![Measured forces during a 20-second myofascial release technique applied to fascia lata ([A] applied normal force, [B] applied shear force) and plantar fascia ([C] applied normal force, [D] applied shear force).](https://www.researchgate.net/profile/Thomas-Findley/publication/23190316/figure/fig4/AS:11431281122690493@1677516637289/Measured-forces-during-a-20-second-myofascial-release-technique-applied-to-fascia-lata_Q320.jpg)
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JAOA • Vol 108 • No 8 • August 2008 • 379Chaudhry et al • Original Contribution
Context: Although mathematical models have been devel-
oped for the bony movement occurring during chiropractic
manipulation, such models are not available for soft tissue
motion.
Objective: To develop a three-dimensional mathematical
model for exploring the relationship between mechanical forces
and deformation of human fasciae in manual therapy using a
finite deformation theory.
Methods: The predicted stresses required to produce plastic
deformation were evaluated for a volunteer subject’s fascia
lata, plantar fascia, and superficial nasal fascia. These stresses
were then compared with previous experimental findings for
plastic deformation in dense connective tissues. Using the three-
dimensional mathematical model, the authors determined the
changing amounts of compression and shear produced in fas-
cial tissue during 20 seconds of manual therapy.
Results: The three-dimensional model’s equations revealed
that very large forces, outside the normal physiologic range,
are required to produce even 1% compression and 1% shear
in fascia lata and plantar fascia. Such large forces are not
required to produce substantial compression and shear in
superficial nasal fascia, however.
Conclusion: The palpable sensations of tissue release that
are often reported by osteopathic physicians and other manual
therapists cannot be due to deformations produced in the
firm tissues of plantar fascia and fascia lata. However, palpable
tissue release could result from deformation in softer tissues,
such as superficial nasal fascia.
J Am Osteopath Assoc. 2008;108:379-390
F
ascia is dense fibrous connective tissue that connects mus-
cles, bones, and organs, forming a continuous network of
tissue throughout the body. It plays an important role in
transmitting mechanical forces during changes in human
posture. Several forms of manual fascial therapies—including
myofascial release and certain other techniques in osteo-
pathic manipulative treatment (OMT)—have been devel-
oped to improve postural alignment and other expressions
of musculoskeletal dynamics.1,2 The purpose of these thera-
pies and treatments is to alter the mechanical properties of
fascia, such as density, stiffness, and viscosity, so that the
fascia can more readily adapt to physical stresses.3,4 In fact,
some osteopathic physicians and manual therapists report
local tissue release after the application of a slow manual
force to tight fascial areas.2,4,5 These reports have been
explained as a breaking of fascial cross-links, a transition
from gel to sol state in the extracellular matrix, and other
passive viscoelastic changes of fasciae.2,4,5
The question of whether the applied force and duration
of a given manual technique (eg, myofascial) could be sufficient
to induce palpable viscoelastic changes in human fasciae is
unresolved, with some authors1,5,6 supporting the likelihood
of such an effect and others7,8 arguing against it.
Our intent in undertaking the present study was to resolve
this question. Therefore, we present an original mathematical
model to determine if forces applied in manual therapy are suf-
ficient to produce tissue deformation in human fasciae.
Background
The mechanical properties of ex vivo rat superficial fascia
(ie, subcutaneous tissue) under uniaxial tension have been
reported by Iatridis et al,9who investigated the potential
importance of uniaxial tension in a variety of therapies
involving mechanical stretch. The mechanical properties of
in vitro human superficial nasal fascia and nasal periosteum
were investigated by Zeng et al10 to determine under which
tissue layer silicon implants should be inserted for improved
results in aesthetic surgical corrections of congenital saddle
nose and flat nose. Similarly, the mechanical properties of
in vitro fascia lata and plantar fascia have been investigated by
Wright and Rennels.11 The results of each of these studies of
fascial mechanical properties can be used in determining the
types and strengths of mechanical forces needed to produce
desired deformations during manual therapy.
Three-Dimensional Mathematical Model for Deformation
of Human Fasciae in Manual Therapy
Hans Chaudhry, PhD; Robert Schleip, MA; Zhiming Ji, PhD; Bruce Bukiet, PhD;
Miriam Maney, MS; and Thomas Findley, MD, PhD
From the departments of Biomedical Engineering (Drs Chaudhry and Findley),
Mechanical Engineering (Dr Ji), and Mathematical Sciences (Dr Bukiet) at
the New Jersey Institute of Technology in Newark; the Department of Applied
Physiology at Ulm University in Germany (Mr Schleip); and the War-Related
Illness and Injury Study Center at the Veterans Affairs Medical Center in East
Orange, NJ (Drs Chaudhry and Findley, Ms Maney).
This study was partially supported by a dissertation grant from the Inter-
national Society of Biomechanics to Mr Schleip’s Fascia Research Project.
Address correspondence to Zhiming Ji, PhD, Department of Mechanical
Engineering, New Jersey Institute of Technology, Newark, NJ 07102-1982.
