Vol. 274, Issue 6, H2188-H2202, June 1998
SPECIAL COMMUNICATION
Gel stretch method: a new method to measure constitutive properties
of cardiac muscle cells
Michael R.
Zile1,2,
Monica
Kelly
Cowles2,
J. Michael
Buckley1,
Kendrick
Richardson1,2,
Bradford A.
Cowles1,
Catalin F.
Baicu1,
George
Cooper IV1,2, and
Vasanti
Gharpuray2
1 Cardiology Section of
Department of Medicine and Department of Physiology, Gazes Cardiac
Research Institute, Medical University of South Carolina and Veterans
Administration Medical Center, Charleston 29401; and
2 Department of
Bioengineering, Clemson University, Clemson, South Carolina 29634
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ABSTRACT |
Diastolic dysfunction is an important cause of
congestive heart failure; however, the basic mechanisms causing
diastolic congestive heart failure are not fully understood, especially
the role of the cardiac muscle cell, or cardiocyte, in this process.
Before the role of the cardiocyte in this pathophysiology can be
defined, methods for measuring cardiocyte constitutive properties must be developed and validated. Thus this study was designed to evaluate a
new method to characterize cardiocyte constitutive properties, the gel
stretch method. Cardiocytes were isolated enzymatically from normal
feline hearts and embedded in a 2% agarose gel containing HEPES-Krebs
buffer and laminin. This gel was cast in a shape that allowed it to be
placed in a stretching device. The ends of the gel were held between a
movable roller and fixed plates that acted as mandibles. Distance
between the right and left mandibles was increased using a stepper
motor system. The force applied to the gel was measured by a force
transducer. The resultant cardiocyte strain was determined by imaging
the cells with a microscope, capturing the images with a CCD camera,
and measuring cardiocyte and sarcomere length changes. Cardiocyte
stress was characterized with a finite-element method. These
measurements of cardiocyte stress and strain were used to determine
cardiocyte stiffness. Two variables affecting cardiocyte stiffness were
measured, the passive elastic spring and viscous damping. The passive
spring was assessed by increasing the force on the gel at 1 g/min,
modeling the resultant stress vs. strain relationship as an exponential [
= A/k(ek
1)]. In normal cardiocytes,
A = 23.0 kN/m2 and
k = 16. Viscous damping was assessed
by examining the loop area between the stress vs. strain relationship
during 1 g/min increases and decreases in force. Normal cardiocytes had
a finite loop area = 1.39 kN/m2,
indicating the presence of viscous damping. Thus the gel stretch method
provided accurate measurements of cardiocyte constitutive properties.
These measurements have allowed the first quantitative assessment of
passive elastic spring properties and viscous damping in normal
mammalian cardiocytes.
stress; strain; finite element; stiffness; viscosity
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INTRODUCTION |
CONGESTIVE HEART FAILURE (CHF) is now the
most common cause of cardiovascular morbidity and mortality (22). CHF
can be caused by a primary abnormality in systolic function, a primary
abnormality in diastolic function, or both (54, 55). Diastolic CHF
occurs in as many as one-third of all patients who develop CHF (14). Despite its importance, the basic mechanisms causing diastolic CHF are
not fully understood. We and others (4, 11, 20, 21, 37, 38) have
hypothesized that changes in both the extracellular matrix and the
cardiac muscle cell, or cardiocyte, are causally responsible for the
changes in diastolic function that occur during the development of
diastolic CHF. To date, however, even the most basic questions about
the role played by the cardiocyte in the development of diastolic CHF
have not been addressed, e.g., 1) Are cardiocyte constitutive properties such as stiffness and viscosity altered in diastolic CHF? and 2)
What cellular structures or processes cause any changes in cardiocyte
constitutive properties? However, before these and other questions can
be addressed, methods for measuring cardiocyte constitutive properties
must be developed and validated.
An ideal method for quantifying cardiocyte stiffness and viscosity
would have the following characteristics: a measurable force could be
applied to the cardiocyte; the resultant change in cardiocyte and
sarcomere length could be measured; the cardiocyte could be stretched
over a physiological range; the method itself would not damage the
cardiocyte either by causing plastic, irreversible changes in the cell
or by changing intrinsic cellular stiffness; the cardiocyte would
return to resting length after stretch; and the cardiocyte would remain
physiologically viable throughout the study.
A variety of techniques have been proposed for examining isolated
cardiocyte stiffness, but none fulfills all of the above criteria. For
example, in some methods force was applied to and strain was measured
in isolated cardiocytes by attaching cells to carbon fibers (15, 24),
by attaching cells to glass microneedles using fiber and glue (9),
urethan foam insulant (16, 17, 36, 46), or
poly-L-lysine (39-44), by
using single- or double-barreled suction micropipettes (3-7, 33),
by impaling cells with glass needles (12), or by wrapping cells around
optical fibers (25, 29, 47, 48). The disadvantages of these techniques
include the fact that in some or perhaps all of the techniques it is
difficult to firmly attach cardiocytes to the test apparatus without
injuring the cardiocyte and changing its intrinsic material properties. Furthermore, the most frequently used techniques (3, 5, 6, 16, 17, 36,
46) do not measure viscous properties, do not directly measure stress
on the cardiocyte itself, require cardiocytes to be skinned, and cannot
characterize cardiocytes in the presence of physiological levels of
calcium. In addition, because only one or two cells from each isolation
can be studied, these techniques cannot be used to correlate mechanical
with biochemical or biosynthetic properties of cardiocytes from either
normal or abnormal hearts.
