In vivo and in vitro measurements of pulmonary arterial stiffness: A brief review.

2012·1 MB·English

by  Tian, Lian

Methodological Approach for Research
In vivo and in vitro measurements of
pulmonary arterial stiffness: A brief review
Lian Tian and Naomi C. Chesler
Department of Biomedical Engineering, University of Wisconsin-Madison, Madison, Wisconsin, USA
ABSTRACT
During the progression of pulmonary hypertension (PH), proximal pulmonary arteries (PAs) undergo remodeling such that they
become thicker and the elastic modulus increases. Both of these changes increase the vascular stiffness. The increase in pulmonary
vascular stiffness contributes to increased right ventricular (RV) afterload, which causes RV hypertrophy and eventually failure.
Studies have found that proximal PA stiffness or its inverse, compliance, is strongly related to morbidity and mortality in patients
with PH. Therefore, accurate in vivo measurement of PA stiffness is useful for prognoses in patients with PH. It is also important
to understand the structural changes in PAs that occur with PH that are responsible for stiffening. Here, we briefly review the most
common parameters used to quantify stiffness and in vivo and in vitro methods for measuring PA stiffness in human and animal
models. For in vivo approaches, we review invasive and noninvasive approaches that are based on measurements of pressure
and inner or outer diameter or cross-sectional area. For in vitro techniques, we review several different testing methods that
mimic one, two or several aspects of physiological loading (e.g., uniaxial and biaxial testing, dynamic inflation-force testing). Many
in vivo and in vitro measurement methods exist in the literature, and it is important to carefully choose an appropriate method to
measure PA stiffness accurately. Therefore, advantages and disadvantages of each approach are discussed.
Key Words: pulmonary arterial stiffness, pulmonary artery, pulmonary hypertension
Pulmonary hypertension (PH) is characterized by chronically pulsatile blood flow. While distal PA remodeling, including
high blood pressure in the pulmonary circulation, including muscularization and narrowing, increases PVR, both
the pulmonary arteries (PAs), capillaries and veins. PH proximal and distal PA remodeling [c9o,10n]tribute to increases
can occur due to left heart disease, lung disease, hypoxia, in pulmonary vascular impedance. Analogously, while
recurrent pulmon[1a]ry embolism, drugs and toxins, or other increases in PVR increase mean PA pressure, increases in
unknown causes. Regardless of the cause, PH is associated impedance increase the pul[m6,9o,11n]ary arterial pulse pressure
with changes in proximal and distal PAs, which decrease as well as mean PA pressure. Important consequences of
pulmonary vascular compliance and increase pulmonary proximal arterial remodeling are loss of pulmonary vascular
vascular resistance, respectively. These pulmonary vascular compliance and proximal PA stiffening.
changes increase right ventricular (RV) aft[2e-8r]load, causing
RV hypertrophy and eventually RV failure. Proximal PA stiffness can predict mortality[ 1in2-1 p6]atients with
pulmonary arterial hypertension (PAH), which is a
Currently, diagnosis of PH is based on an elevated pulmonary subtype of PH. This finding has motivated clinical and basic
vascular resistance (PVR), which is the viscous hydraulic science studies of the material p[1r7o-3p2]erties and mechanical
opposition to the mean blood flow. However, PVR can only behavior of proximal PAs in PH.
provide limited insight into the state of the pulmonary
Here we briefly review the material properties and mechanical
vasculature sin[9c,1e0 ]it does not consider the pulsatile components
behaviors that have been used to assess PA stiffness, with a
of blood flow. These pulsatile components of blood flow Access this article online
can be accessed via the pulmonary vascular impedance, which Quick Response Code: Website: www.pulmonarycirculation.org
is the viscous and inertial hydraulic opposition to mean and DOI: 10.4103/2045-8932.105040
Address correspondence to:
Dr. Naomi C. Chesler
Associate Professor of Biomedical Engineering How to cite this article: Tian L, Chesler
NC. In vivo and in vitro measurements of
University of Wisconsin-Madison
pulmonary arterial stiffness: A brief review.
2146 ECB, 1550 Engineering Drive
Pulm Circ 2012;2:505-17
Madison, WI 53706-1609, USA
Email: [email protected]
Pulmonary Circulation | October-December 2012 | Vol 2 | No 4 505
Tian and Chesler: Measurements of PA stiffness
particular focus on proximal PAs, and then provide an in-depth In contrast, if two arteries have the same elastic moduli
discussion of the in vivo and in vitro techniques available and the same inner diameter but one has a greater wall
to measure PA stiffness. In particular, we review (1) in vivo thickness, the thicker one will be stiffer.
measurement of proximal PA stiffness via pressure-diameter
or -cross-sectional area relationships in human, large animal A summary of commonly used parameters for material
and small animal models, and (2) in vitro measurement of properties and mechanical behavior related to stiffness
proximal PA stiffness as well as material properties such as is shown in Table 1. The material properties typically
elastic modulus via several different testing methods that used to describe arteries are the elastic modulus and
mimic one, two or several aspects of physiological loading. incremental elastic modulus. The elastic modulus is the
DEFINITIONS slope of the stress-strain behavior. However, because the
stress-strain relationship of an artery is usually nonlinear,
an incremental elastic modulus, defined over a particular
stress or strain range is often used. Also, the elastic modulus
Stiffness describes the amount of force required to achieve can be calculated at a particular stress or strain. PA stiffness
a given deformation (or the amount of deformation that is frequently represented by many different parameters.