E-mail: ji@njit.edu
Submitted March 23, 2006; revision received June 20, 2006; accepted August
10, 2006.
ORIGINAL CONTRIBUTION
380 • JAOA • Vol 108 • No 8 • August 2008
In recommending further study of manual therapies,
Threlkeld7noted that the three-dimensional dispersion of
forces in relatively intact regions of the human body had yet
to be investigated. Although mathematical models have since
been developed for the bony movement resulting from applied
forces in chiropractic high-velocity manipulations with human
subjects,12-15 no such attempts have yet been made—to our
knowledge—for other manual therapies, including OMT.
This lack of a mathematical model motivated us to model
the relationship between mechanical forces and deformation
of human fasciae during manual therapy. We believe that this
new mathematical model may be useful in future calculations
of the forces required to induce desired plastic tissue defor-
mations in a manual therapeutic context, including in such
osteopathic manipulative procedures as soft tissue techniques
and fascial-ligamentous release.
Methods
Because fasciae are known to experience finite strain,10 we
used a finite deformation theory of elasticity16 to develop our
three-dimensional model for exploring the relationship between
mechanical forces applied on the surfaces of human fascia in
manual therapy and the resulting deformation of the fascia. In
continuum mechanics, finite deformation theory is used when
the deformation of a body is sufficiently large to overcome
the assumptions inherent in small strain theory.16 This is com-
monly the case with elastomers and other fluids and biolog-
ical soft tissue.16
We then applied this model to manual therapy in a lab-
oratory setting to evaluate the mechanical forces needed to
produce specific types of deformation in fascia lata, plantar
fascia, and superficial nasal fascia. We used previously reported
longitudinal stress-strain data10,11 in the application of our
model.
The inclusion of superficial nasal fascia, which is much
softer tissue than fascia lata and plantar fascia, allowed us to
test whether our model equations could predict significant
compression and shear in pliable tissue compared with stiff
tissue. The present study was conducted with the approval of
the Institutional Review Board at the Veterans Affairs Medical
Center in East Orange, NJ.
New Mathematical Model
Our three-dimensional model (Figure 1) allowed us to deter-
mine the mechanical forces applied on the surfaces of fascia that
result in particular types of deformation. Because of the lack
of more specific data on the structure of superficial nasal fascia
and its mechanical properties, we assumed for the purpose of
this first mathematical model that this fascia was isotropic.
We also followed the assumption that fascia lata, plantar fascia,
and superficial nasal fascia are composed of incompressible
material,10 as are most soft biological tissues.
The basic kinematics and kinetics equations used to eval-
uate the stresses under specified deformations are presented
below and in subsequent pages in equations (1-4, 10, 12, 13).16
The stress results from these equations were required to sat-
isfy differential equations of equilibrium and boundary con-
ditions, which in turn allowed us to determine the mechanical
forces needed to produce the specified deformations.
The metric tensors gij and gij in the Cartesian coordinates
xi(i= 1, 2, 3) in the undeformed state are given by the fol-
lowing:
xrxrxi xj
(1) gij =
––– ––– ,
gij =
–––
–––, (r= 1, 2, 3; i, j = 1, 2, 3)
xixjxrxr
The repeated index, r, in equation (1) means summation over
r.
Similarly, the metric tensors Gij and Gij in the deformed-
state Cartesian coordinates yr(r= 1, 2, 3) are given by the fol-
lowing:
yryryi yj
(2) Gij =
––––––– ,
Gij =
–––––––
, (r= 1, 2, 3; i, j = 1, 2, 3)
yiyjyryr
From equation (1), we find that:
(3) gij = gij = ij (Kronecker delta), g= gij
In equation (3), gij is the determinant of the matrix gij. Thus,
g= 1.
The metric tensors defined in the equations presented
above are the measures of fascial deformation in three dimen-
sions—when the fascia are subjected to normal, longitudinal,
and tangential forces. The physical meaning of these tensors
can be understood by their relation to the strain Eij in the fol-
lowing equation:
Gij _ gij
(4) Eij =
———
2
䡲Deformation of Fasciae—We assumed the manipulation-
caused fascial deformations of shear and elongation along the
x1-axis, extension along the x2-axis, and compression along
the negative x3-axis (Figure 1) to be given by the following:
(5) y1= x1+ k1x3+ k4x1, y2= k2x2, y3= k3x3,
(k3< 1, k1, k2, k4> 0)
In equation (5), the yi-axes in the deformed state of the fascia
coincide with the xi-axes in the undeformed state of the fascia.
