Relationship between multiple predictor variables and normal knee torque production.

Relationship Between Multiple Predictor Variables and Normal Knee Torque Production Knowledge of preinjury status of patients' muscular performance assists clinicians in assessing postinjury baseline status, the magnitude of progress during rehabilitation, and the ability to return to preinjury activity levels. Unfortunately, objective information regarding preinjury muscular performance is not commonly available. The quantitative assessment of muscular performance immediately after injury may not be feasible because of the unavailability of the instrumentation necessary to obtain this information or because of patient status that prevents quantitative examination of either the affected or the unaffected body part (eg, a patient who receives traction for the treatment of an unstable fracture). The clinician's first assessment of the patient typically is performed some time after the injury. The muscular performance of the affected body part can be contrasted with the muscular performance of the contralateral, "unaffected" body part in instances where a unilateral injury is present. The unaffected extremity, however, may have atrophied as a result of reduced activity levels. The availability of normative muscle strength data would allow the clinician to accurately predict the individual patient's preinjury muscular performance status and would assist in the development of treatment goals and in the ability to assess rehabilitative progress.

Numerous investigators have attempted to establish normative muscle strength values for humans. These investigators have reported descriptive statistics for muscle strength[1-8] and correlations between individual body characteristics and strength values for specific muscle groups.[9-17 The magnitude of standard deviations and correlations that have been reported indicates an inability to predict individual muscle strength capability with accuracy. Many studies, however, involved subject groups that were restricted in terms of age and athletic participation, and the results may not be generalizable to a diverse clinical population.[1-12,17-19]

Studies by Molnar and Alexander indicate the value of using multiple variables in regression analyses to predict normal strength production.[10,11] Combinations of anthropometric variables, age, and sex were more valuable than any individual variable in predicting peak isokinetic knee torque at an angular velocity of 30[degrees]/sec[.sup.-1]. Unfortuntely, these studies involved subjects who ranged in age from 7 to 15 years, and the investigators did not use the angular test velocities that are used most commonly in clinical testing.[9,20] The results of the studies by Molnar and Alexander,[10,11] however, indicated the utility of pursuing research that utilizes regression analysis to examine the relationship between muscle strength values and multiple predictor variables for a broad clinical population.

The purpose of this study was to generate predictive models that relate knee extension and flexion torque production to the following independent variables: age, sex, percentage of body fat, height, weight, thigh girth, and side of dominance. Pevious studies relating these individual variables to muscular performance indicated that these variables as a set might predict the dependent measures in our study.[10-13,16-19,21] We recognized that assessment of thigh girth and percentage of body fat might be influenced by the amount of time elapsed after injury. We, therefore, attempted to generate two sets of models designed to predict preinjury knee strength performance based on an assessment of a group of healthy subjects. One set of models was constructed with the intention that anthropometric and demographic characteristics of patients would be assessed before or immediately after injury. A second set of models was constructed based on the premise that clinicians would assess anthropometric and demographic characteristics postinjury, excluding an assessment of percentage of body fat and thigh girth.

Method

Subjects

The subjects for this study were 134 volunteers (70 female, 64 male) between the ages of 10 and 80 years. The female subjects' mean age was 42.9 years (s = 19.9), and the male subjects' mean age was 41.8 years (s = 20.4). Subjects signed sttements of informed consent before participation, and the project was approved by the Committee on the Protection of the Rights of Human Subjects at The University of North Carolina at Chapel Hill. We conducted a screening interview of potential subjects to ensure that each subject included in the study met the following criteria:

1. No history of lower extremity fracture.

2. No history of a neurological condition affecting lower extremity function.

3. No lower extremity muscular strain or ligamentous sprain during the two years before testing that limited normal activity for more than 48 hours.

Each subject received remuneration for participation in the study.

Instrumentation

One of the investigators (MTG) performed all of the height, weight, skinfold, and thigh girth measurements. The investigator measured subject height to the nearest 0.5 in (*1) and subject weight to the nearest 0.5 lb (*2) using a Detecto-Medic scale.(3) Skinfold measurements were performed using either a Skyndex [TM] electronic body fat calculator (*4) or a lange skinfold caliper. (*5) All skinfold measurements were assessed to the nearest 0.5 mm. Percentage of body fat calculations were performed according to formulas for adolescent and adult male and female subjects [21] and were recorded to the nearest 0.1%. Thigh girth measurements were performed using a flexible plastic tape measure and were recorded to the nearest 0.5 in.

