ACCRAC AWARD WINNING PAPER
EFFECT OF SAMPLING RATES ON THE QUANTIFICATION OF
FORCES, DURATIONS, AND RATES OF LOADING OF
SIMULATED SIDE POSTURE HIGH-VELOCITY, LOW-
AMPLITUDE LUMBAR SPINE MANIPULATION☆
Maruti Ram Gudavalli, PhD,aJames DeVocht, DC, PhD,aAli Tayh, BS,band Ting Xia, PhDc
Objective: Quantification of chiropractic high-velocity, low-amplitude spinal manipulation (HVLA-SM) may require
biomechanical equipment capable of sampling data at high rates. However, there are few studies reported in the literature
regarding the minimal sampling rate required to record the HVLA-SM force-time profile data accurately and precisely.
The purpose of this study was to investigate the effect of different sampling rates on the quantification of forces,
durations, and rates of loading of simulated side posture lumbar spine HVLA-SM delivered by doctors of chiropractic.
Methods: Five doctors of chiropractic (DCs) and 5 asymptomatic participants were recruited for this study. Force-
time profiles were recorded during (i) 52 simulated HVLA-SM thrusts to a force transducer placed on a force plate by
2 DCs and (ii) 12 lumbar side posture HVLA-SM on 5 participants by 3 DCs. Data sampling rate of the force plate
remained the same at 1000 Hz, whereas the sampling rate of the force transducer varied at 50, 100, 200, and 500 Hz.
The data were reduced using custom-written MATLAB (Mathworks, Inc, Natick, MA) and MathCad (version 15;
Parametric Technologies, Natick, MA) programs and analyzed descriptively.
Results: The average differences in the computed durations and rates of loading are smaller than 5% between 50 and
1000 Hz sampling rates. The differences in the computed preloads and peak loads are smaller than 3%.
Conclusions: The small differences observed in the characteristics of force-time profiles of simulated manual HVLA-
SM thrusts measured using various sampling rates suggest that a sampling rate as low as 50 to 100 Hz may be
sufficient. The results are applicable to the manipulation performed in this study: manual side posture lumbar spine
HVLA-SM. (J Manipulative Physiol Ther 2013;36:261-266)
Key Indexing Terms: Biomechanics; Manipulation, Spinal; Chiropractic; Manual Therapy
diversified or Gonstead style lumbar, lumbosacral, or
sacroiliac joint chiropractic manipulation/adjustment). Par-
ticipants are placed in a lateral recumbent or side-lying
position, with the superior or free hip and knee flexed and
adducted across the midline. The lumbar spine and pelvis
remained in a neutral position, approximately perpendicular
to the adjusting table surface. A quick, short controlled
movement of the clinician's shoulder, arm, and hand
combined with a slight body drop provide the single impulse
load or thrust to the contact point. Because spinal
of the associated force-time characteristics is important.1-3
Forces applied by doctors to patients can be measured
directly using a force transducer at the doctor/patient
interface (eg, hand to spine).4-12The forces measured are
referred to as applied or contact forces. Van Zoest et al13,14
igh-velocity, low-amplitude spinal manipulation
(HVLA-SM) is a commonly used procedure in
chiropractic practice (eg, also known as side-lying
aAssociate Professor, Palmer Center for Chiropractic Research,
bDesign Engineer, Vizient LLC, Bettendorf, Iowa.
cAssistant Professor, Palmer Center for Chiropractic Research,
☆This is an open-access article distributed under the terms of
the Creative Commons Attribution-NonCommercial-ShareAlike
License, which permits non-commercial use, distribution, and
reproduction in any medium, provided the original author and
source are credited.
Submit requests for reprint to Maruti Ram Gudavalli, PhD,
Associate Professor, Palmer Center for Chiropractic Research, 741
Brady St, Davenport, IA 52803
Paper submitted April 26, 2012; in revised form December 21,
2012; accepted January 18, 2013.
Copyright © 2013 The Authors. Published by Elsevier Inc. All
described a measurement method to quantify the 3-
dimensional forces at the doctor/patient interface using
3-dimensional force transducers and found, in addition to
normal forces, shear forces occurred during thoracic and
lumbar manipulations. The forces transmitted to patients
can also be measured with force plates placed underneath
the patients.15-20These forces are referred to as transmitted
forces or loads. Triano and Schultz15reported on the
transmitted loads to the lumbar spine using a force plate
embedded in the chiropractic table and estimating the
loads in the lumbar spine using inverse dynamics approach
and reported large shear loads and moment loads.