occurs in response to a given force), which is a mechanical The pressure-strain modulus and its inverse, dynamic
behavior. In general, the mechanical behavior of a structure compliance are reasonable metrics of stiffness and require
depends on the material properties, the geometry and the measurements of pressure and diameter at both systole
size or the extent of the material; thus mechanical behavior and diastole. Similarly, the stiffness coefficient and index,
is extrinsic or extensive. Material properties, in contrast, compliance and distensibility require measurements of
do not depend on the size of the structure or geometry; pressure and diameter and/or cross-sectional area at both
thus material properties are intrinsic or intensive. As we systole and diastole. In contrast, the relative area change
describe in more detail below, material properties are (RAC) is not a true measure of stiffness. RAC depends only
calculated from relative deformation (deformation relative on the PA maximum and minimum cross-sectional areas but
to a baseline state, strain) and an area-normalized force not pressure. Thus, a very stiff artery could exhibit a small
(stress). An example of an important arterial material RAC in response to a large pressure change whereas a very
property is elastic modulus; an important component of compliant artery could exhibit the same RAC response to a
both geometry and size is arterial wall thickness. Therefore, very small pressure change. A more appropriate description
two arteries composed of the same material will have of RAC is “area strain” since it reflects the change in area
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Parameter Formula Notes
The slope of stress‑strain (s‑e) curve.
σ
Elastic modulus E=
ε
∆P 2ID2OD 2POD2 P is the pressure. ID and OD are inner and outer diameters at P,
Incremental elastic modulus[33] Einc = ∆ODOD2−ID2 +OD2−ID2 respectively. ΔP and ΔOD are the changes of pressure and outer
diameter over an increment (ΔP), respectively.
P −P
Pressure‑strain modulus [34] E = s d ID
P ID −ID d
s d
Dynamic compliance[10,35,36] Cdyn=IDID×s(−PID−dP)×104 nThege leincvteedrs ief onfo tp raevsasiularbel‑es.t[r36a]in modulus. Diastolic pressure (Pd) is
d s d
ln(P/P) Pr is the standard (reference) pressure. IDr and ID are the inner
Stiffness coefficient[37,38] β = r diameters at pressure P and P, respectively.
1 ID/ID −1 r
r
ln(P /P) Luminal area (A) measured directly or estimated from ID.
Stiffness index[15,16,28] β = s d
2 (A −A )/A
max min min
A −A
Compliance[39,40] C= max min
P −P
s d
A −A
Distensibility[39,41‑43] D= max min
A ×(P −P)
min s d
A −A
Relative area change[12,15,28] RAC= max min
A
min
s: systolic;d: diastolic
506 Pulmonary Circulation | October-December 2012 | Vol 2 | No 4
Tian and Chesler: Measurements of PA stiffness
Note that the units of the parameters listed in Table 1 are performed to measure PA diameter changes over the cardiac
not identical. Which parameters are more diagnostically cycle. With the PA exposed, an electrical strain-gauge
and/or prognostically useful in the pulmonary circulation caliper was sutured to the PA adventitia as close to the true
remains unclear. diameter as possible and the relative movement of two legs
IN VIVO MEASuREMENT
of the caliper induced a change in electr[i4c8a,4l9 r]esistance which
was then converted to PA diameter. This approach
obviously is not practical for routine clinical use.
To assess proximal PA stiffness in vivo, the pressure and
As imaging techniques have advanced in the ensuing years,
inner or outer diameter or cross-sectional area of proximal
several noninvasive methods have been developed that
PAs must be measured. Ideally, these measurements
are suitable for measuring PA diameter. For example, cine-
are made simultaneously but they can also be done
angiography has been used to o[5b0,t5a1]in closed-chest diameter
sequentially and then synchronized with the heart rate
measurements of the right PA. This technique requires
(via ECG or EKG). Since the physiological pressure range
contrast injection but allows sufficient time resolution to
in the pulmonary circulation is generally small, resulting
obtain both d[5i1a]stolic and systolic diameter measurements of
in a limited pressure-diameter/cross-sectional area curve,
the right PA. According to Jarmakani et al., measurement
vasodilator and/or vasoconstrictor drugs are often used to
of the right PA diameter is preferred over the left or main
shift the pressure such that the pressure-diameter/cross-
because of its relatively cylindrical shape and easi[5l2y]
sectional area relationship can be examined in a different
identifiable fixed points during both systole and diastole.
range. In this section, we will review several techniques
used to obtain in vivo measurements of pressure and inner
Computed tomography (CT) has been used to obtain time-
or outer diameter data or cross-sectional area of proximal
averaged main PA[5 3d-5i6a]meter with or without intravenous
PAs in human, and large and small animals.
In vivo measurements in humans contrast medium, but this technique is not fast enough,
In vivo pulmonary artery pressure measurement. to date, to obtain non-tim[e57-]averaged systolic and diastolic
diameter measurements.
