Myers optimization JMPT

ACCRAC AWARD WINNING PAPER

OPTIMIZED PREDICTION OF CONTACT FORCE APPLICATION

DURING SIDE-LYING LUMBAR MANIPULATION

Casey A. Myers, MSc, a Brian A. Enebo, DC, PhD,b and Bradley S. Davidson, PhDc

a Graduate ReEngineering, Uni

b Associate CMedicine ProgramGeneral Internal Mof Medicine, Aur

c Assistant ProUniversity of De

Submit reque2390 S York St,(e-mail: Bradley.

Paper submittaccepted July 4,

0161-4754/$3Copyright ©http://dx.doi.o

ABSTRACT

Objectives: The purposes of this study included the following: (1) to predict L3 contact force during side-lyinglumbar manipulation by combining direct and indirect measurements into a single mathematical framework and (2) toassess the accuracy and confidence of predicting L3 contact force using common least squares (CLS) and weightedleast squares (WLS) methods.Methods: Five participants with no history of lumbar pain underwent 10 high-velocity, low-amplitude lumbar spinalmanipulations at L3 in a side-lying position. Data from 5 low-force criterion standard trials where the L3 contact forcewas directly measured were used to generate participant-specific force prediction algorithms. These algorithms wereused to predict L3 contact force in 5 experimental trials performed at therapeutic levels. The accuracy andeffectiveness of CLS and WLS methods were compared.Results: Differences between the CLS-predicted forces and the criterion standard–measured forces were 621.0 ±193.5 N. Differences between the WLS-predicted forces and the criterion standard–measured forces were −3.6 ±9.1 N. The 95% limits of agreement ranged from 234.0 to 1008.0 N for the CLS and −21.9 to 14.7 N for the WLS.During both the criterion standard and experimental trials, the CLS overestimated contact forces with larger variancethan the WLS.Conclusion: This novel method to predict spinal contact force combines direct and indirect measurements into asingle framework and preserves clinically relevant practitioner-participant contacts. As advanced instrumentationbecomes available, this framework will enable advancements in training and high-quality research on mechanisms ofspinal manipulative therapy. (J Manipulative Physiol Ther 2012;35:669-677)
Key Indexing Terms: Manipulation; Spinal; Lumbar vertebrae; Biomechanics
Accurate and reliable measurement of contact forcesapplied during spinal manipulative therapy (SMT)is an important aspect to research, education,

patient safety, and clinical application. Competent deliveryof SMT requires the practitioner to be adept at modulating

search Assistant, Mechanical and Materialsversity of Denver, Denver, CO.linical Professor and Chiropractor, Integrativeat University of Colorado Hospital, Division ofedicine, University of Colorado Denver School

ora, CO.fessor, Mechanical and Materials Engineering,nver, Denver, CO.sts for reprints to: Bradley S. Davidson, PhD,Denver, CO [email protected]).ed April 20, 2012; in revised form June 21, 2012;2012.6.002012 by National University of Health Sciences.rg/10.1016/j.jmpt.2012.10.010

peak contact force and rate of force application.1-5

However, standards for clinical effectiveness and patientsafety currently do not exist for manipulative forceapplication. In addition, few opportunities exist forpractitioners and students to receive quantitative feedbackon SMT delivery.

Several methods exist to measure in vivo contact forcesduring SMT3,4,6-12 and can be classified into 2 categories:direct measurement and indirect measurement. Direct forcemeasurement is often implemented using pressure matsor load cells placed between the practitioner and thepatient.8,11-13 An advantage of direct measurement is thatforces are measured at the site of contact. However, pressuremats can only measure forces oriented perpendicular to thecontact surface, and shear forces are not considered. Thismethod is commonly used to assess SMTwith the participantlying prone on the treatment table, and care is taken to delivera force perpendicular to the surface.8,11,13-15 As a result,direct measurement has limited application in high-velocity,low-amplitude (HVLA) manipulations of the cervical andlumbar spine because shear and rotational forces are present.

