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Method Article

Quantifying Recovery After Anterior Cruciate Ligament Reconstruction Using the Torque- Velocity Relationship

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DOI:

10.3791/72088

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July 24th, 2026

 ,  ,  , 
1School of Kinesiology, Louisiana State University, 2Department of Orthopedics, University of North Carolina at Chapel Hill, 3Department of Physical Therapy, Louisiana State University Health Sciences Center

In This Article

Summary

This protocol is intended to demonstrate how clinicians can evaluate the torque-velocity relationship following anterior cruciate ligament reconstruction.

Abstract

Following anterior cruciate ligament reconstruction (ACLR), patients often display persistent deficits in quadriceps muscle strength that reduce quality of life and lead to long-term functional impairment. Historically, post-operative assessments of muscle function have focused on maximal isometric torque or peak torque at a single isokinetic velocity, neglecting the variety of demands placed on a muscle group across activities and the precision needed to guide clinical decision-making. The goal of this demonstration is to illustrate how isokinetic testing at different angular velocities can be used to characterize the torque-velocity relationship following ACLR. The protocol includes participant preparation, dynamometer setup, range-of-motion configuration, and alignment of key testing components, including chair position and dynamometer arm length. Strength assessment consists of isometric knee extension testing and concentric isokinetic knee extension and flexion testing at 60°/s, 180°/s, and 240°/s. For the two-point method, torque-velocity is calculated as the difference in normalized torque production between a slow and a fast testing velocity (e.g., 60°/s and 180°/s). For full multi-velocity characterization, peak torque values obtained at each velocity are exported to a spreadsheet or statistical software and analyzed using regression techniques. Previous results have demonstrated that patients following ACLR have knee extensor torque-velocity relationships of the involved limb about half the magnitude of the contralateral limb, using the two-point method, and a lesser slope than the contralateral limb using multiple velocity characterization. The torque-velocity relationship may identify persistent deficits not captured by single-velocity testing and can be used to monitor recovery over time.

Introduction

Anterior cruciate ligament injuries are among the most common in sports, resulting in billions of dollars in healthcare costs in the US annually1. Despite advances in surgical technique and clinical care, following anterior cruciate ligament reconstruction (ACLR), patients regularly develop persistent quadriceps muscle weakness2,3. Deficits in quadriceps muscle function are associated with decreased quality of life, decreased ability to complete activities of daily living, and decreased overall function4,5,6,7. Given the importance of quadriceps function, test batteries including objective assessment of quadriceps are a key piece of multidimensional test batteries used during return-to-sport decision-making8.

Current clinical assessments of muscle function evaluate maximal strength as a measure of muscle capacity, but muscle performance is also influenced by additional physiological principles8,9,10. The force-velocity relationship is a basic physiological principle defined by the inverse relationship between contraction velocity and force production11,12. This model has been demonstrated in a number of different in vitro and in vivo studies, as well as in human whole muscle, via the torque-velocity relationship12,13. The torque-velocity relationship has previously been characterized via isokinetic dynamometry and has been shown to be altered in patients with a history of ACLR as well as due to immobilization, aging, and other pathologies14,15,16,17,18. Given the widespread use of testing at one or two velocities for clinical use, this method was developed to monitor changes in an underlying physiological principle of muscle.

The use of isometric testing and isokinetic testing following ACLR is widespread and widely accepted19,20. Focusing solely on torque production at a single velocity via isometric or isokinetic testing at a single velocity may not be representative of the range of muscular demands during activities of daily living and high-level sport14,21,22. The two-point method of characterizing the torque-velocity relationship has been found reliable and may be clinically useful as long as the chosen velocities have a difference in angular velocity of at least 90°/s15,23. This protocol demonstrates two velocity isokinetic tests for clinical use and the use of multiple velocities to characterize the torque-velocity relationship in greater detail. While this protocol focuses on the analysis of peak torque production, the dynamometer will also allow full export of time-series data for time-series analyses. Peak torque is a measure of maximal force or power generation, but variables such as rate of torque development, time to peak torque, and angle of peak torque demonstrate additional methods to determine participants’ ability to generate force quickly and respond to varying potential demands24,25,26,27.

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Protocol

All representative data were collected following institutional review board approval, and informed consent was obtained from all participants. The protocol below has been performed on participants aged at least 12 years, and 4 months post-ACLR, with no restrictions based on graft type. Exclusion criteria were pregnancy, serious infection near the lower limb, known muscular abnormalities, and a history of cardiopulmonary disorder.