The gold
standard for measuring pulmonary artery pressure (PAP) is PA diameter can be also ob[3t6,a58i]ned from standard
right heart catheterization (RHC). With a catheter positioned transthoracic echocardiogram with good temporal
in proximal PA, the pulmonary pressure waveform can be accuracy and reasonable spatial accuracy depending [o59n]
obtained. Invasive RHC can provide accurate measurements the sound wave frequency produced by the transducer.
of systolic, diastolic and mean PAP with high fidelity solid
state catheters. Fluid-filled catheters are more typically used Intravascular ultrasound (IVUS) method has been used
clinically but these can introduce errors in the pressure widely as well. With an ultrasound catheter positioned
waveform due to zero leveling, da[m44-p46i]ng and insufficient in PA, the inner edge of the artery can be visualized and
frequency response of the catheter. the inner circumfe[r12e,3n5c,6e0- 6o2]f the artery at each location can
then be measured. Moreover, the PA wall thickness
Noninvasively, the peak systolic PAP can be estimated by can be obtained from the ultraso[u63n,64d] images if both
measurement of the tricuspid regu[3r6g,4i7t]ant (TR) jet velocity modalities are used simultaneously. IVUS provides[6 5a]
via continuous wave Doppler. This noninvasive minimally invasive means to track arterial wall motion
technique is sufficient. when only peak systolic PA pressure and can reach higher spatial resolution than conventional
is used to estimate s[t3i6f]fness, e.g., dynamic compliance external 2-dimen[s35i]onal ultrasound, i.e., transthoracic
defined by Dyer et al Nevertheless, this approach has echocardiography. Nevertheless, IVUS h[3a5s,6 6b,67e]en shown
its limitations. Not all individuals have easily identifiable to slightly overestimate the true diameter.
and measureable TR Doppler jet envelope, w[h36i,c47h] precludes
systolic PAP measurement in some subjects. Moreover, The color Motion-Mode (CMM) Doppler tissue imaging
this method cannot be used to measure the pressure-strain (DTI) method was developed several years ago to measure
modulus, PA compliance, or other metrics that require the instantaneous diameter. In this method, the DTI mode
diastolic PAP, unless the diastolic pressure is estimated is activated in B-mode imaging to examine PA motion
from diastolic pulmonary regurgitation velocity or the and then changed to CMM mode with the beam line
relationship between systolic and diastolic pressures. perpendicular to the PA’s superior and inferior walls.
However, these estimates are typically l[e13s,4s7 ]accurate than This is a two-dimensional Doppler echocardiographic
Icno mvipvoa rpaubllme osynsatroyl iac rptreersys duiraem eestteimr oarte csr.oss‑sectional area measurement of instantaneous diameter combining both
measurement. CMM and DTI and can provide higher spatial (1.6-1.9 mm)
and temporal (5 mi[l3l6i]seconds) resolution than conventional
Pulmonary Circula tDione c| aOdcetosb ear-gDoec, eompbeern 2-0c1h2e |s tV osl u2r |g Neor y4 was echocardiography. 507
Tian and Chesler: Measurements of PA stiffness
[80]
Finally, phase-contrast magnetic resonance imaging (MRI) aortas. IVUS has also been used to measu[8r1e] PA cross-
can be used to measure cross-sectional area of the main, sectional area and diameter in large animals.
right and left extralobar PAs with a tem[1p5,o16r,2a7l,2 8r,e31s,3o2,l6u8]tion as
high as 35 ms with modern techniques, which Noninvasive transthoracic echocardiogram measurement
is sufficient to obtain systolic and diastolic measurements. can be applied to large animals to obtain PA diameter,
The inner diameter is then estimated from the cross- although this method is not frequently used. The noninvasive
sectional area by assuming a circular cross-section. While CMM DTI technique described above has been used in large
MRI can provide accurate measurements of PA diameter, it animals suc[h22 a,30s] neonatal calves to obtain inner diameter
is expensive. Also, while the temporal resolution is higher of main PA. As mentioned above, the technique can
Ithna vni CvTo, imt ise laoswuerre tmhaen netcsh oinca rladiroggera aphnyi manadl sIVUS. provide high spatial and temporal resolution, which is
sufficient to accurately measure main, right and left PA
In vivo pulmonary artery pressure measurement.
diameters over a cardiac cycle in large animals. Recently,
To our group has used MRI t[o31 ,m32]easure the cross-sectional area
obtain in vivo PAP measurements in large animals, RHC of proximal PAs in dogs as well as echo (unpublished
can be pe[2r2f,3o2r,6m9,70e-d73 ]with techniques similar to those used data). In particular, 2D phase contrast images were acquired
humans. to obtain cross-sectional area of proximal PAs at 20 time
points over the cardiac cycle with a spatial resolution
Other invasive methods have also been developed. A one- ~1.6 mm, which is sufficient to obtain diastolic and systolic
step method is to insert a pressure microtransducer, fluid- Idnia mvievtoer ms oef athseu mreamin,e rnigth itn a nsdm leafltl P aAns.imals
filled catheter or high fidelity solid state press[u43r,7e4 ,t7r5]ansducer In vivo pulmonary artery pressure measurement.
directly into PA in an open-chest procedure. To make
sure there is no leaking from the stab wound in PA, the The
incision is typically kept quite small. This method is easy to small size of rodents raises difficulties in performing RH[8C2.]
perform but is only suitable for non-survival experiments. However, minicatheters have been available since 1[9835]0
and us[8e4]d in the rat and mouse for RHC since 1972 and
As in humans, noninvasive measurement of the TR jet 2000, respectively.