669

mailto:[email protected]

http://dx.doi.org/10.1016/j.jmpt.2012.10.010

Mathematical Nomenclature

Fx(sp), Fy

(sp), Fz(sp) force vector components at L3 spine contact

Fx(fp), Fy

(fp), Fz(fp) force vector components measured by force platform

Fx(sh), Fy

(sh), Fz(sh) force vector components at shoulder contact

Fx(th), Fy

(th), Fz(th) force vector components at thigh contact

Mx(fp), My

(fp), Mz(fp) resultant moments from force platform about force platform axes

dx(sp), dy

(sp), dz(sp) orthogonal distances from force platform origin to the L3 spinal contact

dx(sh), dy

(sh), dz(sh) orthogonal distances from force platform origin to the shoulder contact

dx(th), dy

(th), dz(th) orthogonal distances from force platform origin to the thigh contact

Fest(sp) spinal contact force estimated from force balancing

ux(fa), uy

(fa), uz(fa) direction cosines of the forearm

lx(fa), ly

(fa), lz(fa) scalar projections of the forearm onto the x, y, and z axes

ex(⋅), ey

(⋅), ez(⋅) error associated with each calculation in the respective coordinate directions

Fpred(sp) predicted components of the L3 contact force Fx

(sp), Fy(sp), Fz

(sp)

W 9 × 9 diagonal weighting matrix|Fpred

(sp) | predicted force magnitude at L3 spinal contact|Fmeas

(sp) | measured force magnitude at L3 spinal contact

670 Journal of Manipulative and Physiological TherapeuticsMyers et alNovember/December 2012Optimized Contact Force Prediction

Indirect force measurement is accomplished byapplying an inverse dynamics paradigm with resultantforces recorded from a force platform embedded in thetreatment table.4,9,16 An advantage of this method is thatthe practitioner maintains clinically realistic contact withthe participant at the site of the manipulation. However,this method ignores energy loss that occurs between theforce application points and the measurement site. Inaddition, this method can only be used when there is asingle contact point between the practitioner and thepatient. For example, Triano and Schultz4 isolated thethrust force during side-lying lumbar spine manipulationby creating structures specifically designed to eliminatethe effect of stabilizing forces from other contacts to theforce platform.

When analyzing manual procedures such as side-lyingSMT, direct and indirect measurement techniques willlikely yield conflicting results of contact force magnitudeand direction. Therefore, one approach to improve contactforce measurement is to combine the 2 methods into asingle framework while preserving the advantages of each.Combining these experimental methods will capture moremeasurements than required and will result in an overde-termined mathematical system. Instead of being a limita-tion, this feature is beneficial when any measurements areunreliable, less reliable than other measurements, orunavailable. Mathematicians and engineers have developeda wide array of tools to solve overdetermined systems.17

Common least squares (CLS) and weighted least squares(WLS) are 2 attractive options that preserve the mathemat-ical structure and measurement dependencies inherent whencombining direct and indirect force measurements of SMT.Common least squares uses a pseudoinversion of arectangular matrix, and WLS performs the same funda-

mental calculation while systematically emphasizing ordeemphasizing the contribution of each measurementaccording to the reliability of the measurement. Weightedleast squares has been successfully implemented in otherbiomechanical applications such as estimating 2-dimen-sional joint torques during quiet stance18 and 3-dimensionaljoint torques during overground walking.19

The objectives of this investigation were (1) tocombine direct and indirect force measurements during aside-lying manipulation into a single mathematicalframework and (2) to assess the accuracy and confidenceof predicting L3 contact force using CLS and WLSmethods. We hypothesized that WLS would producelower error when compared with a CLS approach and thatthe framework and resulting measurement weights can beefficiently used to predict contact force when a therapeuticlevel of SMT is applied.

METHODS

Data CollectionFive participants (3 men: age, 34 ± 6.1 years; height,

180.3 ± 2.6 cm; mass, 83.6 ± 8.3 kg; 2 women: age, 25 ± 3.5years; height, 171.4 ± 1.8 cm; mass, 59.1 ± 1.3 kg) providedinformed consent to participate in this investigation. Eachparticipant had no history of lumbar pain or injury andunderwent 10 HVLA lumbar spinal manipulations at L3 ina right side-lying position.

To best preserve the traditional mechanics of a side-lyingmanipulation, multiple points of contact between thepractitioner and the participant were allowed. Althoughstructures designed to isolate forces applied by thepractitioner4 were not used, practitioner-participant contact

Fig 2. Modified treatment table with embedded force platform inthe body section. Note that the head, body, and foot sections arenot connected.