Thus, although each of the above methods provides useful information,
each has specific limitations in the context of the physiological and
pathophysiological questions that we want to address. Therefore, the
purpose of this study was to validate a new technique for examining
cardiocyte constitutive properties, prove that it avoids the
limitations listed above, and demonstrate its applicability to adult
mammalian cardiocytes isolated from normal animals.
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METHODS |
Preparation of Isolated Cardiocytes
The methods that we use for cardiocyte isolation have been described
before in detail (26). In brief, 10 adult cats of either sex
(1.8-4.0 kg) were anesthetized with meperidine (2.2 mg/kg im),
acepromazine maleate (5 mg/kg im), and ketamine hydrochloride (50 mg/kg
im) and heparinized (1,000 U iv). A left thoracotomy was performed, the
heart was rapidly removed, the aorta was cannulated, and the coronary
arteries were perfused retrogradely for 10 min, first with a
recirculating HEPES-Krebs buffer (in mM: 140 NaCl, 4.8 KCl, 2.4 MgSO4, 1.2 NaH2PO4,
4.0 NaHCO3, 0.5 CaCl2, 12 HEPES, and 12.5 glucose), second with a nonrecirculating buffer of the same composition
without supplemental calcium, and third with a recirculating
calcium-free buffer supplemented with 1.6 mg/ml collagenase B
(Boehringer-Mannheim). Perfusion was terminated when the heart was
flaccid. The heart was removed from the cannula, and the cardiac tissue
was minced and then gently sieved through a 210-µm nylon mesh to
isolate the cardiocytes. After centrifugation the cells were washed
with the HEPES-Krebs buffer and 1% BSA and resuspended in HEPES-Krebs
buffer plus 1% BSA.
All animals received humane care in compliance with the "Principles
of Laboratory Animal Care" formulated by the National Society for
Medical Research and the National Institutes of Health (NIH)
Guide for the Care and Use of Laboratory
Animals [DHHS Publication No. (NIH) 85-23,
Revised 1985].
Gel Stretch Method
Gel composition and preparation.
After isolation cardiocytes were embedded in an agarose gel composed of
2% agarose, HEPES-Krebs buffer, and laminin; the latter is a basement
membrane protein to which the cardiocyte adheres in vivo. Agarose,
consisting of 60% Sea Prep agarose (FMC, Rockland, ME) and 40% pulsed
field agarose (Stratagene, La Jolla, CA), was dissolved in distilled
water by heating to ~80°C. The agarose solution was then allowed
to slowly cool. When the temperature of the agarose solution fell below
40°C, the components of the HEPES-Krebs buffer were added to
produce the same composition as that specified in
Preparation of Isolated Cardiocytes
for this buffer, and laminin (Upstate Biotechnology, Lake Placid, NY)
at a concentration of 25 µg/ml was then added. When the
agarose solution had cooled to exactly 37°C, the cardiocytes were
added. Each component of the agarose solution was vigorously oxygenated
and brought to a pH of 7.4 before incorporation. This suspension of
cardiocytes in agarose solution was then poured into molds.
Gel molds.
An example of the Teflon-coated aluminum mold used to form the agarose
gel is shown in Fig. 1. The front of the
mold was formed by a glass cover slide attached with elastic bands.
Liquid agarose was poured into the fill tube of the mold so that the
cavity used to form the mold was filled from the bottom. This procedure
resulted in a sample that was homogeneous and free of bubbles. When the agarose had cooled to ~30-35°C and gelled, the gel was
extracted from the mold by removing the glass cover slide making up the front of the mold. The cardiocyte-containing gels were then immersed in
HEPES-Krebs buffer, placed in an incubator at a constant temperature of
37°C, and bubbled with oxygen.
The gels had a thin, flat center section with flared ends (Fig. 1).
This geometry was dictated by the stretch apparatus itself, the imaging
system, and the need to keep the cells physiologically intact. The
flared ends allowed the sample to be held firmly within the mandibles
of the test apparatus but allowed the center of the sample to sit flat
over the microscope objective and allowed the applied load to create
the highest stress in the area of interest at the center of the sample.
This geometry resulted in any gel failures during stretch occurring at
the center rather than at the ends of the sample. The cross-sectional
area of the sample in the area of cardiocyte observation was 21 mm2.
After the gel was removed from the incubator and mounted on the
mandibles of the test apparatus, the gel sample itself and the
mandibles that held it were immersed in a chamber filled with HEPES-Krebs buffer placed on a movable inverted microscope stage directly over the objective. The gels were transparent, so that cardiocytes were easily imaged within the gel matrix.
Test apparatus.
A schematic drawing of the gel stretch apparatus is shown in Fig.
2. The gel sample was held between an
adjustable roller made from a 0.25-in. Plexiglas rod and a fixed plate
made from 0.06-in. brass, which acted together as a mandible. Each
mandible was mounted on a low-friction linear motion rail via a
low-friction ball slide (RSR 7 M130, THK, Schaumburg, IL). This linear
motion rail allowed the mandibles to move along a single axis with no angular displacement. Each mandible was then connected to a separate ball screw assembly that consisted of a threaded shaft and a
recirculating ball nut (MBF 0601, THK). The two ball screw assemblies
were arranged in parallel and were connected to each other by two nylon
gears of 36-mm pitch diameter fixed at the ends of the threaded shaft. This coupling resulted in equal and opposite rotation of the shafts, which produced equal and opposite linear motion of the ball nuts. One
ball screw assembly was connected by a flexible driveshaft to the
stepper motor. As the stepper motor turned one threaded shaft, the
second threaded shaft turned an equal amount in the opposite direction
because the two threaded shafts were connected by the two nylon gears.