velocity can be used to estimate systolic PAP; however, this
approach has the same limitations noted above for humans. In rats, more RHC approaches have been successful likely
Recently, our group described a novel correlation between due to their larger size compared to mice. Many catheters
stroke volume and relative area change (RAC) that allowed have been developed and used in rats; examples include a
us to calculate PA pulse pressure in dogs wi[3t2h] acute PH fluid-filled cathe[8t3e]r with a pigtail shape contained in a w[85e-l8l8-]
using only noninvasive imaging techniques. However, fitting cannula, a 3.5-Fr umbilical vessel catheter,[89]
this approach has not been validated in a chronic model a catheter with a ti[p90 ]of a “shepherd’s crook” shape, a
oInf PvHiv oo rp uhlummoannasr.y artery diameter or cross‑sectional area 3-Fr Millar catheter, and a 1.4-Fr Millar[ 9c1a]theter slipped
measurement. over an introducer with a deflectable tip. Depending on
the catheters, different techniques have been developed
In animal models, invasive methods to measure to guide the catheter from right jugular or femoral vein to
PA diameter have been employed frequently. Similar to t[h49e] proximal PAs to measure .PAP.
invasive method that was used in human decades ago,
an electrical recording caliper has been sutured to opposite In mice, Champion et al first u[8s4e,9d2] a closed chest RHC
sides of the main [7P6A,77 ]wall in dog with the chest open and technique in mice successfully. In this approach, a
main PA exposed. The electrical recording caliper was catheter with an outer diameter of 0.25 mm and a specially
later replaced with two miniature ultrasonic, piezoelectric curved tip is passed from right jugular vein to the right heart
crystal tra[4n3,7s4d,7u5,7c8e,7r9s] that were sutured to the adventitia of the and finally to main, right or left PA.
main PA. The transit time of the ultrasonic signal
is converted into distance (outer diameter of PA) through In studies in mice by our group, an open chest technique
the sonomicrometer. Note that these measurements with is used in which a 1.4 F pressure-tip catheter is introduced
electrical calipers or piezoelectric crystals only provide the directly into the RV using a 20-gauge needle. After
outer diameter of the PA. RV pressure readings are obtained, the catheter is
advanced to m[2a4i,9n3] PA for systolic, diastolic and mean PAP
Another invasive approach is the conductance method in measurement. Whether or not the open-chest condition
which the cross-sectional area of the PA is obtained by causes changes in PAP is unclear.
measuring the conductance of the tissue (PA) surroundin[80g]
the catheter and then converting the conductance to area. Finally, the magnitude of the TR jet velocity from noninvasive
Th5i0s8 method was found to correlate well with IVUS on piglet ultraPsuolmunonda rhya Csi rbcueleatnio un s|e Odc ttoob eesr-tDimeceamteb esry 2s0to12li c| PVAol p2r |e sNsou 4re
Tian and Chesler: Measurements of PA stiffness
[94]
in rabbits; but as noted above, only an estimate of the force per unit cross-sectional area required to cause that
sIny svtoivlioc PpAuPlm coanna brey oabrttaeinrye dd.iameter measurement. deformation.
Due Many different strain-energy functions have been proposed
to the difficulties and relatively large spatial errors in for arteries. A detailed review is beyond th[9e5- 9s9c]ope of this
measurement of proximal PA diameter in small animals, paper and details can be found elsewhere. In general,
few in vivo studies have been performed. Nevertheless, the shear strains and stresses, which describe the twisting
recently our group has measuredµ the inner diameter of main deformation and twisting forces per unit areaψ r esψpe(Ectiv, Eely,,
rr qq
PA in mouse from transthoracic e[c93h]ocardiography with aEre) not conEsideEredE. Therefore, the SEF can be expressed as
zz rr qq zz
imaging system precision of 80 m. New techniques and a function of the strain in three directions as =
improvement in instrumentation are still required to make , where , , are the Green-Lagrange strains in the
these measurements feasible, easier and more accurate in radial, circumferential, and longitudinal directions of an
small animals. For example, with smaller-sized ultrasound artery, respectively.
catheters, IVUS could be a superior technique.
IN VITRO MEASuREMENT Fψo r aψn Einc, oEmpressible material, the SEF can be further
rr qq
simplified and expressed in a two-dimensional form as
[=10 0,1(01] ) and the Cauchy stresses can be calculated
∂ψ ∂ψ
aσs −σ =λ σ −σ =λ
There exist many in vitro mechanical testing methods θθ rr θ∂E zz rr z ∂E
2 θθ 2 zz
for quantifying the mechanical behavior and material , (Eq. 2)
λ λ
properties of arterial tissue. Many provide only material
q
pberhoapveirotrise;s f ewwh teercehansiq outehse arll opwro pvriedceis oe nmlyea msuercehmaennitc oafl wherEez z = a(nλd2z −z1 a)re2 the stretch ratios in the cEiθrθc=um(λf2eθr−e1n)tia2l
and longitudinal directions, respectively, and
both in multiple directions (i.e., axial and circumferential).
and .
In addition, to predict the material properties at a stress or
strain not tested, or the mechanical behavior at a pressure
When the artery is loaded with an internal pressure but
or diameter (or length) not tested, a constitutive model
without traction on the outer surface, the pressure can be
which mathematically describes the arterial material
obtained by integ[r9a6]ting the equilibrium equation in the
properties and initial geometry is usually employed. In rPad=ia∫lro d(σirec−tiσon )adsr
this section, we will first briefly discuss the strain-energy ri θθ rr r
function that is used in a constitutive model and then
, (Eq. 3)
r r
detail how to obtain the initial geometry or zero-stress i o
state. With this background in place, we will review the
where and are the inner and outer radii of the artery
most common in vitro testing methods used to measure
at pressure P. Substituting Eq. 2 into Eq. 3, the pressure-
PSAtr satiinff-neesnse.rgy function diameter curve of a pressurized artery can be obtained.
Finally, the pressure-diameter relationship can be used
to calculate the mechanical behavior of the artery for
Biological materials are composite structures made up
comparison with in vivo measurements to validate the
of multiple components and arranged in multiple layers.