Furthermore, a flexible pressure mat has been used to
measure contact forces at the doctor/patient interface in the
thoracic, cervical, and lumbosacral regions. Herzog et
al,4,12Forand et al,6Hessell et al,8Suter et al,9Kawchuk
and Herzog,11and Kirstukas and Backman10measured
doctor/patient contact forces during thoracic HVLA-SM
using a pressure resistance film and reported very large
normal forces with high rate of loading. Only the normal
component of the contact force can be obtained when
using pressure pads or pressure resistance film-type
devices. These reported investigations help advance our
understanding of the magnitude of force during preload
phase and thrusting phase, duration of the manipulation,
rate of loading, and contact area in thoracic and lumbar
High-velocity, low-amplitude spinal manipulation is a
dynamic event that involves delivery of forces at a high
speed in a short duration in the order of 100 to 500
milliseconds. Some investigators have measured the force-
time profiles at the contact hand at a relatively low sampling
frequency of 50 to 100 Hz,7-10whereas others21,22have
measured at a higher sampling rate of 300 to 1000
Hz19,21,22or 2500 to 5000 Hz.23,24However, to the best
of our knowledge, there is little information available
regarding the effect of sampling rate on capturing the force-
time characteristics of HVLA-SM. A study reported by
Hori et al25on the measurement of peak force, power, and
velocity during jumping concluded that up to 100 Hz
sampling rates the differences are small, whereas sampling
rates of 50 and 25 Hz could lead to differences of up to
13%. Because the HVLA-SM delivering speed is similar to
the speed in jumping, it is possible that the sampling rate
may also affect the accuracy of capturing HVLA-SM force-
The objectives of this study were to determine the
minimal sampling rate required to accurately quantify the
force-time characteristics of HVLA-SM, including preload
and peak forces, duration of loading, duration of unloading,
total duration, and rates of loading and unloading and to
quantify the differences in those characteristics when data
were collected at different sampling rates, whereas HVLA-
SM–type thrusts were repeatedly delivered to a force
transducer by experienced doctors of chiropractic (DCs).
Experienced chiropractic clinicians were recruited to
deliver the simulated high-velocity, low-amplitude (HVLA)
thrusts. This study was approved by the Palmer College of
Chiropractic Institutional Review Board. All participants
provided signed informed consent documents.
Experiment 1. Force-time profiles were recorded when 2
clinicians (1 male DC with 23 years of experience and 1
female DC with 31 years of experience) delivered simulated
HVLA thrusts to a miniature force transducer (Model no.
mini45; ATI Industrial Automation, Apex, NC) placed on
the top of a force plate (Model no. 4060-NC; Bertec, Inc,
Columbus, OH). The transducer has a diameter of 45 mm, a
thickness of 15.7 mm, and a contact surface of 15.9 cm2.
Both the force plate and the force transducer are capable of
measuring 3-dimensional forces and moments. Figure 1
depicts a doctor performing a thrust on the force transducer,
which was placed directly on the force plate. Data
recordings were made using Motion Monitor software
with a 16-bit analog-to-digital data acquisition system
(Innovative Sports Training, Inc, Chicago, IL). To investi-
gatetheeffect ofsamplingrate onforce-time characteristics,
the sampling rate of the force plate remained same at 1000
Hz, whereas the sampling rate of the force transducer was
variedat50,100,200, and500Hz.Datacollectedfrom both
force plate and force transducer were exported to ASCII
formatted text files for further data reduction and analysis.
Experiment 2. Three male DCs with an average of 14 (range
12–15) years of experience and 5 asymptomatic participants
were recruited for this study. Upon physical examination, the
contraindication to spinal manipulation. Participants were
included if examination indicated the need for spinal
manipulation. Each DC performed side posture HVLA-SM
Fig 1. A photograph showing the force transducer, force plate,
and the doctor's hand position for delivering simulated HVLA
thrusts. (Color version of figure is available online.)
Journal of Manipulative and Physiological TherapeuticsGudavalli et al
Manipulation Force Time CharacteristicsJune 2013
in between for each participant to receive spinal manipula-
tions. During this experiment, the 3-dimensional force
transducer was placed between the doctor's hand and the
participant's back. Standard side posture treatment table was
used for this study. Force-time profile data were collected
these data, we used the resampling function in MathCad
(version 15; Parametric Technologies, Natick, MA) to
recreate force-time profiles at frequencies of 50, 100, 200,
and 500 Hz to mimic data collection at lower sampling rates.