Fig 1. A, Practitioner and participant positions during the side-lying manipulation showing contact at the thigh, left shoulder, andL3 spinal level. B, Enlarged view of the thigh contact. C, Enlargedview of the shoulder contact.

671Myers et alJournal of Manipulative and Physiological TherapeuticsOptimized Contact Force PredictionVolume 35, Number 9

was limited to 3 locations: (1) practitioner left hand withparticipant left shoulder, (2) practitioner right thigh withlateral aspect of participant left thigh, and (3) practitioner righthand with participant left L3 mammillary process (Fig 1). Amanipulation was discarded if the practitioner contacted theparticipant at an additional location during the thrust (eg,practitioner's chest contacted the participant).

The first 5 HVLA manipulations served as criterionstandard trials. These manipulations were performed with aload cell in the right hand of the practitioner, which directlymeasured L3 contact forces. The surface area of the loadcell was approximately 1 in2 and interacted with thevertebra similar to hypothenar contact when no load cellwas used in the experimental trials. During the criterionstandard trials, the practitioner used a contact force that waslower than normal therapeutic load to minimize discomfortcaused by the load cell. The criterion standard trialscombined direct measurement of the L3 contact force with aset of data that included direct measurement of thigh andshoulder contact force, indirect force measurement, andmotion capture data to generate a prediction algorithm forL3 contact force (described in “Contact Force Prediction”).The last 5 HVLA manipulations served as experimental

trials. The load cell at the L3 contact point was removed forthese manipulations, and they were performed with normaltherapeutic contact and loading. All other measurements inthe data set were collected in the same way as the criterionstandard trials. Data sets from the experimental trials wereused to demonstrate the effectiveness of the contact forceprediction algorithms established during the criterionstandard trials.Direct Force Measurement. Force magnitudes at the partic-ipant contacts (left shoulder, thigh, and L3) wererecorded using uniaxial load cells placed between theparticipant and the practitioner (Cooper Instruments,Warrenton, VA). The load cells were securely fixed tothe practitioner using elastic straps. Aquaplast splintingmaterial (Qfix, Avondale, PA) placed over the skin of theparticipant was used to form a rigid contact surface at thethigh and shoulder (Fig 1).Indirect Force Measurement. Resultant forces and momentsfrom all contacts were measured with a force platform(Bertec Corporation, Columbus, OH) embedded in astandard treatment table (Physical Enterprise, Petaluma,CA). The modified treatment table consisted of 3 isolatedsections: head, body, and foot (Fig 2). The force platformwas embedded only in the body section.

During each manipulation, the participant was supportedprimarily by the body section and, as little weight possible,was placed on the head and foot sections. Therefore, the 3contact forces applied to the participant were absorbed byforce platform instead of the other supporting sections ofthe table.

Contact force direction and practitioner kinematics weremeasured using an infrared motion capture system (Vicon,Centennial, CO). Reflective markers were placed on thepractitioner and load cells during a calibration collection.After calibration, load cell markers were removed and

image of Fig�1

Fig 3. Schematic of the data flow taken to predict spinal contacforce.


t

reconstructed as virtual markers during each manipulation.Direction of the force was defined by a vector perpendicularto the contact surface of the load cell.

Load cell and force platform data were sampled at 2000Hz and conditioned with a low-pass Butterworth filter (zero-phase lag, 20-Hz cutoff). These data were downsampled to100 Hz for synchronization with motion capture data.Average time delay between load cell application and forceplatform measurement was approximately 20 millisecondsfor each participant. Therefore, an equivalent offset wasapplied between the 2 signals for algorithm development.

Contact Force PredictionL3 contact force applied to the participant during the 5

experimental trials was predicted using an algorithmicmodel built from the 5 criterion standard trials. Themodel combined direct measurements from load cells andmotion capture with the indirect measurement of resultantforces and moments from the force platform to form alinear set of overdetermined equations. This was solvedin an optimization routine to predict the L3 contact forcevector (Fig 3).