Mconosrtpithuotivme emtroyd eal.nd residual strain measurement
However, if we treat biological materials as a continuum,
i.e., as homogenous structures with continuous properties,
the concepts of stress, strain and energy in continuum Measurements of arterial morphometry such as wall
mechanics can be app[l9i5e]d and permit relatively simple thickness and inner and/or outer diameters are required
mathematical analysis. A strain-energy function (SEF), to quantify the mechanical behavior of artery. However,
which describes the strain energy per unit volume stored quite often we can not measure the geometry at a specific
iψn a ψm(aEt)erial, can be written as pressure in vitro due to the shortness of the PA itself
(e.g., main PA) or due tissue availability because the tissue
= E, (Eq. 1) may be dissected into several parts for different studies.
Typically, the morphometry of a PA ring only is measured
where is the Green-Lagrange strain thLat describes the at the unloaded state, i.e., at zero internal pressure and zero
deformation Lof the material relative LtoL a baseline state. longitudinal force (Fig. 1A).
For example, if a bar of an initial length  0‑ is stretched to
a new length , the stretch ratio is = / 20, and the Green- It is well known that residual strain exists in an artery ring at
Lagrange strain can be calculated as ( 1)/2. With a an unloaded state. When an artery ring is cut radially, it opens
SPEuFlm, tohnaer ys tCriraciunla tcioann | b Oec troeblear-tDeedc etmob tehr e2 0s1t2r e|s Vso, l w2 h| iNcho 4is the as shown in Figure 1B. The opened artery is generally ta5k09en
Tian and Chesler: Measurements of PA stiffness
as the stress- or strain-free state. Compared to the opened
artery ring, the closed artery ring has different inner and
outer circumferences and the deformation results in residual
strain in the closed artery ring. This deformation is in the
circumferential direction and the residual strain is called
circumferential residual strain. Although small, the residual
strain can have a large effect on the strain distribut[i3o0n,96 a,1c0r2-o10s4s]
the artery wall at the physiological pressure.
(A) (B)
It is important to note that residual strain exists in the
circumferential, longitudinal and radial directions but those Figure 1: Schematics of (A) a closed artery ring and (B) an opened artery
in the circumferential direction are typically considered the ring after one radial cut.
most important. To release circumferential residual strain,
one well-[a10c5c]epted way is to cut the ring along a single radius
(Fig. 1B). When the artery ring is opened with a single cut,
the opening angle (OA) is obtained by measuring the angle
between the two lines connecting the middle point of the
inner arterial wall to the edges of the open sector (Fig. 1B).
The OA can be linke[2d9] to the histological and mechanical
properties of artery.
Since arteries have three layers, each with different
constituents evident by histology, the circumferential
residual strain may not be fully released by one radial cut.
Indeed, the residual strains in each layer may be different.
To measure these, the three layers need to be separated. This
process can also release longitudinal residual strain, which
can be measured by comparing the length of each separat[1e0d6]
layer to the length of the intact longitudinal arterial strip. (A) (B)
However, the process of separating the media from the Figure 2: Schematics of (A) uniaxial tensile test and (B) ring/tension test.
adventitia is technically difficult and can cause damage.
Thus, the circumferential and longitudinal residual strains
in different artery layers are generally not considered. The
morphometry of an artery cut once radially is usually taken in tension. As such, this test is more accurately termed as
ausn thiae xrieafelr teennces isltea ttee fsotr stretch or strain calculations. uniaxial tensile test.
In general, the sample undergoes five or more loading
A uniaxial test is a procedure in which a rectangular strip and unloading cycles at a constant stretch rate for
cut out of an artery is pulled in one direction, usually along preconditioning, and the force-displacemsent data are
the longest length direction of the artery sample (Fig. 2A). taken from the last loading cycle. Then, with force and
In general, the artery sample is prepared as a long rectangle displacement obtained, the Cauchy stress ( ) and Green-
Fλ 1
and uniaxial loading is performed in the circumferential or Lσa=grang,eE s=tra(inλ 2(E−)1 c)an be calculated as
A 2
longitudinal direction. In traditional mechanics, samples to 0
be tested in this way are cut in a dog bone shape with the F ,A (Eq. 4)
center narrower than the edges to reduce boundary effects, λ
but this is typically not done for arteries because tissue size where is the force, 0 is the cross-sectional area of the
is limited. A length to width ratio of at least 5:1 is generally sample at the unloaded condition, and is the stretch ratio
considered sufficient to ignore boundary effects. The tissue inL the loLading direction, which is calculated aλs =ra Lti/oL of the
sample is then mounted in the testing system with both deformed (loaded) to undeformed (unloaded) lengths
ends of the sample held by grips or hooks and immersed in (  and 0, respectively) of the sample, i.e., 0. The
a physiological solution (PBS, PSS or PSS with drug) at the elastic modulus as a function of strain can be obtained
physiological temperature. The force on the artery sample is directly from the stress-strain curve as the slope at a given
measured by a load cell and recorded simultaneously with strain.
the displacement of the grip or hook. While hard materials
such as bone and metal can be tested in this configuration in To predict behavior under conditions not directly
bo5t1h0 compression and tension, arteries can only be tested measPuulrmeodn airny Cair cuunlaitaioxni |a lO ctteonbseri-lDee cteemstb e(r e2.0g1. 2u |n Vdoel r2 b| iNaox i4al
Tian and Chesler: Measurements of PA stiffness
F A
λ
stretch), a strain energy function can be used. Assumψin g where is the force, 0 is the cross-sectional area of the
ψtheE arEtery is hEomogeEneous and incompressible with a sample at the unloaded condition, and is the stretch ratio
qq ZZ qq ZZ
strain-energy function in a two-dimensional form as = in the circumferential direction. The factor 2 accounts for
( , ) with and denoting for the Green-Lagrange the two sides of the ring that are loaded simultaneously.