1. Method 1: Participant preparation and dynamometer setup

NOTE: A consistent dynamometer setup is critical to ensure valid, reproducible torque evaluation across sessions and participants. As recommended by the manufacturer, the dynamometer should be calibrated monthly. The torque, velocity, and position data in this protocol were exported at 100 Hz, and no additional smoothing or filtering was applied beyond the manufacturer’s signal processing. This protocol should not be completed before a patient has completed open-chain knee extension during rehabilitation.

  1. Begin all procedures with the uninvolved limb.
  2. Have the participant complete a standardized warm-up consisting of approximately 5 min of treadmill walking at a standardized pace of 3.0 mph.
  3. Turn the dynamometer on and attach the dynamometer arm.
  4. Position the chair at a back angle of 85° and set the dynamometer rotation to 40° consistent with manufacturer standards.
  5. Seat the participant with hips flexed to approximately 85° and instruct them to maintain an upright posture and avoid grabbing the handles of the dynamometer during testing.
  6. Adjust the back translation so that the popliteal fossa is positioned approximately 3–4 cm anterior to the edge of the seat.
  7. Adjust chair position and dynamometer arm orientation until the mechanical axis aligns with the lateral femoral condyle.
  8. Position the dynamometer arm resistance pad approximately 5 cm proximal to the lateral malleolus on the anterior portion of the lower leg28,29.
  9. Secure the test limb to the dynamometer arm. Ensure the shank remains neutral to avoid rotation when securing it to the dynamometer arm with a strap. Stabilize the participant using straps across the torso and pelvis.
  10. Secure the testing thigh with a strap to prevent hip flexion and secure the contralateral limb using the available restraint. In addition to restraints, patients must be cued to only try to extend and flex the tested limb for the duration of the test.
  11. Passively move the limb through a full range of motion arc to ensure that no additional adjustments are needed. Record chair position, dynamometer position, and arm length for future assessment.

2. Method 2: Setting the range of motion

NOTE: Use software-based stops and manual stops.

  1. Set anatomical zero at 180°/full knee extension. If the participant lacks full knee extension, use the dynamometer offset function to account for the limitation. Enter the difference from the current limb position to the anatomical zero degrees into the dynamometer offset. Range-of-motion limitations may alter waveform analysis and peak torque angle.
  2. Set the dynamometer limit of extension at 175° (5° knee flexion from anatomical zero or maximum available knee extension).
  3. Set the dynamometer limit of flexion at 70° (110° knee flexion from anatomical zero or maximum available knee flexion if 110° cannot be reached).
  4. Adjust the manual stops accordingly.
  5. Limb weight should be measured as close to maximal knee extension as possible without compromising participant comfort and not exceeding. Instruct the patient to relax and weigh the limb 3–4 times in quick succession until the weight appears stable.
    NOTE: If limb weight fluctuates less than 1.5 Nm, consider the weight stable. Once the weight is accepted, the software will automatically apply gravity correction. Corrected values should be used for all analyses.

3. Method 3: Assessing strength

NOTE: Consistency in cuing and instructions is critical. Instruct patients to kick as hard and fast as possible. Provide verbal encouragement.

  1. Begin testing with the uninvolved limb
  2. Provide standardized verbal instructions such as: "Kick as hard and fast as possible," "Pull your leg back down as hard and fast as possible," and "You are always moving the machine, and it is not moving you."
  3. Provide strong verbal encouragement during all trials.

4. Method 4: Isometric testing

  1. Perform isometric knee extension testing at a joint angle of 90 degrees of knee flexion.
  2. Begin with three familiarization repetitions. Instruct the participant to kick out and maintain a contraction at 25% of their perceived maximum, followed by 50% and 75%, with 30 seconds of rest between contractions. This rest interval is consistent with other investigations utilizing isokinetic and isometric dynamometry24,26.
  3. Instruct the participant to kick out as hard and fast as possible and to maintain their contraction for 3–5 seconds.
  4. Perform 2–3 maximal trials with 30 seconds of rest between trials.

5. Method 5: Isokinetic testing

  1. Perform concentric isokinetic knee extension and flexion testing at the following velocities: 60°/s, 180°/s, 240°/s.
    NOTE: Dynamometer settings pair agonist and antagonist motions by default during concentric isokinetic testing, but these results will focus on the knee extensors, as that is where previous deficits have been identified.
  2. At each velocity,
    1. Perform 4 consecutive submaximal practice repetitions, progressing from low to near maximal effort (25–75%).
    2. Perform 8 maximal effort repetitions.
    3. Provide real-time visual feedback displaying the torque vs time or torque vs position curves and consistent verbal encouragement.
    4. Allow 30–60 seconds of rest between tests at each new velocity. This rest interval is consistent with other investigations utilizing isokinetic and isometric dynamometry24,26. Single-velocity testing often uses rest intervals of 30 seconds, but investigations utilizing multiple velocity testing have demonstrated that rest intervals of 60 seconds appear sufficient to reduce the potential effects of fatigue24,30,31. If participants show signs of excessive fatigue, consider site-specific increases in rest time.
  3. Repeat the entire protocol on the ACLR limb.
  4. Instruct participants to discontinue testing if they experience sharp pain or discomfort.

