached a magnitude of as high as 1.98Fssl (score of the CAT). However, in the repeatability test (lower panel), the fluctuations around the level of Fssl were smaller compared to the CAT with a maximum score of 1.40 Fssl. Summary of the scores, for the CAT and for the repeatability tests, for all the subjects, is presented in Table 2. The mean score values of the CAT and the repeatability tests for all the participants were 1.99 and 1.55, respectively, with a statistically significant difference (p<0.05) between them. Ten out of the eleven subjects rendered a higher force than intended by their self imposed limit. It is also seen that, except in 3 examinees, the CAT algorithm caused a higher force than the repeatability test.

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Fig. 5. Force applied (normalized to Fbl): comparison between CAT and repeatability tests (subject 1). The value of Fssl was in this case 0.5 MVCi. Test score denotes the highest force value attained during the CAT test. The marked arrows indicate beginning of a testing cycle. For summary of the entire population, see Table 2.

Comparison between force rate to maximum and task score (average of highest 5% of samples) obtained from each task in the CAT was made, and is demonstrated for one examinee in Fig. 6, with a correlation of r=0.67 between the two parameters. A high correlation between these two quantities indicates good attentiveness and responsiveness. The average Force rate to Maximum was generally higher in the repeatability tests compared to the CAT. The results across the entire population of the correlation presented in Fig. 6 are summarized in Table 2.

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Fig. 6. Comparison between average force rate to maximum and task score (y=1.22x−0.01; R=0.67, subject #5). For summary of the entire population, see Table 2.

4. Discussion 

Clinical assessment of the musculoskeletal system is highly dependent on the patient’s cooperation as well as on the examiner’s subjective impression. The latter can be minimized if evaluation is made by using biomechanical measuring apparatuses. Mind-distracting techniques practiced by clinicians usually ignore the need for adaptation to the patient’s individual physical and mental capacities. Our developed individualized CAT model is based on real-time feedback for objective measuring of joint performance.

The method developed was demonstrated in this study on healthy and cooperative subjects. Accordingly, the MVC’s in both the initial and final states were considered to be true MVC’s. Each subject was trained to memorize a self selected sub-maximal limit force which she was not supposed to exceed upon performing the tasks that she was given. The developed algorithm for the CAT was thus intended to distract her mind and to cause her to apply a higher force than she actually intended. This mind-distraction technique finds particular relevance in cases of false impairment, where the examinee either unintentionally or deliberately attempts to put an artificial upper limit on his/her force, in which case his true capacity (e.g. his/her MVC) cannot be disclosed in a straight forward measurement.

According to the principles of CAT, the highest result achieved by an examinee expresses his/her capacity. CAT techniques were initially developed and implemented in the field of education [11]. In our study we expand the use of this method for the assessment of physical capacity. We thus developed a measuring system based on CAT theories and including the following elements. (a) Existence of an initial examinee level of performance was ensured by selecting a low-enough intensity force. This level was used as the starting point of the testing, as required in CAT [6]. (b) There was a logic, consistent and systematic proceeding of the tasks [4]. (c) The testing level correlated with the examinees’ ability and, at the end of testing, evaluation of the subject’s ability was the direct outcome of the testing-level, as suggested by Hambelton et al. [5]. (d) As suggested by Hays et al. [7], the tasks delivered to the examinees were well characterized by their parameters and an ending criterion was used to stop the testing when the expected result was achieved.

The difference between the final and initial MVC’s, reveal that some fatigue developed during the test. Although fatigue normally displays a nonlinear decay, a linear trend of fatigue development was assumed for simplicity (Eq. (1)). This assumption did not affect the principal result of this study, namely the score of CAT (shown in Table 2), representing the exerted force in excess of the Fssl.

The developed algorithm for CAT was successful in causing 10 out of the 11 participants to exert more force than they intended to. Furthermore, in 8 out of the 11 examinees, this force increase was statistically significant (p<0.05) compared to the repeatability score. The highest CAT score was 3.2 for an Fssl value of 0.3 MVC. In all the subjects, the force output undulated in sequence with the testing cycles and in accordance with the difficulty levels during test progression (illustrated in Fig. 5), indicating the algorithm influence on the examinees.

Exceeding the Fssl by the examinee took place in the majority of cases within the first two cycles of the test. If it did not happen in the first cycle, it did in the second one indicating that the first cycle provided an appropriate iteration for ensuring the success of the algorithm. By applying a linear regression test, no obvious relationship was found between the Fssl level selected by each examinee and the value of the algorithm score.

Because the CAT algorithm aimed at ’tricking’ the joint memory, repeatability tests could only be made several days after the CAT. In the repeatability tests the scores were, in all subjects except in one, higher than the Fssl (although they remained significantly lower than the CAT scores). The average force rate to maximum was found higher in the repeatability tests compared to the CAT, indicating that in the former the examinees experienced more caution in performing the changing tasks. Of interest was the observation that in those cases where CAT proved more successful, force rate to maximum and Fmax correlated better with one another. It should be noted that, indeed, the lowest correlations were found in examinees 4 and 11, where the CAT scores were relatively low.

Although the termination criterion was uniform, in some subjects the highest scores were achieved at early cycles of the testing procedure as compared to others. It could be questioned whether additional cycles would have not yielded an even higher score, should the tests be extended beyond the termination time. This, however, remains to be verified.

The objective of this study was to show that, in cases of self-imposed upper force limit, it is possible to obtain from the tested subject higher forces than he/she intended to deliver. The testing procedure was thus intended to ‘trick’ the memory by an interactive CAT, incorporating a dual-screen system: A real-scale screen for the operator, and a scaled screen for the examinee in which the real difficulty of the task was scaled in accordance with the development of the testing procedure. The testing results indicated that the CAT algorithm indeed succeeded in extracting from the examinee a higher force than she intended to deliver (p<0.05).

In conclusion, the computer adaptive testing algorithm thus developed, based on real time converted-scale feedback, yielded mind distraction in most (10 out of 11) of the participants in our study. Further validations, using various CAT strategies and extended termination criteria are required to verify whether the CAT method described in our research will really and consistently improve clinical evaluation of muscle strength. Finally, it would be of interest to study the applicability of the method in physical training procedures, i.e., adaptive training. If proved successful, this could improve training progress in the course of rehabilitation.