Also in equation (5), k1denotes the shear ratio due to the
application of the tangential force. The maximum shear occurs
at the surface of the fascia, where the fascial thickness is at its
maximum. The shear is zero at the bottom of the fascia, where
fascial thickness is zero. In addition, k4is the extension ratio due
to the applied longitudinal force, k3denotes the compression
Chaudhry et al • Original Contribution
ORIGINAL CONTRIBUTION
JAOA • Vol 108 • No 8 • August 2008 • 381
The strain invariants I1, I2, and I3(which are needed to eval-
uate stresses) are given by the following:
G
(8) I1= grsGrs , I2= grsGrs, I3= —
g
In equation (8), Gis the determinant of the matrix Gij, while G
from equation (6) is: k22[(1 + k4)2k32]. The invariants in equa-
tion (8) are invariants in strain that do not change with the coor-
dinate system.
Using equations (3) and (6) through (8), we get the fol-
lowing:
(k32+ k12)11
(9) I1= k12+ k32+ k22+ (1 + k4)2; I2= ———— + — + — ;
(1 + k4)2 k32k22k23
G
I3= — = k22 [(1 + k4)2 k32]
g
Because the fasciae are assumed to be incompressible, we
have:
1
I3= 1, thus, k2= ————
k3(1 + k4)
To determine the tensor Bij (which is needed to evaluate
stresses), we can use the following equation:
(10) Bij = I1gij – girgjsGrs
ratio due to the applied normal pressure, and k2is the exten-
sion ratio resulting from the compression caused by manual
therapy on the surface of the fascia.
Typically, in OMT and other forms of manual therapy,
compression and shear are applied to most fasciae. However,
in some cases, such as with fascia lata, extension is also applied,
such as by bending the lower leg at the knee. It should be
noted that smaller values of k3mean more compression. For
example, k3= 0.90 means 10% compression. The values for k2
can be determined in terms of k3and k4using the incom-
pressibility condition described in equations (9) through (11).
Thus, using equations (2) and (5), we get the following (in
which zero represents the value of the corresponding tensor
elements):
(1 + k4)20 k1(1 + k4)
(6) Gij = 0 k220
k1(1 + k4) 0 k12+ k32
(k32+ k12)–k1
———— 0 ————
k32(1 + k4)2k32(1 + k4)
(7) Gij =1
0 —— 0
k22
–k11
———— 0 ——
(1 + k4)k32k32
Chaudhry et al • Original Contribution
ORIGINAL CONTRIBUTION
Normal Force
x2,y2
x1,y1
x3,y3
Face ADFE: x1=0
Face BCGH: x1=a
Face ABHE: x2=-b
Face DCGF: x2=b
Face EFGH: x3=0
Face ABCD: x3=c
AB
C
D
E
FG
H
O
Longitudinal
Force
Tangential
Force
Figure 1. Three-dimensional model of fascial element subjected to
normal, tangential, and longitudinal forces in the undeformed state.
The axes (x1, x2, x3) in the undeformed state coincide with the axes (y1,
y2, y3) in the deformed state. The six faces of this modeled fascial ele-
ment are designated with capital letters. The symbols a, b, and crep-
resent the coordinate values of the faces along the x1, x2, and x3axes.
382 • JAOA • Vol 108 • No 8 • August 2008
Therefore, using equations (3), (7), and (10), we obtain:
k12+ k22+ k320 –k1(1 + k4)
(11) Bij = 0 k12+ k32+ (1 + k4)20
–k1(1 + k4) 0 k22+ (1 + k4)2
䡲Stress Evaluation—The stresses placed on fascia can be
evaluated by using the following equation13:
(12) ij = gij + Bij + pGij
In equation (12), we note the following:
WWW
(13) = 2 —, = 2 —, p= 2 —
I1I2I3
In equation (13), Wis the strain energy function.
In our mathematical model, we used the form of the strain
energy function for isotropic soft tissues described by
Demiray.17 This function is given by:
(14) W= C1[eC2(I1–3)– 1]
In equation (14), C1and C2are mechanical parameters to be
determined, with C1analogous to the modulus of elasticity and
C2a dimensionless constant. These parameters are both anal-
ogous to the elastic parameters in the small deformation theory
of elasticity.16 The values of these parameters can be deter-
mined by curve fitting, as explained in “Estimation of Mechan-
ical Constants” on page 383. In equation (14), e= 2.71828,
which is the base of an exponential function.
Using equations (3), (5), (11), and (12), we find that the
stresses are given by the following set of equations (with the
superscripts after representing indices in the tensor nota-
tion):
(k32+ k12)
11 = + (k12+ k22+ k32) + p—————
k32(1 + k4)2
1
22 = + k12+ k32+ (1 + k4)2+ p(——)
k22
p
(15) 33 = + k22+ (1 + k4)2+ ——
k32
12 = 21 = 0
23 = 32 = 0
pk1
13 = 31 = –[k1(1 + k4)] – ————
k32(1 + k4)
In these equations, pis a scalar invariant denoting the pressure
used for incompressibility constraint.