The investigators measured knee flexion and extension torque production using a Cybex [R] II isokinetic dynamometer. (*6) Torque and range-of-motion voltage signals from this instrument were processed by an IBM-PC computer (*7) using commercially available computer software. (*8)

Procedure

The principal investigator (MTG) first measured subject height and weight with the subject's shoes removed. The dominant leg was determined by asking each subject which leg would be preferred for kicking a ball. Thigh girth for each leg was measured at a point midway between the greater trochanter and the proximal pole of the patella with the subject in the supine position, with the knee extended and the lower leg relaxed.[22] Skinfold measurements were performed over the biceps brachii muscle, the triceps brachii muscle, the subscapular region, and the iliac crest in the manner described by Durnin and Rahaman.[22]

We tested the dominant and nondominant legs of each subject at test velocities of 60[degrees] and 180[degrees]/sec. The order of dominant-nondominant leg testing and the order of test velocities were randomized for each subject. Each subject sat in the testing apparatus with hips and knees flexed at approximately 90 degrees. We stabilized each subject with thigh, pelvic, and chest straps. Before testing we followed the computer software procedures to correct all torque values for the effects of gravity acting on the mass of the lower leg and the mass of the dynamometer arm. Peak torque values were identified as those peaks that occurred after the "overshoot" artifact attributable to deceleration of the dynamometer arm and limb. [23]

Each subject performed one practice series of five submaximal knee extension-flexion repetitions at the first test velocity to become familiar with the testing condition and to minimize any practice effect. After two minutes of rest, the subject performed three maximal knee extension-flexion efforts. We encouraged each subject with the words "push" and "pull" during each knee extension and flexion effort, respectively. After another two minutes of rest, the subject performed a second series of three maximal knee extension-flexion efforts at the same angular test velocity. We recorded the largest of the six peak knee extension torque values and the largest of the six peak knee flexion torque values obtained during the two data collection series at the first test velocity. We used an identical procedure for the second test velocity for the same lower extremity. We then repositioned the subject and conducted the same testing protocol for the contralateral leg.

Reliability Testing

The principal investigator evaluated the intrarater reliability of the method for assessing knee strength by testing six subjects twice, with two days between the muslce strength tests. Both legs of each subject were tested using the previously described method, providing eight peak torque values for each subject of a total of 48 observations for each test day.

The principal investigator also evaluation the reliability of using the two skinfold calipers by measuring the four skinfold sites on five subjects with both calipers. The principal investigator measured these 20 skinfold sites two days later with the Lange skinfold caliper to assess intrarater reliability. A second investigator measured the same 20 skinfold sites with the Lange skinfold caliper to assess interrater reliability. The principal investigator measured the thigh girth of both legs for 10 subjects on two different days to evaluate intrarater reliability. A second investigator also measured the same 20 thigh girths to assess interrater reliability.

The Pearson product-moment correlation (r) between the two sets of 48 peak torque measurements was .93. The correlation between 20 skinfold measurements by each of the two skinfold calipers was .99. Intratester reliability on 20 repeated measurements of skinfold was .99. Interstater reliability was .95 between the principal investigator and a second examiner for 20 skinfold measurements. Intratester reliability was .99, and intertester reliability was .92 for 20 repeated measurements of thigh girth.

Data Analysis

The four dependent variables in this study were peak knee flexion and extension torque performed at 60[degrees] and 180[degrees]/sec. Each of these variables serve as the dependent variable in a separate stepwise regression procedure for two analysis strategies. The first analysis examined the relationship between peak torque production and variables that could be assessed before or immediately after injury. The independent variables in each of the four regression procedures for this firm analysis were as follows: age, sex, height, weight, percentage of body fat thigh girth, and side of lower extremity dominance. Sex and side of lower extremity dominance were coded numerically as dichotomous variables (ie, dominant leg = 1, nondominant leg = 2, male = 1, and female = 2). The default significance level for entry into and removal from the regression models was .15.

An analysis preliminary to the stepwise regression analysis examined the relationship between age and the four torque-dependent variables. This analysis was accomplished by a visual inspection of the four scatterplots and by simple correlations. The correlation between age and each of the dependent variables was relatively low (r = -.17 to -.35), and the scatterplots indicated a curvilinear (polynomial) relationship between knee torque production and age. Age squared (age [2]), therefore, was included as an independent variable in the four regression analyses to better represent the curvilinear relationship between torque production and age.

A second analysis was conducted with the same data, excluding percentage of body fat and thigh girth measurements. A separate regression procedure was conducted in this analysis for each of the four torque variables as previously described. This analysis evaluated the utility of predicting preinjury muscular performance based on age, age squared, height, sex, weight, and side of lower extremity dominance. All data analyses were conducted using Systat statistical software (9) and an IBM-PC/XT computer.(7)

Results

Descriptive statistics for all anthropometric and demographic variables appear in Table 1 and are grouped by age and sex. Table 1 also includes descriptive statistics for all peak torque values.