Forthe first experiment, the doctors delivered a total of52
custom-developed programs in MATLAB (Mathworks, Inc,
Natick, MA). Force-time profile plots were generated from
the raw data. For the second experiment, we obtained 60
force-time profiles (12 from data collection and 48 from
examiners identifiedthe preloadphase andthe beginning and
end of the thrust using visual inspection. Preload and peak
load amplitude, durations of loading and unloading, and rate
of loading and unloading as well as power spectrum density
were computed using MATLAB and MathCAD programs.
These parameters are defined in a manner similar to what has
beendescribed byHerzogetal,4Triano etal,18,20and Cohen
et al.17The magnitude of preload, magnitude of peak load,
time topeakload,average rateofloading,andaverage rateof
unloading were then calculated.
We performed descriptive analyses on the preload, peak
load, duration of thrust loading, duration of unloading, rate
of loading, and rate of unloading. The differences in these
values as computed using data collected at 50, 100, 200,
and 500 Hz by the force transducer against the data
collected at 1000 Hz by the force plate. The percentages of
those differences were also calculated.
Figure 2 shows a typical graph of force-time profile
collected at 50 and 1000 Hz sampling rates. The descriptive
statistics (mean ± SD) for the force-time profiles from the
first experiment of 52 simulated spinal manipulations are
preload force at 94.4 ± 71.7 N, peak normal force at 432.5 ±
122.8 N, duration of loading at 154 ± 70 milliseconds, rate
of loading at 2692 ± 1633 N/s, duration of unload at 420 ±
257 milliseconds, rate of unloading at 1567 ± 1334 N/s, and
duration of thrust at 574 ± 260 milliseconds, respectively.
The descriptive statistics for the force-time profiles based
on the second experiment of 12 HVLA-SM on asymptom-
atic participants are preload force 106.3 ± 55.5 N, peak
force at 327.6 ± 90.7 N, duration of loading at 261 ± 163
milliseconds, rate of loading at 1077.6 ± 571.9.2 N/s,
duration of unload at 509 ± 143 milliseconds, rate of
unloading at 683.3 ± 259.4 N/s, and total duration of thrust
at 770 ± 212 milliseconds, respectively.
Figure 3 shows a typical power spectral graph of a force-
time data during HVLA-SM. The maximum meaningful
frequency was defined as the highest frequency with power
density above the background white noise, for example, the
manipulations, the maximum power occurred at a mean
frequency of 3.34 Hz (minimum, 1 Hz; maximum, 12 Hz)
and the frequency where the power has reacheda plateau had
a mean value of26 Hz(minimum, 16 Hz; maximum,41 Hz).
Tables 1 and 2 summarizes the differences in preload,
peak load, durations of loading and unloading, total
duration, and rates of loading and unloading when
normalized to these characteristics determined at 1000 Hz.
The thrusts that were quantified in experiment 1 of the
present study were simulations of HVLA-SM delivered by
pressing on a force transducer. The simulations are
reasonable as their force-time profile characteristics includ-
ing preload and peak forces, durations, and rates of loading
values are in the range reported in the literature for the
thoracic, lumbar, and sacroiliac HVLA-SM4,15,21,6,26,14,22
and experiment 2 of the present study.
Biomechanics researchers are aware that the recom-
mended sampling rates are at least twice the Nyquist
frequency.27If sampled at a rate that is too low, it is possible
to miss important information. For example, the character-
Fig 2. A graph of typical force-time profile for data sampled at 50
and 1000 Hz.
Gudavalli et al Journal of Manipulative and Physiological Therapeutics
Volume 36, Number 5 Manipulation Force Time Characteristics
of data occupying excessive storage and requiring more
cumbersome data processing and reduction. Therefore,
recommended sampling frequencies for walking are 50 to
100 Hz for motion capture, running and sprinting at 100 to
200 Hz, javelin throw at 200 to 300 Hz, 1000 Hz for ground
reaction force data collection.27The recommendation for
electromyographic data sampling frequencies are 1000 Hz or
higher.27The power spectral density analysis on HVLA-SM
at an average frequency of 26 Hz, indicating that, in theory, a
sampling rate of 52 or above may provide adequate
information about the HVLA-SM force-time characteristics.