䡲Equations of Equilibrium—It should be noted that all of
the stresses in our mathematical model are constants. There-
fore, the equations of equilibrium in Cartesian coordinates
are satisfied because pis a constant in the following:
p p p
—— = —— = —— = 0
y1y2y3
To determine the value of p, we used our model to make the
normal stress (33) vanish when there is no deformation
(ie, when k1= k4= 0 and k3= k2= 1). Then, we find that p= –(
+ 2). Substituting this value of pin the equations for other
stresses in (15), the stresses then reduce to the following:
k32+ k12(k32+ k12)
11 = 1- ————— +k12+ k22+ k32- 2 ————
k32(1 + k4)2k32(1 + k4)2
12
22 = 1- —— +k12+ k32+ (1 + k4)2- ——
k22k22
12
(16) 33 = (1- —— )+(1 + k4)2+ k22- ——
k32 k32
k12k1
13 = 31 = ———— + ———— - k1 (1+k4)
k32(1 + k4) k32(1 + k4)
12 = 21 = 23 = 32 = 0
For the stresses in equation (16), the following should be noted:
1
k2= ————
k3(1 + k4)
䡲Boundary Conditions (Formulae for Applied Forces)—We
next determined the surface forces placed by manual therapy
on the fascial faces that were initially located (ie, located before
deformation) at x1= a, x2= b, and x3= c(Figure 1). All the fas-
cial faces become curved in the deformed state during manual
therapy, so the directions of the unit normal to these faces (ie,
the vectors perpendicular to the faces) change.
For the face that was initially located at x1= a, the unit
normal vector →
in the deformed state is given by the following:
→
→ G1
= ———
G11
In the above equation, G1is the contravariant base vector.
Chaudhry et al • Original Contribution
ORIGINAL CONTRIBUTION
→
JAOA • Vol 108 • No 8 • August 2008 • 383
On the face that was initially located at x3= c(Figure 1), the
applied normal force (N) can be evaluated as the following:
(19) N= k3233 = (k32– 1)+ [k22k32+ (1 + k4)2k32– 2]
Because k3<1, the force in equation (19) is compressive, as
would be expected. The applied tangential force (T) along
B’C’ is zero throughout the duration of manual therapy,
whereas the applied tangential force along C’D’, which is ini-
tially CD (Figure 1), on the x3= cface can be evaluated as:
k3
(20) T= ——— [31(1 + k4)2+ 33(1 + k4)k1] = k1k3+ k1k3k22
1 + k4
The applied normal and tangential forces, as well as the exten-
sion force, must vanish if there is no shear, extension, and
compression (ie, k1= k4= 0 and k3= 1). Equations (19) and
(20) confirm this assumption.
Using equations (13) and (14), we arrive at the following:
(21) = 2C1C2eC2(I1–3) and = 0
Thus, by using equations (19) and (21), the normal pressure (N)
is reduced according to:
(22) N= 2 (k32– 1)C1C2eC2(I1–3)
From equations (20) and (21), we see that the tangential force
(T) along CD becomes:
(23) T= 2k1k3C1C2eC2(I1–3)
Using equation (18), the extension force (F) becomes:
k32(1 + k4)2
(24) F= 2C1C2eC2(11–3) ————— – 1
k32+ k12
Equations (22) through (24) are the formulae for deter-
mining the applied forces (ie, normal, tangential, and extension)
during manual therapy (Figure 1). Using specified values of k1
through k4and the mechanical constants (C1and C2), we can
determine the applied forces (N, T, and F) from the above
equations of our mathematical model. Conversely, if the values
of applied forces are known, we can use the equations to deter-
mine the values of k1through k4.
Estimation of Mechanical Constants
In estimating the mechanical constants, C1and C2, for fasciae
in the above formulae for applied forces, we first determined
the constants for the superficial nasal fascia. We used the avail-
able experimentally obtained in vitro finite stress-strain data10
for superficial nasal fascia along the longitudinal direction.
This longitudinal stress is given by the following:
(25) = E
Using equation (8), we get the following:
k3(1 + k4)
n1= ————— , n2= 0, n3= 0
k32+ k12
In the above equation, n1, n2, and n3are the normal components
of the unit normal vector.
The force on the face x1= ais given by the following16:
→→ →
P= PkGk= ikniGk
The component of this force along B’C’, which was initially BC
(Figure 1), becomes:
→
→G2
P· ———
G22
Using the above equation together with equations (6) and
(16), we find that the force along B’C’ becomes 0. Along the line
that was initially BH (Figure 1), the force is given by:
→
→G3
P· ———
G33
Using this equation with equations (6) and (16), we find that
the force along B’H’, which was initially BH, is given by the fol-
lowing:
k3(1 + k4)
(17) ———— [k1(1 + k4)11 + 13(k12+ k32)]
k32+ k12
The force along the normal direction on the x1= aface is given
by the following:
→
→ G1k32(1 + k4)2k32(1 + k4)2
(18) P· ——— = ————— (11) = —————
G11 k32+ k12k32+ k12
k32+ k12k32+ k12
1 – ————— + k12+ k22+ k32– 2 —————
k32(1 + k42)k32(1 + k42)
The forces in the above equations (17) and (18) are shown as
per unit area of the deformed fascial surface. In addition, the
forces given by equation (17) are provided by the tissues adja-
cent to the fascial face x1= a.