6. Method 6: Data processing and outcome measures

NOTE: For clinical use, assess symmetry in peak torque production across all velocities and confirm decreases in torque as contraction velocity increases. If the coefficient of variation across trials for any isokinetic velocity exceeds 10%, retest if time allows, unless the patient reports pain.

  1. Identify peak torque (the highest instantaneous torque value) for each velocity and contraction type from the repetition that produced the highest peak torque.
  2. Normalize torque values to body mass (Nm/kg).
  3. Identify a primary set of two velocities for torque-velocity calculation using the two-point method (e.g., 60°/s and 180°/s). For two-point calculations, calculate the torque-velocity as the difference in normalized torque production at the slow and fast velocities.

7. Method 7: Multi-velocity torque-velocity characterization (optional)

  1. Export peak torque values for each tested condition, including isometric (0°/s) and all isokinetic velocities (60°/s, 180°/s, 240°/s).
  2. Enter the data into the Microsoft Excel spreadsheet software:
    1. Column A: Angular Velocity
    2. Column B: Peak Torque Involved (Nm)
    3. Column C: Peak Torque Uninvolved (Nm)
      NOTE: Raw and normalized torque values produce proportional slopes within an individual participant. For comparison between participants, body mass and other individualized factors may be included as covariates in statistical models.
  3. Create an additional row using the SLOPE function in the spreadsheet software using =SLOPE(torque_values, velocity_values)
  4. Create an additional row to analyze symmetry using =(involved_limb_slope/uninvolved_limb_slope)*100 (Figure 1).
  5. Record the resulting slope value
  6. If desired, export the complete torque, position, velocity, and time-series data for subsequent analysis. Exported data may be used to calculate additional variables, such as the rate of torque development (change in torque over time) and other torque-time characteristics26,32.

Angular velocity vs. peak torque graph, illustrating torque production data and symmetry analysis.
Figure 1. Simplified representative torque-velocity dataset and quick analysis workflow. Peak torque values were exported into spreadsheet software and plotted against angular velocity using a linear regression line. This represents simplified data entry for a single participant and should be expanded with additional columns for each participant and testing session for longitudinal assessment. Please click here to view a larger version of this figure.

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Results

Successful completion of this protocol should result in the highest torque output at zero velocity (isometric) and a progressive decline in torque with increasing isokinetic contraction velocities12. In a previous cohort, when examining patients with a history of ACLR, this progressive decline was greater in uninvolved limbs than in ACLR limbs14. Individual torque-time or torque-position graphs should demonstrate relatively consistent contractions. The ideal coefficient of ...

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Discussion

This protocol describes a clinically feasible method for evaluating the quadriceps torque-velocity relationship using multimodal dynamometry following ACLR. Persistent quadriceps weakness is common across age groups and ACLR graft types36,37. Traditional test batteries for patients returning to sport post-surgery focus on maximal strength but may not fully assess quadriceps function across a range of contractile demands 14. Single-velocity testing at slow isokine...

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Disclosures

The authors have no conflicts of interest or disclosures to report.

Materials

List of materials used in this article
NameCompanyCatalog NumberComments
Computer workstationAny commercial manufacturerN/AUsed to operate dynamometer software and export data
Digital InclinometerAny commercial manufacturerN/AUsed to verify anatomical zero position if desired
HUMAC NORM Testing and Rehabilitation SystemCSMi Solutionshttps://csmisolutions.com/Computerized multimode dynamometer used for isometric and isokinetic knee strength testing
Spreadsheet softwareMicrosoftExcel (version dependent)Used for data entry and data processing of torque data
TreadmillAny commercial manufacturerN/AUsed for standardized warm-up prior to testing

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Isokinetic TestingQuadriceps StrengthKnee ExtensionMuscle Function AssessmentPeak TorqueDynamometer SetupRange Of MotionConcentric Isokinetic Testing
Quantifying Recovery After Anterior Cruciate Ligament Reconstruction Using the Torque- Velocity Relationship
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