strains in the circumferential and longitudinal directions, The circumferential strain is calculated as in Eq. 4. Again,
respectively, and witsh shear strains neglected, the stresses the artery is assumed to be homogeneous. This type[ 10o9f]
rr
can be expressed as in Eq. 2. In this case, the stress in testing system can be used to test large or small PAs,
the radial direction is zero in the uniaxial tensile test. which is an important advantage over the uniaxial test
When Fthe samsple is loaded in circumferential direction, in which typically only larger arteries can be gripped in
Z ZZ
the force and stress in the longitudinal direction are also
the testing system. To obtain stress-strain information
zero ( = 0;  = 0). When the sample is loasded in the at different loading conditions, a SEF needs to be used as
qq
longitudinal direction, the longitudinal stress is non-
in the uniaxial tensile test. However, since longitudinal
zero but the circumferential stress is zero ( = 0). By
testing is not possible, one must assume that the stress-
fitting the idealized stress-strain relationship expressed
strain relationship is the same for both circumferential and
as in Eq. 2 to the measured stress-strain data for both
longitudinal directions.
circumferential and longitudinal strip samples, all material
parameters in the SEF can be obtained. Finally, the stress-
This test is relatively easy to perform and has the same
strain relationship at different stretch conditions can
advantages as the uniaxial tensile test and the same
be calculated and the pressure-diameter relationship
limitations. Most often this type of test is used to measure
can be predicted for additional proximal PA stiffness
the forces induced by contraction and relaxation due
calculations.
to smooth[10 9m-11u1s]cle cells activation and endothelial cell
sBiiganxailainlg t.est
With the appropriate apparatus at hand, the uniaxial tensile
test is easy to perform, and the sample preparation only
requires a small strip, which is frequently feasible. The
For a biaxial mechanical test, a rectangular or nearly
testing system can also be used to perform creep or stress-
square thin, flat (i.e., planar) sample of artery is pulled in
relaxation tests in which the strain as a function of time is
two directions simultaneously (Fig. 3). For arterial tissue,
measured under a constant stress or the stress as a function
these two directions are usually the circumferential and
of time is measured under a constant strain, respectively.
longitudinal directions. The artery sample is prepared
These two tests can provide the viscoelastic properties of
with the directions of the edges corresponding to the
an artery, which affects hemodynamic pulse wave damping.
longitudinal and circumferential directions. The stretch or
Nevertheless, some disadvantages exist. First, cutting an
artery into a rectangular strip may disturb the structural strain in both circumferential and longitudinal directions
integrity at the lateral edges of the strip, which cou[10ld7] are typically obtained optically by measuring the relative
affect the validity of the measured stress and strain. displacement of four small pre-marked dots in the middle
In addition, in the above calculation of stress (Eq. 4), the region of the pla[n10a8r] tissue sample surface, generally the
artery is assumed homogeneous and thus ignores potential intimal surface. With the forces in both directions
differences in structure and function between the intima, measured, the stresses can be calculated as
media and adventitia. Finally, the uniaixal tensile test
cannot fully characterize the anisotropic (d[1i0r0,e10c8t]ionally-
dependent) material properties of an artery. That is,
the uniaxial tensile test can only provide stress-strain data
in one direction per sample, with the other two directions
free of force, which is not physiological. In vivo, an artery
is loaded three-dimensionally.
Ring/tension test
In the ring/tension test, an artery ring is pulled by two
appropriate hooks or clips which go thr[o10u9]gh the lumen of
the artery ring as shown in Figure 2B. With the force
and displacement recorded, the circumferential stress is
calculaFteλd as
σ = ,
θθ 2A Figure 3: Schematic of biaxial test.
0
(Eq. 5)
Pulmonary Circulation | October-December 2012 | Vol 2 | No 4 511
Tian and Chesler: Measurements of PA stiffness
Fλ Fλ
σ = 1 1 ,σ = 2 2 ,
11 L T 22 L T
20 0 10 0 The deformed artery dimensions under different inflation
F F (Eq. 6) pressures (Fig. 4C) are then measured from im[17a,1g8,e11s3 c]aptured
by at least two cameras at different angles. For this
L L
where 1 and 2 are the forces in direction T1 and 2 test, it is important to obtain an artery sample with uniform
respectively, 10 and 20 are the lengths of the unloaded thickness and a section large enough that the diameter of
sample in direction 1 and 2 respectively, and 0 is the the sample region unde[r17 p,11r3e,1s1s4]ure is at least 10 times the
thickness of the unloaded sample. Similar to the uniaxial test, thickness of the sample. During inflation, the shape
additional PA stiffness parameters can be calculated using of the artery section becomes ellipsoid and the stretch
an SEF based on fitting the measured stress-strain data. can be estimated by measuring the arc length before and
after inflation in both circumferential and longitudinal
Compared to the uniaxial tensile test, the biaxial test is better directions. Combined with the inflation pressure, the
able to characterize the anisotropic behavior of an artery, ellipsoidal geometry data (vertical semi-axis, horizontal
since both circumferent[1ia00l, 1a08n]d longitudinal directions are semi-axis, etc) are used to calculate the stre[1s7,s18e,1s1 5i]n the two
loaded simultaneously. Also, the applied force and directions. Details can be found elsewhere. This test
thus amount of stretch in each direction (circumferential is similar to the biaxial test since both circumferential and
and longitudinal) can be controlled, allowing the simulation longitudinal directions are stretched simultaneously. To
of in vivo stretch states under physiological conditions. obtain the stress-strain data at different pressure/stretch
Limitations include some experimental and theoretical conditions and pressure-diameter data, a SEF can be used,
issues. Experimentally, the problems include difficulty in as in the biaxial test.