Using the mathematical procedure described above for the
fascial faces that were initially located at x2= band x3= c
(Figure 1), we find that on the face x2= b, the shear force van-
ishes but the normal force does not. The normal force on this
face is given by k2222. This force must be provided by the
adjacent tissues because no external force is applied on this face.
Chaudhry et al • Original Contribution
ORIGINAL CONTRIBUTION
384 • JAOA • Vol 108 • No 8 • August 2008
In equation (25), is the longitudinal Euler’s stress, and Eis the
Green’s strain tensor.18 Green’s strain tensor is the strain tensor
referring to the undeformed coordinates, whereas Euler’s
strain tensor refers to deformed coordinates. The stress corre-
sponding to Euler’s strain is Euler’s stress.18 Green’s strain
tensor can be calculated by the following:
1
(26) E= –– (2– 1)
2
In equation (26), is the stretch ratio. In equation (25), and ,
which were taken from one of the in vitro human superficial
nasal fascia specimens (n10js) reported in Zeng et al,10 are: =
16.85, = 1.99. We chose this specimen, which was the softest
of all four specimens of fascia reported by those researchers,10
to determine if our model equations could predict significant
compression and shear in such an extreme case.
We also used the longitudinal stress-strain relation for
incompressible material16 in our model. This relation is
expressed by the following set of equations:
12
(27) = 2C1C2(2– —)eC2(I1–3), with = 0, I1 =2+ —,
1
using 12= 2, 22= 32= —
We next used the theoretical stress given by equation (27)
and the experimental stress given by equation (25) to calculate
the values of C1and C2that would allow the theoretical and
experimental curves of stress-stretch ratio to be as close to
each other as possible (Figure 2). Our model minimized the sum
of the squares of difference between the theoretical and exper-
imental values of stress by using the least-square method19
directly on equations (25) and (27), in conjunction with a finite-
difference method adapted from Newton’s method for non-
linear equation systems.20 The computed value of C1was
0.0327 MPa, and that of C2was 8.436 MPa.
Following the above procedure in conjunction with the
available in vitro longitudinal stress-strain data from Wright
and Rennels,11 we determined the values of the elastic constant,
C1, and the dimensionless constant, C2, for fascia lata and
plantar fascia (Table 1). The mechanical constants for superfi-
cial nasal fascia were determined based on Zeng et al.10
Model Equations in the Laboratory Setting
We used our model equations to evaluate the deformations
produced as a result of manual therapy in a subject’s fascia lata,
plantar fascia, and superficial nasal fascia. These fascia were
subjected to normal pressure and shear forces (ie, without the
longitudinal force). Fascia lata and plantar fascia are common
sites for soft tissue osteopathic manipulative techniques in
patients.21
The subject in our laboratory setting was the lead author
of the present study (H.C.). Manual therapy was provided by
Jason DeFillipps, a rolfer who trained at the Rolf Institute in
Boulder, Colo. Rolfing, which is also referred to as structural
integration in osteopathic medicine, is a manual technique in
which the practitioner is trained to observe both obvious
movement of the skeleton and more subtle motion evidenced
by slight muscle contraction visible through the overlying
skin.1,22 Rolfers are not trained in diagnosis and treatment of
specific conditions—as are osteopathic physicians—but rather
in therapies to improve posture and general ease of func-
tion.1,22
First, we conducted a laboratory test on the superficial
nasal fascia of the subject to determine the amount of com-
pression and stretch that is produced under the measured
values of normal pressure and shear force. This test allowed
us to compare the elastic properties of the subject’s nasal fascia
with that of the in vitro nasal fascia specimen reported by
Zeng et al.10 For this test, the subject lay supine on a rigid plat-
form on a force plate of the EquiTest computerized dynamic
posturography apparatus (SmartEquitest System 2001; Neu-
roCom International Inc, Clackamas, Ore), which is capable of
measuring the vertical ground reaction force and the shear
force with a resolution of 0.89 N.
The therapist manipulated the nasal fascia of the subject
with two fingers oriented caudally at a 30-degree angle to the
surface of the skin just superior to the cartilaginous structure
of the nose. Both normal and tangential pressure were applied
with the rolfing technique (ie, structural integration).1This
technique is generally regarded as the form of manual therapy
that uses the greatest pressure.1The ground reaction and shear
forces were collected with the EquiTest device for 20 seconds,
sampled at a rate of 100 Hz, both before and during myofas-
cial manipulation. Because we encountered technical prob-
lems with the initial synchronization in data collection for
superficial nasal fascia, we did not use the data collected
during the first 4 seconds for this tissue. In the case of fascia lata,
however, we were able to use the data generated through the
entire 20-second collection period.