From the data we obtained in sampling at different
frequencies, the mean differences are smaller than 5% in
durations and rates of loading for all lower frequencies
compared with those at 1000 Hz. The differences in the
magnitudes of the loads are smaller than 3%. This suggests
that data acquisition at the lower frequencies examined in
the present work does not substantially reduce the accuracy
of measurement. However, we observed larger SDs at lower
frequencies, indicating that the accuracy of results may
degrade if sample size is too small.
This study provides information that was not previously
available as to how sampling frequency influences the
measurement of force-time profile characteristics of manual
therapy techniques such as HVLA-SM. For example, some
the order of only 50 to 100 Hz. Based on the findings of this
study, this equipment may be used without loss of accuracy.
This will allow researchers the confidence to apply these
sensors with lower sampling rate in their studies, while
taking advantage of the pliable nature of these devices that
make themmoresuitableformeasurement betweendoctor's
hand and the participant's spine. Other equipment such as
force sensors and force plates has the capacity to sample at
for some applications. However, in some applications such
higher frequencies may not provide better accuracy and yet
would produce excessive volume of data and consequently
increase the data processing time and cost.
The results from this study are useful for researchers and
clinicians and to understand the force-time profile charac-
teristics collected at various sampling rates during manual
HVLA side posture spinal manipulations. Knowledge that
Fig 3. Power spectrum density of a representative dataset collected at 1000 Hz with power in logarithm scale.
Table 1. Percentage differences of measured force-time profile characteristics using the force plate at 1000 Hz and those using the
force transducers at 50, 100, 200, and 500 Hz
50 Hz (n = 20) 100 Hz (n = 12) 200 Hz (n = 10) 500 Hz (n = 10)
MeanSD MeanSD MeanSDMeanSD
Duration of load
Duration of unload
Rate of load
Rate of unload
Journal of Manipulative and Physiological TherapeuticsGudavalli et al
Manipulation Force Time CharacteristicsJune 2013
smaller sampling frequencies give reasonably accurate
results can be useful to select the equipment for measuring
forces and design future studies. This implies that training
of students and clinicians can be done using low sampling
rate force-measuring equipment that is more pliable and,
therefore, causes less interference with their normal
delivery of the thrust.
The findings in this study relate to the specific
techniques used by the 3 DCs and, therefore, cannot be
extrapolated to other manipulation techniques or other
practitioners. As well, the patients were not symptomatic,
and therefore, force applied in the treatment setting may be
different. These experiments are based on the doctor's
delivering on force transducers as well as side posture
lumbar HVLA-SM on asymptomatic participants. This
study was not intended to characterize treatment techniques
delivered through impulse adjusting instruments28,29that
deliver much quicker thrusts than manually delivered
thrusts. Chiropractic techniques using treatment tables
with drop mechanism may also have different characteris-
tics requiring a higher sampling rate.
In addition, different regions of spine may have different
compliance characteristics; thus, forces from this study (eg,
to the lumbar spine) may not be similar to other areas of the
body (eg, cervical/thoracic spine, upper/lower extremities).
The current study only mimicked the lumbar HVLA-SM.
Caution is needed when attempting to generalize the
findings of this study to manual treatment on other body
regions. Furthermore, this study only evaluated the normal
component of the force-time profile characteristics, whereas
shear components were not. Therefore, further studies are
needed to address these limitations.
Small differences were observed in the characteristics of
force-time profiles of simulated and actual side posture,
HVLA lumbar spine manipulation thrusts measured using
various sampling rates. This suggests that a sampling rate as
low as 50 to 100 Hz may be adequate to describe these
FUNDING SOURCES AND POTENTIAL CONFLICTS OF INTEREST
with support from Research Facilities Improvement Pro-
gram Grant number C06 RR15433-01 from the National
Center for Research Resources, National Institutes of
Health. No conflicts of interest were reported for this study.
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Table 2. Percentage differences of side posture, HVLA lumbar spine manipulation characteristics measured at 1000 Hz and those
resampled at lower frequencies
50 Hz (n = 12) 100 Hz (n = 12) 200 Hz (n = 12)500 Hz (n = 12)
Mean SDMeanSDMean SDMean SD
Duration of load
Duration of unload
Rate of load
Rate of unload
• This study demonstrates that sampling rates
of 50 to 100 Hz for measurement of HVLA-
SMs performed by DCs. The differences in
force-time characteristics are smaller than 5%
of 1000 Hz sampling rates.
Gudavalli et alJournal of Manipulative and Physiological Therapeutics
Volume 36, Number 5Manipulation Force Time Characteristics