The first analysis strategy examined the relationship between peak torque production and variables that could be assessed before or immeidately after injury. The results of each of the four stepwise regression procedures for this first analysis are given in Tables 2 through 5. The models generated for each of the four torque variables are also included in tables 2 through 5. These models indicate that 64% to 76% of the variance of peak knee extension and flexion torque can be explained by using combinations of the following variables: age, age squared, sex, height, weight, percentage of body fat, and thigh girth.

The second analysis strategy examined the relationship between peak torque production and variables that could be assessed after injury. This analysis assumes that preinjury body weight could be obtained by clinicians either by patient history or from medical records, and the analysis excludes an assessment of percentage of body fat and thigh girth. The results of each of the four stepwise regression procedures for this second analysis are given in Tables 6 through 9. The models generated for each of the four torque variables are included in Tables 6 through 9. These models indicate that 61% to 76% of the variance of peak knee extension and flexion torque can be explained by using combinations of the following variables: age, age squared, sex, height, and weight.

Discussion

The results for both analysis strategies indicate a significant relationship between peak knee torque production and multiple anthropometric and demographic variables. The combined predictive ability of multiple independent variables was significantly greater than the predictive ability of any single variable. The results support the conclusions of Molnar and Alexander[10,11] with regard to the value of age, height, and weight as predictors of peak torque production.

Interestingly, age was selected as a predictor variable only for the two regression models predicting peak knee extension torque at 180[degrees]/sec. Age may share a significantly amount of variability with muscle strength for a young group of subjects. The correlations between age and peak torque production, however, were relatively low (r = - .17 to - .35) for the wider range of ages in this investigation. Molnar and Alexander found that age shared a significant amount of variability with height and weight for a young group of subjects ranging in age from 7 to 15 years.[10,11] This shared variability suggests that the positive relationship between age and torque production for the younger subjects in this study was represented by the inclusion of height and weight in all of the prediction models.

The preliminary scatterplot analysis indicated the curvilinear relationship between age and peak torque production. The decline in peak torque production with aging was apparently represented by the inclusion of age squared in the models. Age squared was selected as a significant predictor variable and was assigned a negative regression coefficient in all of the models, representing the muscle strength decrease occurring in later years.[12,16,18,19]

The results for the first analysis strategy also indicate the value of including thigh girth and percentage of body fat measurements as predictors of peak knee torque production. Both variables were selected for three of the models, and percentage of body fat was selected for the fourth model. A recent study by Doxey documented that thigh girth corrected for subcutaneous body fat thickness explained a significant amount of anterior and posterior thigh muscle thickness. [24] Several researchers have reported a significant relationship between muscle cross-sectional area and isometric strength. [22,25,26] The inclusion of thigh girth and percentage of body fat in models generated in this investigation indicates the potential value of using these variables to predict muscle performance.

The magnitude of the constant in the prediction equations for the first analysis strategy (Tabs. 2-5) suggests that female subjects produced about 9 to 17 ft.lb (* 10) less knee torque than male subjects of equivalent age, height, weight, percentage of body fat, and thigh girth. Wilmore, however, reported that women have greater lower extremity muscle strength than men when lean body mass is covaried statistically. [27] The apparent inconsistency between our results and the results of Wilmore may be explained by the difference in body fat distribution between male and female subjects and by the inclusion of thigh girth as a predictor variable in our study. Female subjects have relatively more subcutaneous adipose tissue in the femoral region than male subjects with comparable percentage of body fat.[28, 29] Female subjects, therefore, have relatively less lean muscle tissue in the femoral region than male subjects and thus may be less capable of producing knee torque than male subjects with comparable thigh girths and percentages of body fat. This factor may explain the inclusion of sex as a valuable predictor variable in the regression models.

A comparison of variables included in the two sets of models (Tabs. 2-9) indicates that thigh girth and percentage of body fat significantly improved the percentage of explained variance for three of the four torque variables. The inclusion of thigh girth significantly improved the percentage of explained variance for the fourth torque variable. The percentage of torque variability predicted by the two sets of models did not differ, however, by more than 3% for any of the four torque variables.