Results
Measurements of Compression and Shear
The values at any time, t, during the 16-second collection
period for change in ground reaction forces before and during
myofascial manipulation of the subject’s superficial nasal fascia
are plotted in Figure 3A (applied normal force) and Figure 3B
(applied shear force). The change in the measurements shown
in Figure 3A and Figure 3B is the normal force and the tan-
gential (ie, shear) force, respectively, applied by the manual
therapist. These forces were converted into the normal pressure
and the tangential stress by dividing the forces by the area of
pressure application, which was 1.27 in2(8.18 cm2).
The predicted values of k3and k1(the compression and
shear ratios, respectively) at any time, t, during the 16-second
collection period for superficial nasal fascia were determined
numerically by solving the set of nonlinear equations (22) and
Chaudhry et al • Original Contribution
ORIGINAL CONTRIBUTION
JAOA • Vol 108 • No 8 • August 2008 • 385
(shear force). The plots for values of the compression ratio (k3)
and shear ratio (k1) for fascia lata are not presented because they
were negligibly small under the applied loads. In the case of
fascia lata, a predicted normal load of 9075 N (925 kg) and a tan-
gential force of 4515 N (460 kg) are needed to produce even
1% compression and 1% shear. Such forces are far beyond the
physiologic range of manual therapy.
Although the shear force applied to the subject’s plantar
fascia was measured using the EquiTest apparatus, it was not
possible to measure the normal force on the plantar fascia
using this device (ie, the normal force is parallel to the surface
of the device’s platform). For measuring the normal force, we
(23). These values are plotted in Figure 3C (k3) and Figure 3D (k1).
The applied pressure, on average, was 52 kPa.
Figure 3A illustrates that a maximum applied compressive
force of approximately 100 N occurs at the time of about t= 7.25
seconds. The force at this time must produce the maximum
observed compression of the subject’s superficial nasal fascia.
This conclusion can be verified from the data in Figure 3C,
which shows that a maximum compression of k3= 0.91
(ie, 9% compression) also occurs at about t= 7.25 seconds. A
similar relation between the timing and amount of maximum
applied shear force (Figure 3B) and maximum shear produced
(Figure 3D) was also observed.
These data allowed us to compute the time history of
compression and stretch of superficial nasal fascia produced
during manual therapy. The resulting theoretical predictions
based on our mathematical model are physiologically rea-
sonable. Thus, as much as 9% compression and 6% shear can
be achieved in superficial nasal fascia with forces in the range
typically applied during manual therapies.
The same laboratory procedure and mathematical mod-
eling used for the subject’s superficial nasal fascia was also
applied to the subject’s fascia lata and plantar fascia, based
on equations (22) and (23).
The plots of applied normal force and applied shear force
for the subject’s fascia lata during the 20-second data collection
period are presented in Figure 4A (normal force) and Figure 4B
Chaudhry et al • Original Contribution
ORIGINAL CONTRIBUTION
Stress, MPa
Stretch Ratio (
)
Experimental Stress-Stretch Ratio
Theoretical Stress-Stretch Ratio
1.0
0.2
0
1.00 1.05 1.10 1.15 1.20
0.4
0.6
0.8
Figure 2. Experimental and theoretical stress-stretch ratio curves for superficial nasal fascia.
Table 1
Mechanical Constants for Fasciae,
Based on In Vitro Stress-Strain Data
Mechanical Constant, MPa*
Fascia Type C1C2
Fascia lata11 2.883 32.419
Plantar fascia11 0.931 61.775
Superficial nasal fascia10 0.033 8.436
* C1is a constant analogous to modulus of elastcity; C2is a dimensionless
constant.
386 • JAOA • Vol 108 • No 8 • August 2008
used the Xsensor pressure mapping system (X3 Lite Seat
System, Version 4.2.5; XSENSOR Technology Corp, Cal-
gary, Canada). This system can also be used to measure the
maximal therapeutic pressure application to an area of fascia
(Figure 5), a measurement that is useful to the manual thera-
pist in patient treatment. The plots of normal and shear forces
applied to the plantar fascia are presented in Figure 4C (normal
force) and Figure 4D (shear force).
As with fascia lata, the plots for values of the compression
ratio (k3) and shear ratio (k1) for plantar fascia are not pre-
sented because they were negligibly small under the applied
loads. We found that, for plantar fascia, a normal load of
8359 N (852 kg) and a tangential force of 4158 N (424 kg) are
needed to produce even 1% compression and 1% shear. These
forces are far beyond the physiologic range of manual therapy,
as were the forces that were needed to produce compression
and shear in fascia lata. Thus, we conclude that the dense tis-
sues of fascia lata and plantar fascia both remain very stiff
under compression and shear during manual therapy.
It was also observed, from equations (22) and (23), that for
a specified value of compressive stress Nand shear stress T, the
values of k3(compression) and k1(shear) are not independent.