Thus the two mandibles moved in equal and opposite linear directions.
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Fig. 2.
Schematic drawing of agarose gel stretch apparatus. Gel was held
between 2 mandibles. Agarose gel and cardiocytes within gel were
stretched when force, measured by a load cell, was applied to gel by
moving mandibles in opposite directions using stepper motor and
dual-direction ball screw assemblies. Cardiocyte and sarcomere length
were measured by imaging cardiocytes with an inverted microscope.
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The stepper motor operated at a rate of 240 steps per revolution,
creating a displacement in the screw shafts of 1 mm per rotation. One
step of the stepper motor resulted in an increase in the distance
between the mandibles by 8 mm. Because of the mechanical vibration
created by the stepper motor it was mounted in a remote location away
from the test apparatus, thus reducing the vibration being translated
to the cardiocytes under investigation. The stepper motor was
controlled by a custom-designed electronic circuit developed for this
application. This circuit allowed a desired load to be chosen. This
load was then converted to the appropriate stepper motor rotation. The
actual load created by this rotation was compared with the desired
load, and then adjustments in the stepper motor rotation were made in a
continuous fashion through a feedback system. Actual loads were
recorded at 5-min intervals manually.
The load applied to the gel was measured with a load cell (model 31, Synsotec, Columbus, OH) positioned on the left mandible arm so that the
mandible had a 2:1 mechanical advantage. The indicated load was
converted to gel stress using the following computation: stress () = force/area
|
(1)
|
where
gf = geometric factor (0.5), L = load in grams, g = acceleration due to gravity (9.81 m/s2), and G-CSA = cross-sectional area of the gel sample (0.000021 m2). Stress applied to the gel
did not equal the stress on the cardiocyte within the gel. Stress on
the cardiocyte was calculated using the finite-element analysis
described in FEM.
Cardiocyte and sarcomere strains were calculated by imaging
cardiocytes at variable loads. Strain (
) was calculated as nominal or engineering strain
|
(2)
|
where
Li = initial
length and Ln = new length obtained after stretch.
Stretch protocol.
Load on the gel was increased at a rate of 1 g/min. This resulted in a
strain rate in the gel of ~10 µm/min. This increased cardiocyte
stress at a rate of ~1
kN · m
2 · min1
and cardiocyte strain at ~0.1 µm/min. Simultaneous adjustment of
the sample position on the microscope stage was necessary to keep the
cell centered and in focus. At 5-g intervals, images were captured.
Load on the gel was increased to a maximum of 40 g and then decreased
at a rate of 1 g/min to 0 g, with images being captured at 5-g
intervals. A 40-g load applied to the gel corresponded to a gel stress
of 10 kN/m2. Stretch was performed
under load control rather than length control, because length values
required manual measurement and were not available on-line. Only those
cells whose long axis was parallel to the direction of stretch were
studied.
Custom image analysis system.
Changes in cardiocyte length, diameter, area, and sarcomere
length were measured using our custom image analysis software, "MIPSY," described in detail in a previous paper (32). MIPSY software ran on an MS-DOS 386 computer with a PC Vision plus frame grabber. Cardiocytes were imaged using an inverted microscope with a
×40 Hoffman modulation contrast objective. Images were captured
using the image acquisition module of MIPSY through a high-resolution
monochrome video camera (CCD-72, Dage-MTI, Michigan City, IN). Images
were digitized with 512 × 512 line resolution and 256 gray
levels. Distance measurements were calibrated using a hemocytometer
grating with the MIPSY calibration module. Cardiocyte length, diameter,
and cell area were calculated from manually digitized cell profiles
using the MIPSY morphology module. Sarcomere length was calculated as
the average peak-to-peak distance from a manually selected area of the
intensity profile chosen for a uniform peak-and-valley profile. Average
sarcomere length was determined by measuring 15-20 peak-to-peak
distances. The software automatically calculated the number of peaks
and the average sarcomere length in micrometers. This method correlates
well with results from laser diffraction measurements of sarcomere
length.
Cardiocyte Constitutive Properties
Measurement of cardiocyte stiffness.
This cellular property was quantified using the same principles used to
measure myocardial stiffness in the intact heart. Stiffness was
assessed by examining the relationship between cardiocyte stress and
cardiocyte strain. Stress, defined as force per unit cross-sectional
area of the cardiocyte, was expressed in kilonewtons per square meter.
Strain, which was unitless, was defined as the change in cardiocyte
size or sarcomere length, relative to the starting length, produced by
the application of this force. If cardiocyte stiffness increased, the
stress vs. strain relationship would shift toward the left, so that, in
a stiffer cardiocyte, any given increment of stress applied to the
cardiocyte would result in less strain, and the cardiocyte would be
deformed to a smaller degree. However, the slope and position of the
cardiocyte stress vs. strain curve is affected by a number of
determinants, including the passive elastic spring and viscous damping.
The passive spring consists of all the cellular elements that resist stretch in a time-independent manner. To calculate the differences in
the passive spring properties between two populations of cells, the
rate at which force is increased, and thus the displacement rate, must
be a constant, slow rate. In addition, the level of myofilament
activation must be at or near zero. This technique is described in
Protocol A: Assessment of passive elastic
spring. Damping elements consist of those cellular
structures or processes that resist stretch in a time-dependent manner,
i.e., they resist more when stretched faster. Differences in viscous
damping between two populations of cardiocytes can be determined using
the "loop area method," described in detail in
Protocol B: Assessment of viscous
damping.
Measurement of cardiocyte stress.