The 3 components of the spine contact force (Fx(sp), Fy

(sp),Fz(sp)) with respect to a global coordinate system (x, y, z) can

be estimated using 3 independent methods. Each methodrelies on a different combination of the force, moment, andkinematic measurements: force balancing, moment balan-cing, and direction-constrained force balancing.Force Balancing. The force balancing method combinesdirect contact force data from the load cells at the shoulderand thigh contacts with indirect resultant force data from theforce platform. Because orientation of each force is knownwith respect to the global coordinate system, the spinecontact forces are calculated as follows:

F spð Þx ¼ F fpð Þ

x − F shð Þx − F thð Þ

x

F spð Þy ¼ F fpð Þ

y − F shð Þy − F thð Þ

y

F spð Þz ¼ F fpð Þ

z − F shð Þz − F thð Þ

z

ð1Þ

whereFx(fp),Fy

(fp), andFz(fp) are resultant force vectors recorded

from the force platform; Fx(sh), Fy

(sh), and Fz(sh) are force

vectors calculated at the shoulder contact; and Fx(th), Fy

(th), andFz(th) are force vectors calculated at the thigh contact.

Moment Balancing. The moment balancing method com-bines moments calculated using force data from the loadcells at the shoulder and thigh contacts and distance fromfixed coordinate system axes with indirect resultant momentdata from the force platform:

0 d spð Þz d spð Þ

y

d spð Þz 0 d spð Þ

x

d spð Þy d spð Þ

x 0

264

375

F spð Þx

F spð Þy

F spð Þz

8><>:

9>=>;

¼M fpð Þ

x − F shð Þz d shð Þ

y − F shð Þy d shð Þ

z − F thð Þz d thð Þ

y −F thð Þy d thð Þ

z

M fpð Þy − F shð Þ

z d shð Þx − F shð Þ

x d shð Þz − F thð Þ

z d thð Þx −F thð Þ

x d thð Þz

M fpð Þz − F shð Þ

y d shð Þx − F shð Þ

x d shð Þy − F thð Þ

y d thð Þx −F thð Þ

x d thð Þy

8><>:

9>=>;ð2Þ

where Mx(fp), My

(fp), andMz(fp) are resultant moments recorded from

the force platform at the force platform origin; dx(sp), dy

(sp), and dz(sp)

define orthogonal distances from the force platform origin to the L3spinal contact; dx

(sh), dy(sh), and dz

(sh) define orthogonal distancesfrom the force platform origin to the shoulder contact; and dx

(th),dy(th), and dz

(th) define orthogonal distances from the force platformorigin to the thigh contact.Direction-Constrained Force Balancing. The direction-constrainedforce balancing method provides an additional constraintto the force balancing method. The scalar magnitude ofthe spinal contact force is calculated using the same dataas Eq. 1:

Fspð Þest ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiF fpð Þ

x −F shð Þx −F thð Þ

x

� �2 þ F fpð Þy −F shð Þ

y −F thð Þy

� �2þ F fpð Þ

z −F shð Þz −F thð Þ

z

� �2rð3Þ

and is reoriented to coincide with the line of thrust, whichis assumed to be delivered in line with the practitionerforearm:

F spð Þx ¼ F

spð Þest u

fað Þx

F spð Þy ¼ F

spð Þest u

fað Þy

F spð Þz ¼ F

spð Þest u

fað Þz

ð4Þ

where ux(fa), uy

(fa), and uz(fa) define the direction cosines of

the forearm:

u fað Þx ¼ l fað Þ

xffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffil fað Þx

2 þ l fað Þy

2 þ l fað Þz

2q ;

u fað Þy ¼ l fað Þ

yffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffil fað Þx

2 þ l fað Þy

2 þ l fað Þz

2q ; ð5Þ

u fað Þz ¼ l fað Þ

zffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffil fað Þx

2 þ l fað Þy

2 þ l fað Þz

2q

and lx(fa), ly

(fa), and lz(fa) are scalar projections of the

practitioner forearm onto the global axes.By combining Eqs. 1 to 3 into a single system, an

overdetermined mathematical representation is formed,which has more equations than unknowns. Although eachof the 3 methods can be used to solve for the L3 contactforce, a significant limitation in each is the rigid-body

image of Fig�3


assumption. Because neither the practitioner nor theparticipant behaves as rigid bodies, errors that are notcaptured in Eqs. 1 to 3 exist in the experimentalmeasurement and an error term must be included. Theresulting system takes the matrix form A⋅F (sp) = b + e:

1 0 0

0 1 0

0 0 1

0 d spð Þz d spð Þ

y

d spð Þz 0 d spð Þ

x

d spð Þy d spð Þ

x 0

1 0 0

0 1 0

0 0 1

266666666666666664

377777777777777775

F spð Þx

F spð Þy

F spð Þz

8><>:

9>=>;

¼

F spð Þx − F shð Þ

x − F thð Þx

F spð Þy − F shð Þ

y − F thð Þy

F spð Þz − F shð Þ

z − F thð Þz

M fpð Þx −M shð Þ

x −M thð Þx

M fpð Þy −M shð Þ

y −M thð Þy

M fpð Þz −M shð Þ

z −M thð Þz

Fspð Þest ⋅ i fað Þ

Fspð Þest ⋅ j fað Þ

Fspð Þest ⋅ k fað Þ

8>>>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>>>:

9>>>>>>>>>>>>>>>>>>>=>>>>>>>>>>>>>>>>>>>;

þ

eFxeFy

eFzeMxeMy

eMzefaxefay

efaz

8>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>:

9>>>>>>>>>>>>>>>>>=>>>>>>>>>>>>>>>>>;

ð6Þ

where ex(⋅), ey

(⋅), and ez(⋅) represent the error associated with

each row calculation in the global coordinate system.The system was solved using 2 approaches: CLS and

WLS. The CLS procedure predicts the spine contact forcesby left-multiplying b by A+, which is the 3 × 9pseudoinverse of A:

Fspð Þpred ¼ Aþ⋅b ð7Þ

where Fpred(sp) represents the components of the predicted L3

contact force (Fx(sp), Fy

(sp), Fz(sp)).

Although the CLS is valid for an overdetermined systemand creates some robustness in the solution, it cannot betuned to account for systematic error.

The WLS procedure accounts for systematic error byweighting the contribution of each calculation using thefollowing form:

minimize f Fspð Þpred;W

� �

¼ A⋅F spð Þpred ¼ b

� �T

W A⋅F spð Þpred ¼ b

� �� ð8Þ

where W is a 9 × 9 weighting matrix of scalars only in thediagonal elements. These scalars emphasize or deempha-

size the contribution of the individual rows in Eq. 6 to thespinal contact force calculation.

A participant-specific W was determined through anoptimization procedure using the 5 sets of criterion standarddata. A nonlinear downhill simplex was used to evaluate theobjective function:

minimize f Fspð Þpred

� �¼ ∑ F spð Þ

meas

− Fspð Þpred

� �2ð9Þ

where |Fmeas(sp) | is the magnitude of the measured L3 spinal

contact force collected during the criterion standard trialsand |Fpred

(sp) | is the magnitude of the predicted L3 spinalcontact force. A total of 2400 iterations were used todetermineW. Convergence was confirmed when changes inthe objective function fell below 0.01.

Data AnalysisA 5-fold cross-validation technique was used on the

criterion standard trials from each participant to create theparticipant-specific weighting matrix used to predict L3contact force. To accomplish the 5-fold method, 50milliseconds surrounding the peak force in 4 of the 5 criterionstandard trials were simultaneously optimized using Eqs. 8and 9. The resulting W was used to predict the L3 contactforce on the remaining criterion standard trial for validation.17

This process (4 criterion standard then 1 validation) wasrepeated for every possible combination of the 5 criterionstandard trials (Fig 4). The W matrix that produced thesmallest error between predicted force and measured forcewas used to predict L3 contact force for the participant in theexperimental trials (therapeutic load, contact force unknown/not directly measured with load cell) using Eq. 8.

Predicted contact forces using CLS and WLS werecompared with the validation measurement to evaluate theerror of each approach. Bland-Altman plots were generatedfor visual comparison, and 95% limits of agreement werecalculated (mean difference ± 2 SDs).

Peak forces were compared across contact points (leftshoulder, thigh, and L3) using a 1-way repeated-measuresanalysis of variance, followed by pairwise comparisonsusing Tukey Honestly Significant Difference test. Peakforces at the L3 contact were compared across criterionstandard and experimental trials using a paired t test. Levelof significance was set at α = .05 for all statistical tests.