The predictive models generated in the second analysis (based on postinjury assessment) may be more appropriate than the first set of models for use with patients who have experienced muscle atrophy and body composition changes after injury. These models may provide a fairly accurate prediction of preinjury muscle performance and enable the clinician to establish realistic rehabilitative muscle strengthening goals. The clinician's choice of which of the two sets of models to use with patients assessed before or immediately after injury will depend on the clinician's skill in measuring percentage of body fat and thigh girth and the desire to perform these measurements. The inclusion of these two variables in the prediction models contributed only an additional 2% or 3% of explained variability. The additional explained variance gained by including these variables, however, may make a clinically significant difference in the magnitude of peak knee torque predicted for the individual patient who has an unusual body composition. Two patients may have identical anthropometric and demographic characteristics, except that one patient may have an appreciably higher percentage of body fat than the other patient. The equations that do not include percentage of body fat would predict identical torque-producing capability for the two patients. The equations that include percentage of body fat, however, would predict that the patient with greater percentage of body fat would produce less torque than the other patient.

Clinical Application of the Models

An example application of one of the models may assist in demonstrating the clinical use of the results of this study. For the purpose of this example, we will assume that a hypothetical patient has sustained a tibial shaft fracture requiring external fixation. The clinician examines the patient immediately postinjury and obtains the following patient data: age = 26.5 years (to the nearest month), male (coded, 1), height = 72.5 in, weight = 152 lb. thigh girth = 17.5 in, and percentage body fat = 11.2%. For this example, we will estimate the patient's preinjury peak knee extension torque at 60 [degrees]/sec (ETS) using the following prediction equation (Tab. 2):

ETS = -89.820 - (0.010 X age [.sup.2.])- (15.210 X sex) + (1.787 X height) + (0.601 X weight) + 3.504 X thigh girth) - (1.219 X % body fat)

(1)

Substitution for the six predictor variables in this equation would occur as follows:

ETS = -89.820 - (0.010 X 702.3) - (15.210 X 1) + (1.787 X 72.5) + (0.601 X 152) + (3.504 X 17.5) - (1.219 X 11.2)

ETS = 156.5 ft.lb

(2)

Conclusions

The results of this study indicate the feasibility of predicting peak knee torque production at two angular velocities on an isokinetic device for individuals with diverse anthropometric and demographic characteristics. The predictive models generated in this study may be useful to clinicians in establishing knee muscle strengthening goals for patient rehabilitative programs. Clinicians routinely gather the data necessary to apply the straightforward prediction equations presented in this study. Clinicians can predict preinjury muscle performance on isokinetic testing devices based on age, sex, and anthropometric data acquired before or immediately after injury. We intend to gather additional data to validate these prediction models and add to the database from which these models were generated.

Acknowledgment

We gratefully acknowledge the contribution of time and instrumentation provided by the staff of the Physical Therapy Department, North Carolina Memorial Hostpial, Chapel Hill, NC, and the assistance provided by Dr. Philip Witt for interrater reability testing.

(1) 1 in = 2.54 cm.

(2) 1 lb = 0.4536 kg.

(3) Detecto Scales Inc, 475 Northern Blvd, Great Neck, NY 11021.

(4) Caldwell, Justiss, & Co, Inc, PO Box 520, Fayetteville, AR 72701.

(5) Cambridge Medical Instruments, 73 Spring St, Ossining, NY 10562.

(6) Cvbex, Div of Lumex, Inc, 2100 Smithtown Ave, Ronkonkoma, NY 11779.

(7) International Business Machine Corp. 1000 NW 51st St, Boca Raton, FL 33432.

(8) Isoscan II, Isotechnologies Inc, PO Box 1239, Hillsborough, NC 27278.

(9) Systat Inc, 2902 Central St. Evanston, IL 60201.

(10) ft.lb = 1.356 N.m.

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M Gross, PhD, PT, is Assistant Professor, Division of Physical Therapy, The University of North Carolina at Chapel Hill, CB# 7135, Medical School Wing E 222H, Chapel Hill, NC 27599-7135 (USA).

P McGrain, PhD, is Assistant Professor, Division of Physical Therapy, The University of North Carolina at Chapel Hill.

N Demilio, MS, PT, is Director, Physical Therapy Assistant Program, Nash Community College, Old Carriage Rd, Rocky Mount, NC 27804. He was Senior Physical Therapist, North Carolina Memorial Hospital, Chapel Hill, NC, at the time this study was conducted.

L. Plyler, BS, PT, is a physical therapist residing at 416 Emerson Dr, Raleigh, NC 27609. He was a student in the baccalaureate physical therapy program, Division of Physical Therapy, The University of North Carolina at Chapel Hill, at the time this study was conducted.

This research was supported in part by a grant from the US Department of Health and Human Services, Public Health Service General Research Support Award 5-S01-FR-05406.

This article was submitted February 16, 1988; was with the authors for revision for two weeks: and was accepted June 29, 1988.