If the values of k3and k1are specified, the values of compres-
sive stress and shear stress depend on each other. The relation
between these variables is given by the following:
k32– 1
N/T= ———
k1k3
Chaudhry et al • Original Contribution
Figure 3. Measured forces and predicted force values during a 16-
second myofascial release technique applied to superficial nasal fascia:
(A) applied normal force, (B) applied shear force, (C) predicted values
of compression ratio (k3), and (D) predicted values of shear ratio (k1).
Smaller values of the compression ratio mean more compression,
consistent with the pattern of normal force. The pattern of shear
ratio follows the pattern of shear force.
ORIGINAL CONTRIBUTION
Normal Force, N
Time, s Time, s
Shear Force, N
Shear Ratio (k1)
Superficial Nasal Fascia
Compression Ratio (k3)
AB
CD
100
90
80
70
60
50
40
30
20
10
0
0 2 4 6 8 10 12 14 16
0 2 4 6 8 10 12 14 16
1
0.99
0.98
0.97
0.96
0.95
0.94
0.93
0.92
0.91
35
30
25
20
15
10
5
0
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
JAOA • Vol 108 • No 8 • August 2008 • 387
force values) in our model because there is a wide variation in
the cross-sectional area of fasciae, and the thickness in the area
of cross section (ie, width multiplied by thickness) has a neg-
ative correlation with subject age.23 The experimental stress
values used in our model were evaluated by dividing the
force values (246 N-623 N) by the estimated area of cross sec-
tion (0.312 cm2).23
To compare our predicted stress range for the plastic
deformation of 3% to 4.13%, based on our equation (24) in a
three-dimensional setting and with an experimental stress
range provided by Threlkeld,7we calculated the longitudinal
stress Ffor the two dense fasciae (fascia lata and plantar fascia)
using the following values:
k1= 0 (no shear), k3= 1 (no compression), k4= 0.03-0.0413
(for extension)
Similarly, the relation between compressive stress and
shear stress from equations (22) and (24) can also be estab-
lished. Thus, the manual therapist cannot apply the forces
arbitrarily if the fascia is to remain intact.
Comparison of Predicted Stresses for Plastic
Deformation Under Longitudinal Force
We find from experimental measurements by Threlkeld7of
therapeutic pressure on fascia lata, which is plotted in Figure 5,
that plastic deformation in the range of 3% to 4.13% elongation
in the microfailure region of connective tissue occurs in the
stress range of 788 N/cm2to 1997 N/cm2. It is important to note
that in Figure 5, 3% elongation can be observed at 4 mm dis-
placement when microfailure begins, and 4.13% elongation is
interpolated when microfailure ends, at 5.5 mm displacement.
We used experimental stress values (but not experimental
Chaudhry et al • Original Contribution
ORIGINAL CONTRIBUTION
Figure 4. Measured forces during a 20-second myofascial release tech-
nique applied to fascia lata ([A] applied normal force, [B] applied
shear force) and plantar fascia ([C] applied normal force, [D] applied
shear force).
Normal Force, N
Time, s Time, s
Shear Force, N
Fascia Lata
AB
80
70
60
50
40
30
20
10
0
-10
45
40
35
30
25
20
15
10
5
0
0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20
Shear Force, N
35
30
25
20
15
10
5
0
Normal Force, N
80
70
60
50
40
30
20
10
0
-10
CD
Plantar Fascia
388 • JAOA • Vol 108 • No 8 • August 2008
The ranges of predicted stress values we found for plastic
deformation of fascia lata and plantar fascia are provided in
Table 2, with comparison to the known experimental fascial
stress range reported by Threlkeld.7Also in Table 2 are the
predicted values of compression and shear ratios. Predicted
results for superficial nasal fascia are not included in Table 2
because superficial nasal fascia is not dense fascia and, thus,
should not be compared with known experimental stress
ranges for dense fascia.
The differences between our predicted values for plastic
deformation of fascia lata and plantar fascia and the experi-
mental values for plastic deformation of general fascia7can be
attributed to the fact that mechanical properties of the fasciae
of our subject (H.C.) may be different from those of the in vitro
sample of connective tissue reported by Threlkeld.7More-
over, Threlkeld7obtained his experimental values for stress
range by assuming a linear stress-strain relation, whereas our
predictions are based on the actual nonlinear stress-strain rela-
tion observed in our volunteer subject.
We also note that for superficial nasal fascia, the predicted
stresses for plastic deformation are very low (3.46-
4.92 N/cm2)—as would be expected because superficial nasal
fascia consists of very soft tissues.
Comment
Our mathematical model of deformation of human fascia
can also be used for fascia that is deformed by elongation only
(k3= 1, k1= 0), compression only (k4= k1= 0), or shear only
(k3= 1, k4= 0).
We can use the values of the mechanical parameters
obtained in the present study to perform finite element anal-
yses on the actual irregular shape of fasciae. As previously
noted, the mathematical model we present in the current study
is based on the assumption that fascia is an isotropic material.