gripping the tissue without inducing d[a10m8]aging and applying
constant forces along sample edge. Theoretically, the One advantage of this test is that it can be used to calculate
stress calculation requires the assumption of homogeneity stress-strain data in both circumferential and longitudinal
whereas in fact the artery is generally heterogeneous. directions simultaneously. This test is also suitable for
Additionally, the homogeneity of deformation within the curved planar samples, which is not true for the in-plane
specimen is questionable and thus the region in which the biaxial test described above or the whole artery inflation/
marked dots are placed for stretch measurement should be deflation test described below. Another advantage of this
small an[10d8 ,f1a12r] away from the outer edge to reduce boundary test is that it is suitable for particularly short arteries, such
effects. Finally, the artery at its zero-stress state could as the main PA, which could not be tested in a whole artery
be curved and thus the prepared tissue sample is generally inflation/deflation test without significant end effects.
not perfectly planar. As a result, the true stretch may be not However, this test also has its limitations.
uniform through arterial wall thickness due to the bending
of the non-planar tissue sample during the biaxial test. Such First, as mentioned above, the test requires a thin, flat
non-uniform deformation is not accounted for in the stretch sample, which may not be possible to obtain in diseased
oBru sbubblseeq tueesntt material property calculations. states. Second, the sample is loaded equally in the
circumferential and longitudinal direct[i1o1n6]s and the loading
cannot be independently controlled. Third, the data
In the bubble test, a planar artery section is mounted on collection and analysis techniques ar[1e1 7]typically more
a circular channel filled with physiological solution that complicated than some other methods. Moreover, this
allows pressure inflation from one side (Figures 4A and B). test is only suitable for quasi-static testing since the image
(A) (B) (C)
Figure 4: Schematics of (A) sectional view of bubble test fixture; (B) perspective view of the fixture; and (C) the inflation of artery membrane under pressure.
512 Pulmonary Circulation | October-December 2012 | Vol 2 | No 4
Tian and Chesler: Measurements of PA stiffness
of the inflated artery cannot be captured with high quality
at high frequencies with currently available equipment.
Nevertheless, this can be improved in principle with
improved imagi[n11g7 ]systems. Finally, the shear behavior can
be not captured and tissue samples must be sufficiently Figure 5: Schematic of inflation-force test.
intact, and have no holes or leaks, that they can withstand
Ipnreflsasutiroizna-tifoonr.ce test
discussed here. At a fixed axial stretch, the pressure and
diameter relationship can directly provide relative area
A third type of biaxial test is the inflation-force (or tension)
change (RAC), compliance and distensibility defined as in
test. In this case, a whole artery with no side branches
Table 1. To estimate the stress-strain relationship, the SEF
is pressurized at a fixed axial length or stretched at a
can be employed. In particular, with geometry data and the
fixed pressure (Fig. 5). One widely used testing system
zero-stress state geometry (reference state) as well as the
is the pressure myograph (Danish Myotechnology). This
assumption of incompressibility, the circumferential stretch
system has a pressure transducer at each end of the artery
can be estimated for a given longitudinal stretch under
specimen and a force transducer on one end (on the cannula
different pressures. The radial stretch can be calculated
used to mount the tissue to the system). A CCD camera
with the incompressibility condition. Fitting the SEF to
above or below the specimen is used to measure arterial
the tested data by substituting Eq. 2 into Eq. 7 enables
diameter and often wall thickness, depending on the optical
calculation of the material properties, which then can be
density of the tissue. Thus, pressure, axial force, diameter
used to generate the stress-strain or pressure-diameter
and often wall thickness can be measured simultaneously.
relationship.
One limitation of this system is the time resolution of the
data acquisition.
Alternatively if the artery is assumed to be homorgeneous
and isotropic (with directionally-independent material
To address these limitations and allow collection of
properties), the circumferential stre[1s19s] at a point ( ) inside
frequency-dependent material properties, our group
the artery wPar2ll canr b2e estimated as
has developed a system that combines a high-frequency σ (r)= i 0 +1 ,
dynamic pump with a CCD camera a[n11d8] high-frequency θθ (r02−ri2)r2 
amplifiers for the pressure transducers. The CCD camera (Eq. 8)
is able to capture images at a frequency of at least 20 Hz,
from which the outer diameter can be measured with
where ri and r0 are respectively the internal and external radii
commercial software (IonOptix). The amplifiers are able
of the artery at internal pressure P. For a thin-wall artery, t[h95e]
to measure pressure without frequency-dependence in Pr
σaver=age ic,ircumferential stress can be simply estimated as
amplitude up to 100 Hz and only a slight phase delay above θθ T
20 Hz. Currently, however, this system uses an arteriograph
(Eq. 9)
that does not integrate a force transducer (Living Systems
Instrumentation) and thus does not provide axial force data.
where T is the wall thickness of the artery at pressure P.
Note that this stress is an average across the wall.