Data derived from the gel stretch method included measurements of
stress on the gel and strain in the cardiocyte. In addition to plotting
stress on the gel vs. strain in the cardiocyte, it was necessary to
measure stress on the cardiocyte itself and to plot stress on the
cardiocyte vs. strain in the cardiocyte. The three steps necessary to
measure stress on the cardiocyte were to
1) define the material properties of
the agarose gel itself, 2) develop a
finite-element model (FEM) to describe cardiocyte constitutive
properties, and 3) calculate
cardiocyte stress from experimental data using the FEM-determined
cardiocyte constitutive properties.
MECHANICAL PROPERTIES OF AGAROSE GEL.
Tensile tests were performed to determine the material properties
of the agarose gel using a vitrodyne test apparatus (Liveco, Burlington, VT). Gel specimens consisted of either the gel alone or the
gel plus cardiocytes. The specimens were stretched at three different
strain rates of 10, 100, and 1,000 µm/s until failure. These rates
were chosen in part because cardiocytes and the myocardium lengthen
after contraction at ~100 µm/s. In addition to the rate of 100 µm/s, we chose strain rates 10 times higher and lower than this
physiological in vivo rate. A clear distinction should be made between
these experiments done using the vitrodyne test apparatus and those
done using the stretching device shown in Fig. 2. The vitrodyne
provides precise measurements of force and length during variable-rate
uniaxial stretches but does not allow cardiocytes to be imaged. Thus
these vitrodyne studies were designed to characterize the gels
themselves and not the cardiocytes. In contrast, studies using the
stretching device shown in Fig. 2 allowed us to image the cardiocytes
but only at one slow stretch speed of 1 g/min.
A polynomial relationship of the form
|
(3)
|
was
assumed for the mechanical behavior of the gel. The constants
C1 and
C2 were
determined by fitting the experimental data to the polynomial curves by
a least-squares analysis, with a requirement that
R2 > 0.99 for
all of the groups tested. Five gels were examined at each strain rate
with and without cardiocytes. A total of 30 gels were studied.
FEM.
From the experiments performed in this study, the following data were
obtained: 1) the stress applied to
the gel, 2) the resultant strain of
the gel, 3) the average stress vs.
strain relationship of the gel specimens, and
4) the strain in the cardiocyte
embedded in the gel that resulted from the stress applied to the gel.
Using this information, we determined the nonlinear elastic properties of the cardiocyte with a FEM. The FEM is a very powerful technique when
used to find numerical solutions to problems with irregular geometries
and/or nonlinear material behavior. This method was ideally
suited for the experimental problem presented by this study, in which
the gel and the cardiocyte within that gel were modeled as nonlinear
elastic materials. The characteristics of the FEM are presented below.
The software package Patran (McNeal-Schlendler, Costa Mesa, CA) was
used for preprocessing, which consisted of defining the model geometry,
discretization of the geometry into a finite number of elements,
defining material properties, and imposing load and boundary
conditions. The software package ABAQUS (Hibbitt, Karlsson, and
Sorenson, Pawtucket, RI) was used for the actual processing, which
consisted of computing the stiffness matrixes and the numerical solution of the resulting system of equations.
The FEM had the following characteristics. Because the volume
fraction of cells within the gel was small (<0.1%), we assumed that
there was a single cell embedded in an infinitely large gel medium. For
practical purposes, a cylinder of 150-µm radius and 1,400-µm height
was used. These choices were based on the fact that cardiocytes are
roughly rod-shaped cells with an average length and diameter of ~140 × 20 µm. Because the cell was cylindrical, with stretch
occurring in one direction along the long axis, instead of modeling the
entire volume of the cell, we used an axisymmetric model for a single
plane of the cell. Because there were planes of symmetry above and
below the cell and on either side of the cell, only one-fourth of the
cell and gel was modeled. Both the gel and cell were modeled as
hyperelastic, incompressible materials. Because these were biological
materials, a large displacement analysis was used. A displacement of 60 µm was examined. Boundary conditions for both the cell and gel were
applied along the lines of symmetry. Convergence and error analysis
were used to determine the appropriate number of elements, which
approximated 9,000. Material properties for the system were defined
using the constitutive equations for the agarose gel [ = (51 kN/m2) + (343 kN/m2)2]
and the cardiocyte ( = C1 + C22).
Because the gel was mainly composed of water, and thus assumed to be
incompressible, a Poisson's ratio of 0.5 was used for the entire
system. On the surfaces of symmetry, the conditions of symmetry (i.e.,
normal displacement and shear stresses vanish) were applied. A perfect
bond was assumed at the cardiocyte-gel interface (i.e., normal and
shear stresses and displacements are continuous). This assumption was
based on studies described in Cardiocyte Bond to
Agarose Gel that showed a <1% difference in strain
between the agarose gel, 15-µm embedded microspheres, and the
embedded cardiocytes. A uniaxial tensile displacement in the longitudinal direction was applied in increments to the cardiocyte-gel system. An initial guess for the cardiocyte properties
(C1,
C2) was made on
the basis of experimental data (gel stress vs. cardiocyte strain) and
an elastic analysis of the agarose gel system. The predicted values of
both longitudinal and lateral cardiocyte strain from the FEM were
compared with the experimentally observed values. Constants
C1 and
C2 were adjusted
accordingly until the strain values from the model matched the strain
values from the experiments. Once this iterative process was complete,
the newly determined constitutive equation was used to plot cardiocyte
stress vs. cardiocyte strain for each set of experimental data. An
example of this iterative process is shown in Fig.