However, in some parts of the body, there are clear direc-
tional differences in fascial structural properties—differences
that are often exploited by surgeons in planning skin inci-
sions.24 If fascia is anisotropic, then the elastic properties of
anisotropic fascia in three dimensions must be determined in
future calculations to obtain accurate predictions of tissue
deformation under applied force.
We used available in vitro data for dense fasciae7,11 to
evaluate the magnitude of forces required to produce specific
deformations in these fasciae. We concluded that the magni-
tude of these evaluated forces is outside the physiologic range
of manual therapy. This conclusion is supported by the find-
ings of Sucher et al6that in vitro manipulation of the carpal
tunnel area on human cadavers leads to plastic deformation
only if the manipulation is extremely forceful or lasts for sev-
eral hours.
Ward25 describes manual techniques central to osteo-
pathic medicine (integrated neuromusculoskeletal release,
myofascial release) that are designed to stretch and reflex-
ively release restrictions in soft tissue. These techniques incor-
Chaudhry et al • Original Contribution
ORIGINAL CONTRIBUTION
Figure 5. Plot of experimental measurements of max-
imal therapeutic pressure application (N/cm2) on fascia
lata,7generated with the Xsensor pressure mapping
system (X3 Lite Seat System, Version 4.2.5; XSENSOR Tech-
nology Corp, Calgary, Canada).
JAOA • Vol 108 • No 8 • August 2008 • 389
pable effects are more likely the result of reflexive changes in
the tissue—or changes in twisting or extension forces in the
tissue.25
The mechanical forces generated by OMT and other forms
of manual therapy may stimulate fascial mechanoreceptors,
which may, in turn, trigger tonus changes in connected skeletal
muscle fibers. These muscle tonus changes might then be felt
by the practitioner.8Alternatively, in vivo fascia may be able
to respond to mechanostimulation with an altered tonus reg-
ulation of its own—myofibroblast-facilitated active tissue con-
tractility.26,27 Such alternative explanations for fascial response
to OMT and other manual therapies require further investi-
gation.
Acknowledgments
We thank Jason DeFillipps, certified rolfer, for performing manual
therapy in the present study.
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porate fascial compression, shear, traction, and twist. Our
results indicate that compression and shear alone, within the
normal physiologic range, cannot directly deform the dense
tissue of fascia lata and plantar fascia, but these forces can
impact softer tissue, such as superficial nasal fascia.
Conclusions
We have developed a three-dimensional mathematical model
for establishing the relationship between the mechanical forces
and fascial deformations produced in manual therapy. The
experimental results for the longitudinal stress-strain relation
for fascia lata, plantar fascia, and superficial nasal fascia pre-
viously reported10,11 were compared with our original data.
Because fascia is known to experience finite strain when sub-
jected to longitudinal force,10 a finite deformation theory16
was used to predict the magnitude of the mechanical forces
applied on the surface of fascia subjected to a specified finite
deformation. Thus, with the help of the equations developed
in the present study, the amount of deformation produced in
fascia subjected to a known mechanical force can be deter-
mined. Conversely, if the amount of deformation is known, the
magnitude of force needed to produce it can be determined.
The mathematical model described in the present study
should be of great value to osteopathic physicians and other
manual therapists, helping them determine the amount of
force required to deform connective tissue to a given extent. In
addition, we used our new model to determine changes in
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Our calculations reveal that the dense tissues of plantar
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the human physiologic range—to produce even 1% com-
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ficial nasal fascia, deform under strong forces that may be at
the upper bounds of physiologic limits. Although some manual
therapists3,4 anecdotally report palpable tissue release in dense
fasciae, such observations are probably not caused by defor-
mations produced by compression or shear. Rather, these pal-
Chaudhry et al • Original Contribution
ORIGINAL CONTRIBUTION
Table 2
Stress Ranges for Plastic Deformation of In Vitro Fasciae,
With Compression and Shear Ratios
Fascia Type Stress Range, N/cm2Compression and Shear Ratio Under Stress
Fascia lata*1275.00-1949.00 Negligibly small
Plantar fascia*869.65-1454.00 Negligibly small
General Fascia†788.00-1997.00 Data not provided
* Predicted stress range based on the authors’ original calculations.
† Experimental stress range based on analysis by Threlkeld7using Xsensor pressure mapping system
(X3 Lite Seat System,
Version 4.2.5; XSENSOR Technology Corp, Calgary, Canada).
390 • JAOA • Vol 108 • No 8 • August 2008
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Chaudhry et al • Original Contribution
ORIGINAL CONTRIBUTION
Principles to an Osteopath means a perfect plan and specification to build in form a house, an
engine, a man, a world, or anything for an object or purpose. To comprehend this engine of life
or man which is so constructed with all conveniences for which it was made, it is necessary to
constantly keep the plan and specification before the mind, and in the mind, to such a degree that
there is no lack of knowledge of the bearings and uses of all parts.
Andrew Taylor Still, MD, DO
“Principles” from Philosophy of Osteopathy (1899)
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