RESULTS

The mean absolute difference between the CLS-predicted force and the measured force was 621.0 ± 193.5N. The mean absolute difference between the WLS-predicted force and the measured force was −3.6 ± 9.1 N.The 95% limits of agreement, or the range in which 95% ofthe prediction errors occurred, were 234.0 to 1008.0 N forthe CLS and −21.9 to 14.7 N for the WLS.

Fig 4. Measured L3 force (◆) and predicted L3 force (○) from 1 participant showing 1 iteration of the k-fold cross-validation procedureThe weighting matrix, W, was optimized to minimize predictive error of L3 force in 4 criterion standard manipulations. L3 force from a fifthcriterion standard manipulation was used to validate the optimized W by comparing the predicted force with the measured force. This wasrepeated 5 times for each participant, and the W with the smallest error was used to predict L3 force in the experimental trials.


During both the criterion standard and experimentaltrials, the CLS overestimated contact forces with largervariance than the WLS (Fig 5).

Estimated peak force at L3 during the experimentaltrials was 88.4 ± 26.0 N greater than the peak forcemeasured during the criterion standard trials for all 5participants. In addition, within-participant variability wassmaller for the peak force delivered during the experi-mental trials (Table 1).

Significant analysis of variance (P = .009) indicateddifferences in peak forces across contact points. Pairwisecomparisons demonstrated that peak force at L3 wasgreater than peak force applied at the left shoulder, butwith no differences between peak forces at L3 and thethigh and between shoulder and thigh. Significant t test(P b .001) indicated that predicted peak forces at L3

.

during experimental trials were greater than predictedpeak forces at L3 during criterion standard trials (Fig 6).

DISCUSSION

Direct and indirect methods of contact force measure-ment were combined into a single mathematical framework.Using this framework, the accuracy and confidence ofpredicting L3 contact force using a CLS approach and WLSapproach were assessed during side-lying manipulation.Spinal contact forces produced during side-lying spinalmanipulation predicted using a WLS approach producedlower error when compared with a CLS approach. Inaddition, theWLS approachwas successfully used to predictthe L3 contact force during manipulation that closelymatched what would be performed in a clinical setting.

image of Fig�4

Fig 5. Bland-Altman plot of the CLS (▲) force prediction and the WLS (○) force prediction (top panel) and enlarged Bland-Altman plotfor the WLS force prediction only (bottom panel). This plot illustrates the average value of the measured force and the predicted force onthe horizontal axis and the difference of the predicted force and the measured force on the vertical axis (prediction error). The dashedline shows the average prediction error of the CLS, and the solid line shows the average error of the WLS. Shaded regions represent the95% limits of agreement for the 2 methods.

Table 1. Average peak force magnitudes (SD) measured at the force platform and the 3 contact points during experimental trialsat a therapeutic load

The L3 peak force magnitudes measured during the criterion standard trials are highlighted in gray.


Combining direct and indirect measurements intro-duces a novel framework to predict contact forces duringSMT while preserving clinically relevant contact between

practitioner and participant. For example, contact pointsat the shoulder and thigh, which remove tissue slack andstabilize the patient, have not been incorporated into

image of Fig�5

Unlabelled image

Fig 6. Average peak force magnitudes and SD measured at the 3contact points during the experimental trials. The L3 contact forcewas compared between the experimental and criterion standardtrials. *Significant difference.


force measurement during SMT. This approach alsoaccounts for the unique style of each practitioner byincorporating practitioner kinematics at the contact siteinto the force estimation.

Key characteristics of HVLA spinal manipulation (preloadforce and high rate of force application during thrust)9,15

were present when using the WLS approach, whereas theCLS approach did not demonstrate clear patterns containingthese characteristics. A peak contact force of 337.2 ± 66.9 Nduring the experimental trials was slightly lower thanprevious indirect measurement4 but falls within previouslyreported range (300-500 N) of using direct measurement.15

The WLS approach of force prediction may provide abetter understanding of how all SMT contact forcescontribute to patient outcomes during a complex therapy.It is common for the practitioner to stabilize the patient withone hand, thrust with the other hand, and exert a rotationaltorque with their body weight through their lowerextremity. However, force magnitude and direction atthese contact points have not been reported. An averagepeak force of 180.8 ± 52.9 N was delivered at the shoulder,267.3 ± 48.5 N at the thigh, and 337.2 ± 66.9 N at the L3spinal level. This is an interesting outcome considering thatthe thigh contact force is not different in magnitude than theL3 contact force, but the longer lever arm results in a muchgreater rotational moment about the spine. The therapeuticeffects of these differences warrant further investigation.