3. This example shows the experimentally derived values of gel stress vs. cardiocyte strain and the
FEM-predicted values of gel stress vs. cardiocyte strain for
iterations
1, 2, and 5. The constitutive properties of
the cardiocyte expressed as
C1 and
C2 in
iteration 5 were then used to
determine values of cardiocyte stress that corresponded to measured
values of cardiocyte strain.
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Fig. 3.
Example of iterative process used in finite-element model (FEM).
Experimental data were compared with values of gel stress () vs.
cardiocyte strain () predicted by FEM. With each iteration,
constants C1 and
C2 were adjusted
until values from model matched values from experiment. Note
that both here and in Figs. 5-8, is by definition a unitless
value (µm/µm), whereas is expressed as
kN/m2.
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Experimental Protocols
Protocol A: Assessment of passive elastic spring.
This property was evaluated by applying force to the gel at a
constant rate of 1 g/min (as read by the load cell), resulting in a gel
displacement rate of ~10 µm/min. To reduce myofilament activation
to a minimum, cardiocytes were treated with 7 mM 2,3-butanedione monoxime (BDM), 0.1 mM EGTA, and no added calcium. BDM is known to
inhibit actin-myosin cross-bridge interactions, and EGTA chelates calcium. Cardiocyte images were recorded at 5-g intervals from 0 to 40 g (0-10 kN/m2). Data were
plotted initially as gel stress vs. cardiocyte strain, and then, with
the FEM, were replotted as cardiocyte stress vs. cardiocyte strain.
Protocols A and
B were performed on cardiocytes isolated from five normal cats. Between five and eight cardiocytes were
studied from each cat. A total of 30 cardiocytes were studied. Data
from all cardiocytes from a given animal were averaged. The mean data
for a group of animals were derived from these averaged values.
Assessment of the cardiocyte passive elastic spring properties was
performed using six methods.
1) The cardiocyte stress vs. strain
data were plotted, and the general shape and relative position of this
relationship were noted. 2) The
change in cardiocyte stress as a function of cardiocyte strain
(d/d) was calculated at a specific cardiocyte strain. At strains
of 1, 5, and 8%, d/d was calculated by measuring the slope of a
tangent drawn to the stress vs. strain relationship at that specific
strain (Fig.
4A). 3) The energy (E) imparted to the
cardiocyte during an increase in stress was assessed. This energy was
calculated as the integral of force (F) applied to the cardiocyte and
the distance (D) that the cardiocyte
moved as a result of this force application (Fig. 4B). Distance was equal to the
difference between the initial muscle length
(Li) and the
the cardiocyte length after the application of stress
(Ln). This
energy was calculated by assessing the integral area under the
cardiocyte stress vs. cardiocyte strain curve during an increase in
stress (Fig. 4C). Stress () is
equal to the force per cross-sectional area of the cell (C-CSA)
|
(4)
|
Strain ()
is equal to the distance moved by the cell divided by the initial
length of the cell
|
(5)
|
Thus
energy imparted to the cardiocyte during an increase in force can be
calculated as (Fig. 4D)
|
(6)
|
The
average C-CSA was 2,865 µm2, or
2.865 × 109
m2. The average distance was 10.88 µm, or 1.08 × 105
m. The average initial length was 1.36 × 104 m.
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Fig. 4.
Schematic drawing describing methods used in protocol
A to assess changes in passive elastic spring
properties. A: change in cardiocyte
stress as a function of cardiocyte strain (d/d).
B: energy calculated as integral of
force (F) applied to cardiocyte and distance
(D) that cardiocyte moved as a
result of force application. C: energy
calculated by assessing integral area under cardiocyte stress vs.
cardiocyte strain curve during an increase in stress.
D: calculations.
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Methods 4-6 were based on fitting
the cardiocyte stress vs. cardiocyte strain data to a specific
equation. Three equations were used. These three equations were chosen
to facilitate comparison of data obtained in the gel stretch method
with those used by other investigators in examining the constitutive
properties of isolated cardiocytes, isolated muscle strips, and intact
myocardium.
Method 4 used the equation
|
(7)
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where
k represents the slope of the natural
log of the stress vs. strain relationship. Although this
relationship is linear and can be fit through the origin, neither
Eq. 7 nor the natural log of the
stress vs. strain data can be analyzed at values of zero stress or zero
strain. In addition, the actual fit of the cardiocyte stress vs.
cardiocyte stain data to this equation has no optimal
value.
Method 5 used the equation
|
(8)
|
where
k represents the curvilinearity or
nonlinearity of this relationship, and
A represents the initial slope or
steepness of this relationship. Using this equation the actual fit of
the cardiocyte stress vs. cardiocyte strain data was quite good, and values of zero stress and zero strain are accommodated.
Method 6 used the equation
|
(9)
|
This
equation provides the best fit for the cardiocyte stress vs. cardiocyte
strain data, can be used with values of zero stress and zero strain,
and is the most common equation used by investigators examining the
constitutive properties of isolated mammalian cardiocytes. As in
Eq. 5,
k is a function of the nonlinearity, and A is a function of the steepness of the cardiocytes
stress vs. cardiocyte strain relationship.
Protocol B: Assessment of viscous damping.
Cardiocyte viscous damping properties were assessed by
calculating the area within the stress vs. strain loop during a
sequential increase and decrease in stress, the loop area
method. In engineering terms, damping in a mechanical
system is proportional to the resistance to a change in the shape of a
mechanical element within that system. The size of this resistance is
dependent on the rate of change in the shape of the mechanical element.