Depending the testing system, then, the internal pressure,
outer diameter (or inner diameter), and/or the axial force
The dynamic inflation-force test is the best in vitro
are measured simultaneously during an inflation/force test.
mechanical test in terms of mimicking the physiological
The internal pressure (P) asnd tshe meassured axial force (F) loading condition. The measured pressure-diameter data
qq
can be expressed as functions of the circumferential, rad[9i6a]l can be directly compared to the in vivo measured data if the
aPn=d ∫lor0n(gσitu−diσnal) sdtrre,sses ( , rr and ZZ, respectively) in vivo longitudinal stretch is used in vitro. However, the
r1 θθ rr r shear force exerted on the artery wall due to the blood flow
F =π∫r0[2(σ −σ )−(σ −σ )]rdr. in vivo is generally not considered in the in vitro test. Other
ri zz rr θθ rr (Eq. 7) issues should also be kept in mind. In particular, the artery
should be long enough to reduce boundary effects (length
to diameter ratio greater than five, for example). If the
At a fixed pressure, the axial force varies with the end-to-end length of the sutured artery tube is too long,
longitudinal stretch. Although the axial force-stretch buckling can occur, depending on the longitudinal stretch.
relationship can indicate the material behavior in the axial After buckling, the longitudinal stretch increases and the
(or longitudinal) direction, it does not provide proximal measured pressure-diameter data cannot be combined with
PPAu lsmtoifnfanrye sCsir causl attyiopni c| aOllcyto dbeerf-iDneecdem. Tbehru 2s0 1th2i |s Vboelh 2a |v iNoor 4is not the data before buckling as a continuous curve for anal5y1s3is.
Tian and Chesler: Measurements of PA stiffness
Experimental challenges include the preparation of bubble- (i.e., decellularized) or[ c21e,1r2t7a,1i2n8] proteins (e.g., collagen) prior
free physiological solution during perfusion, which can to mechanical testing. Mechanically, the artery can
affect the measured data especially for high frequency tests. separated into layers based on the histology (intima, media
Like the bubble test, tissue samples must be sufficiently and adventitia layers if possible) and individual layers can
iTnotrasctio sno ttheast tthey can withstand pressurization. then be tested. Due to the difficulty of layer separation and
in testing the sponge-like adventitial layer, the adventitial
layer is usually trimmed and only the intima-media layer is
In a torsion test, either a whole artery section or a planar tested. In this type of test, some characteristics of individual
section of an artery is twisted. For the former, in addition layers can be measured. The uniaxial tensile test has been
to an applied internal pressure and longitudinal stretch, performed on the separated[2 9i]ntima-media layer of the
the artery is subjected to a torque th[a1t2 0t,1w21]ists the artery main PA from adult bovines. Typically, neither bubble
around the longitudinal axis (Fig. 6A). For the latter, nor inflation-force testing can be performed on either
two types of tests have been used. One is the rotational biochemically or mechanically processed tissues because
shear test. In this test, a flat section of artery is prepared they leak when perfused.
with its edge fixed on a rigid plate and center attached to
another rigid disc[ 1t2h2]at transfers the torque to the artery While tests after biochemical or mechanical processes can
section (Fig. 6B). The other one is the simple shear provide data and new insights, the interactions between
test. In this test, a cuboid artery section is prepared and components or layers are also eliminated and these
sandwiched between top and bottom plates. While one plate interactions may play an important role in the overall
delivers t[h12e3, 1d2i4s] placement, the other one measures the force material[ 12p9r]operties and mechanical behavior of intact
(Fig. 6C). With the torque or shear stress and the shear arteries.
strain known, the shear modulus or the shear stress-strain SuMMARY
relationship can be obtained. Detailed test[i9n5,1g2 0s-y12s5t]em setup
and calculations can be found elsewhere.
Since arteries are soft materials in general and can have Proximal pulmonary arterial stiffness is an important
large deformations, and care should be taken to ensure the factor contributing to RV afterload and thus could be a
artery is well attached to the plate, the rotational and simple useful prognostic parameter for PH. Although different
shear tests on a planar artery are not easy to perform. The definitions have been proposed to obtain PA stiffness, all
inflation/force/torsion test requires a complex testing these calculations require pressure and/or cross-sectional
system and this system is not often used to examine the area or diameter measurements. Therefore, accurate
shear stress-strain behavior of PAs. Nevertheless, the measurement or estimation of these data is important.
torsion or shear test was proposed as a necessary test For in vivo measurements, we have provided a review of
combined with biaxial or inflation-force test t[1o2 6b] etter available methods in human and large and small animal
cMhaercahctaerniziec tahel atneissottirnopgi c aprfotpeerr tibesi oofc ahretemry.ical or models. To measure pulmonary artery pressure, right heart
mechanical processing catheterization is standard and often performed in human
and large animals, although noninvasive echocardiography
and MRI techniques are increasingly being used. For small
Performing mechanical tests after biochemical or animals, it is more common to insert a catheter directly
mechanical processes can provide additional insight into PA or RV in a nonsurvival surgery. To obtain the
into the components of the arterial wall responsible for dynamic geometry of proximal PAs (cross-sectional area
material properties and mechanical behaviors. For example, or diameter) over a cardiac cycle, echocardiography and
arteries can be processed biochemically to remove cells MRI are currently the preferred techniques because they
(A) (B) (C)
Figure 6: Schematics of (A) inflation/force/torsion test; (B) rotational shear test; and (C) simple shear test.
514 Pulmonary Circulation | October-December 2012 | Vol 2 | No 4