Manual therapy students may benefit from the dataproduced using this method as they learn and refine theirpractice of SMT. Peak force, peak moment, preload force,time to peak force, and rate of force production are allmeasures that have been used to assess changes in SMTperformance.20-24 However, this is primarily measured using

instrumented mannequins20-22,25 or, in cases when humanparticipants are used, with qualitative verbal and visualfeedback.26 The method developed in this investigationprovides multiple sources of quantitative feedback on forceapplication while maintaining relevant clinical contact. Inaddition to helping train students to produce consistent forceapplication, interacting with these data may also increaseunderstanding of SMT biomechanics and ultimately lead tobetter treatment planning and application of SMT.

LimitationsThe purpose of this investigation was to provide a proof of

concept for novel spinal manipulative force prediction, andseveral limitations currently prevent deployment of thisframework in settings outside a research laboratory. First,instrumenting the practitioner with load cells may alter theforce application when compared with a normal clinicenvironment. Future study could reduce this limitation throughalternate methods of force instrumentation that provides moredirect contact with the participant. Second, the magnitude ofthe force delivered during the criterion standard trials and usedto develop the predictive algorithm was lower than the forceapplied during the experimental trials. Lower force applicationwas necessary to minimize potential patient discomfort thatwould occur if large therapeutic loadswere applied through thecontact surface of the load cell. Therefore, prediction error ispossible at the higher force levels applied in the experimentaltrials. However, training the algorithm on a wide range offorces (average variability of 45.1 N) in the criterion standardtrials helps to minimize prediction error at these larger forces.Third, the motion capture hardware used to measurepractitioner kinematicsmay be both cost and space prohibitive.Although the encumbrances in each of these factors aresteadily declining with technological advances, these items areunavailable in many research and education settings. Last, thisframework was developed and tested only on HVLAmanipulation in a side-lying position. As measurementhardware becomesmore accessible and thesemethods undergofurther refinement, these limitations will be reduced, makingcombined measurement available in settings outside theresearch laboratory.

Future StudiesFuture investigations will examine the general appli-

cation of this framework to other SMT methods andtreatment locations. In addition, the relationship betweenforce application and clinical outcomes can be betterestablished with accurate measurement of spinal manip-ulative forces. We anticipate that combining these forceestimation methods with assessment of muscle activityand pain in patients with and without low back painwill lead to a better understanding of the underliningmechanisms of SMT.

image of Fig�6


CONCLUSION

In summary, we present a novel method to predict spinalcontact force that combines direct and indirect measure-ments into a single framework that preserves clinicallyrelevant contact points. The WLS approach produced anacceptably low error when predicting the force appliedduring a side-lying manipulation. With further advances ininstrumentation and computational refinement, we antici-pate that this method will enable advanced training methodsand high-quality research on mechanisms of SMT.

Practical Applications

• By combining direct and indirect force measure-ments into an optimized framework, multiplesources of information on force application areused while maintaining relevant clinical contact.

• These methods can be used to train clinicians andstudents to produce consistent force application.

• Interacting with these data may also increaseunderstanding of SMT biomechanics, and ulti-mately leading to better treatment planning andapplication of SMT.

ACKNOWLEDGMENT

The authors thank Andrea Wanamaker for her assistancein designing and fabricating the instrumentation necessaryto perform this investigation.

FUNDING SOURCES AND POTENTIAL CONFLICTS OF INTEREST

This project was supported byAwardNo. R00AT004983-03 (to B.S.D.) from the National Institutes of Health(National Center for Complementary and Alternative Med-icine). The content is solely the responsibility of the authorsand does not necessarily represent the official views of theNCCAM or the National Institutes of Health. No conflicts ofinterest were reported for this study.

REFERENCES

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