The presence of this resistance causes a loss of mechanical energy by
converting mechanical energy into heat energy. By the application of
force, or stress, to a cardiocyte, causing that cardiocyte to elongate,
energy is imparted to the cell. This energy can be quantified as the
product of the force, or stress, and distance, or strain (Fig.
4B). When stress is increased, the
area within the stress-strain relationship is equal to the potential
energy gained by the cell during the application of force (Fig.
5A).
When stress is decreased, the energy returned to the system is equal to
the product of stress and strain (Fig. 5B). If there is damping in a given
system, there will be a difference between the energy gained by the
system during the application of a stress and the energy returned to
the system when this stress is decreased (Fig.
5C). This area between these two
stress-strain relationships represents the energy lost to heat. This
loop area reflects the amount of viscous damping that exists within a
system (Fig. 5D).
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Fig. 5.
Schematic drawing describing "loop area method" used in
protocol B to assess presence and
extent of viscous damping. A: area within stress-strain
relationship is equal to potential energy gained by cell during
application of force. B: when stress
is decreased, energy returned to system is equal to product of stress
and strain. C: with damping in a given
system, there is a difference between energy gained by system during
application of a stress and energy returned to the system when this
stress is decreased. D: loop area
reflects amount of viscous damping that exists within a system. CSA,
cross-sectional area.
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Protocol C: Effects of physiological calcium concentration.
In some techniques that have been used to assess cardiocyte
constitutive properties, the cells cannot be studied in the presence of
physiological levels of calcium. The purpose of
protocol C was to determine the
effects of physiological calcium levels on the cardiocyte stress vs.
strain relationship. In experimental protocols
A and B the level of
myofilament activation was kept at a minimum by treating cells with
BDM, EGTA, and no added calcium. In protocol
C BDM and EGTA were omitted, and cardiocytes were studied in solutions containing 2.5 mM calcium.
Protocol C was performed on
cardiocytes isolated from five normal cats, and five to eight
cardiocytes were studied from each cat. A total of 30 cardiocytes were
studied. Data from all cardiocytes from a given animal were averaged.
The mean data for a group of animals were derived from these averaged
values. The methods used to analyze data obtained from
protocol C were the same as
methods 1-6 discussed for
protocol A.
Cardiocyte Viability in Agarose
In developing the gel stretch technique, it was hypothesized that
cardiocytes would remain physiologically viable within the agarose gel.
To prove that cardiocytes embedded in an agarose gel remained viable,
cardiocyte protein synthesis rate and cardiocyte mechanical shortening
in response to electrical stimulation were measured.
Protein synthesis rate.
Protein synthesis rate was measured in cardiocytes embedded in
the 2% agarose matrix. These results were compared with the protein
synthesis rate measured in cardiocytes plated on laminin-coated plastic
culture trays.
LAMININ-COATED TRAYS.
After isolation, the calcium-tolerant cardiocytes were suspended in
M199 (GIBCO) with Earle's salts at a concentration of 50,000 rod-shaped cells/ml. To facilitate adhesion to the culture dish, the
cardiocytes were plated in M199 on laminin-coated wells at a density of
2 × 105 rod-shaped
cells/well. Fibroblast contamination was minimized by differential
adhesion after 1 h of incubation. After overnight incubation, the
cultures were rinsed to remove nonadherent cardiocytes and incubated in
a chemically defined medium as described before (19, 51).
The protein synthesis rate was measured by pulse labeling as
previously described (18, 28). Briefly, cardiocytes were radiolabeled
for 4 h in medium containing 0.4 mM
3H-labeled phenylalanine
([3H]Phe, 7 mCi/ml), a
concentration that facilitates rapid expansion of the intracellular Phe
pool and equilibrium of intracellular Phe specific radioactivity with
Phe in the culture medium (27, 28). On completion of the labeling
period, the cardiocytes were rinsed three times in Hanks' balanced
salt solution containing 10 mM Phe and scraped into standard sodium
citrate buffer (300 mM sodium chloride, 30 mM sodium citrate)
containing 0.25% (wt/vol) SDS. The protein was precipitated by adding
concentrated HClO4 to a final
concentration of 6%. The material was centrifuged and washed three
times in 6% HClO4, heated in 6%
HClO4 to 80°C for 15 min, and
washed three more times in 6%
HClO4. The protein was solubilized
in 0.3 M NaOH at 37°C for 1 h. Aliquots were used to measure
radioactivity by liquid scintillation counting and for determination of
protein concentration using the bicinchoninic acid method (BCA,
Pierce). To calculate absolute rates of protein synthesis from
incorporation of
[3H]Phe into protein,
the specific radioactivity of Phe in the culture medium was used as the
immediate precursor pool. We have demonstrated in prior studies that
the specific radioactivity of the Phe tRNA pool, the immediate
precursor for protein synthesis, equilibrates to ~80% of the Phe in
the culture medium in both quiescent and electrically stimulated
cardiocytes (18). The rate of total protein synthesis (nmol
Phe · mg
protein1 · h1)
was calculated by dividing the incorporation of Phe into protein [disintegrations/min (dpm) · mg
protein1 · h1]
by the specific radioactivity of Phe in the medium (dpm/nmol).
AGAROSE-EMBEDDED CARDIOCYTES.
After isolation, cardiocytes were placed in liquid agarose at 37°C.
The agarose was poured into four-well trays (50,000 cells/ml). The
agarose was allowed to gel and then was superfused with medium. The
average gel thickness was 2-3 mm. Cardiocytes were allowed to
incubate overnight, and the medium was changed.
The protein synthesis rate was measured in agarose-embedded cells by
adding [3H]Phe to the
perfusate for 4 h. The gel was rinsed in phosphate-buffered saline to
which 10 mM Phe was added. The gel was dissolved with 14% perchloric
acid (PCA), and the protein was precipitated, washed, and solubilized
in NaOH. Total protein was measured using a commercially available
assay (BCA, Pierce), and radioactivity in aliquots was measured by
liquid scintillation counting.
Mechanical response to electrical stimulation.
One measure of cardiocyte viability is the ability of the cells
to respond to electrical stimulation by mechanical shortening. The
percentage of cardiocytes that respond to electrical stimulation, the
extent of shortening, and the electrical threshold for stimulation were
compared in cardiocytes plated on laminin-coated plastic culture trays
vs. cardiocytes embedded in a 2% agarose matrix.
Adult feline cardiocytes, which are normally quiescent in
culture, were induced to contract synchronously via electrical field stimulation as described before (19, 51). To set the threshold voltage
for contraction, the lowest voltage required to stimulate >50% of
the cells was determined and then exceeded by 10%, resulting in an
approximate response ratio of 70%. The resulting strength of the
electrical field was ~4 V/cm between electrodes. The cardiocytes were
stimulated at a frequency of 1 Hz and pulse duration of 5 ms. The
culture medium was changed daily over the course of the experiments.
Cardiocyte Bond to Agarose Gel
The bond between the gel and the cardiocytes during increases and
decreases in force was examined by placing 15-µm microspheres in the
agarose gel along with the cardiocytes. Strain in the whole agarose
gel, strain between microspheres at variable distances from the
cardiocyte, and strain within the cardiocyte at variable distances
along its length were examined. These studies showed that strain in the
gel was clearly different from strain in the cell. At 10 kN/m2 gel strain was 0.12, whereas
cell strain was 0.02. At 40 kN/m2
gel strain was 0.25, whereas cell strain was 0.08. By examining sarcomere strain along the length of the cell, these studies showed that strain along the length of the cell was uniform. Finally, strain
between microspheres in close proximity to cardiocytes was examined.
These studies showed that strain between microspheres in close
proximity to cardiocytes was nearly identical to that of the strain
within the cardiocytes. There was a <1% difference in
the strain measured between microspheres and strain measured within the
cardiocyte, indicating the presence of a near-perfect bond between the
cardiocyte and the laminin-doped agarose gel matrix.
Data Analysis and Statistics
Means ± SE are shown for each group of data. Differences
between group means for assessment of agarose gel properties and for
assessment of the effects of physiological calcium concentrations, considered significant at P < 0.05, were determined using a multiway analysis of variance and a
Newman-Keuls multiple-sample comparison test. For studies of cardiocyte
viability, differences in protein synthesis rates and mechanical
responses to stimulation were determined using an unpaired
t-test.
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RESULTS |
Mechanical Properties of Agarose Gel
The first step required to measure stress on the cardiocyte was to
define the mechanical properties of the agarose gel. Agarose stress vs.
agarose strain was measured at three strain rates (10, 100, and 1,000 µm/s) in agarose gels with and without cardiocytes. Examples of
agarose stress vs. agarose strain data for gels stretched at 100 µm/s
are shown in Fig.
6A. Group
data are shown in Fig. 6, B and
C, and in Table 1.
These data indicate that the stress vs. strain relationship of the
agarose gel itself had a nonlinear elastic shape. There were no
significant differences in the agarose stress vs. agarose strain
relationship between gels stretched at 10 vs. 100 or 1,000 µm/s. In
addition, there were no significant differences in the agarose stress
vs. agarose strain relationship between gels with cardiocytes and gels
without cardiocytes stretched at any strain rate. Thus, over the range
of strains tested, the agarose gel behaved as a nonlinear elastic
material with no viscous properties, and the presence of cardiocytes
within the agarose gel did not alter its nonlinear elastic properties.
The equation that was used in the FEM to define the material properties
of the agarose gel was = (51 kN/m2) + (343 kN/m2)2.
The finding that the agarose gel behaved as a nonlinear elastic material with no viscous properties was further confirmed using the loop area method. When gel stress vs. gel strain was examined during a sequential increase and then decrease in force, no
hysteresis was seen, so that there was no area between these
superimposable curves.
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Fig. 6.
Mechanical properties of agarose gel.
A: examples of agarose gel stress vs.
strain relationship for 5 gels stretched at 100 µm/s. Group data
examining agarose stress vs. agarose strain were obtained at 3 strain
rates (10, 100, and 1,000 µm/s) in agarose gels without cardiocytes
(B) and agarose gels with
cardiocytes (C). Stress vs. strain
relationship of agarose gel itself had a nonlinear elastic shape. There
were no significant differences between stress vs. strain relationship
at any strain rate in gels with or without cardiocytes. Thus, over
range of strains tested, agarose gel behaves as a nonlinear elastic
material with no viscous properties; presence of cardiocytes within
agarose gel did not alter its nonlinear elastic properties.
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Protocol A: Passive Spring
An example of the changes in cardiocyte size produced by application of
10 kN/m2 stress to the agarose gel
is shown by the photomicrographs in Fig.
7C. Group data for
stress on the agarose gel vs. cardiocyte strain during an increase in
stress using protocol A for all normal cells are plotted in Fig. 7A.
Concurrently obtained data for sarcomere strain are shown in Fig.
7B. At ~10
kN/m2 stress on the agarose gel,
cardiocyte strain was 0.08 ± 0.001 and sarcomere strain was 0.081 ± 0.003 (with a sarcomere length = 2.2 ± 0.1 µm). The FEM was
used to calculate precise values for the constants
C1 and
C2. For normal
cardiocytes during an increase in stress,
C1 = 188 kN/m2 and
C2 = 3,425 kN/m2. These precise values for
the constants were then used to determine stress on the cardiocyte
itself and the cardiocyte stress vs. cardiocyte strain relationship
during an increase in stress for the group of normal cardiocytes (Fig.
7D). From the cardiocyte stress vs.
cardiocyte strain relationship, d/d at
0.01, 0.05, and 0.08 strain as well as the
area under the stress vs. strain curve, energy gained by the cardiocyte
during the increase in stress and the constants
A and
k from Eqs.
7-9 were determined. These data are presented in
Table 2. At 0.08 strain, d/d was 464 kN/m2, the energy gained was 5.4 × 1010 N · m, and,
using Eq. 9,
A was 23.0 kN/m2 and
k was 16.
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Fig. 7.
Data derived from protocol A (passive
elastic spring; BDM, EGTA, 0 Ca2+). Group data examining
agarose gel stress vs. cardiocyte strain relationship are shown in
A, agarose gel stress vs. sarcomere
strain relationship data in B,
cardiocyte stress vs. cardiocyte strain relationship data in
D, and an example of change in
cardiocyte size produced by application of a force of 10 kN/m2 in
C. Stress vs. strain relationship is
curvilinear, with a stress of 10 kN/m2 resulting in a strain of
8%.
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Protocol B: Viscous Damping
An example of the gel stress vs. cardiocyte strain relationship during
a sequential increase and then decrease in stress is plotted in Fig.
8A. There were clear
differences between the slope and position of the gel stress vs.
cardiocyte strain relationship during the increase in stress compared
with the stress vs. strain relationship during the decrease in stress.
In addition, there was a finite loop area enclosed by these two curves
(i.e., the area between the solid and dashed lines) in this cardiocyte.
The average loop area for cardiocytes was 83 ± 4. The presence of a
finite loop area indicates that there is viscous damping in cardiocytes. That is, if there were no viscous damping, the two curves
would have been superimposable.
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Fig. 8.
Data derived from protocol B (viscous
damping). Example of gel stress vs. cardiocyte strain relationship
during a sequential increase and then decrease in stress in a
cardiocyte is shown in A, and example
of cardiocyte stress vs. cardiocyte strain relationship is shown in
B. In both examples, there is a clear
and finite loop area enclosed by the 2 curves during an increase and
decrease in stress, indicating existence of viscous damping in normal
cardiocytes. Stress vs. strain relationship during an increase in
stress is distinctly different from stress vs. strain relationship
during a decrease in stress, as indicated by differences in equations
for each curve shown in B.
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The FEM was used to determine the constants
C1 and
C2 for the stress
vs. strain curve during the increase in stress (data presented above)
and the constants
C1,
C2, and
C3 for the stress vs. strain curve during the decrease in stress. For the decrease in
stress, C1 = 200 kN/m2,
C2 = 10,250 kN/m2, and
C3 = 180,000 kN/m2; these values were
significantly different from those obtained during the increase in
stress. These constants were used to determine cardiocyte stress
and the cardiocyte stress vs. strain relationship plotted in Fig.
8B. The area under this curve was
0.545 kN/m2, the energy returned
to the system was 2.124 × 1010 N · m, and, using
Eq. 9,
A was 22.5 kN/m2 and
k was 60.
The area between the cardiocyte stress vs. cardiocyte strain curve
during an increase in stress and the cardiocyte stress vs. cardiocyte
strain curve during a decrease in stress was 0.469 kN/m2. Thus the energy lost to
heat in the process of overcoming viscous damping was 1.827 × 1010 N · m.
Resting cardiocyte and sarcomere lengths at 0 kN/m2 before the increase in
stress were similar to these lengths at 0 kN/m2 after the decrease in
stress. These data indicate that cardiocytes did not undergo plastic,
irreversible changes during gel stretch.
Protocol C: Effects of Physiological Calcium
Concentrations
In protocols A and
B, cardiocytes were studied in the
presence of BDM, EGTA, and no added calcium. In
protocol C, cardiocytes were studied
in the absence of BDM and EGTA and in the presence of 2.5 mM
Ca2+. In the presence of
physiological calcium, cardiocytes remained quiescent and responded
normally to electrical stimulation with no significant change in
resting sarcomere length. During stretch, cardiocytes remained
quiescent. Figure 9 shows data from this protocol. Data are plotted as gel stress vs. cardiocyte strain in Fig.
9A. The FEM was used to determine
C1 and
C2 for both
groups of cells. The constants in cardiocytes studied in the presence of physiological calcium were
C1 = 300 kN/m2 and
C2 = 1,020 kN/m2. Both the constants and the
cardiocyte stress vs. strain relationship determined from them were not
significantly different in the presence of physiological calcium
compared with cardiocytes treated with BDM, EGTA, and no calcium.
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Fig. 9.
Data derived from protocol C (calcium
effects). Cardiocytes were studied under 2 experimental conditions: in
presence of BDM, EGTA and no added
Ca2+ or in absence of BDM and EGTA
but in presence of physiological
Ca2+.
A: agarose gel stress vs. cardiocyte
strain relationship. B: cardiocyte
stress vs. cardiocyte strain relationship. Presence of physiological
calcium did not alter these relationships.
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From the cardiocyte stress vs. strain relationship shown in Fig.
9B, d/d at 0.01, 0.05, and 0.08 strain as well as the area under the stress vs. strain curve, energy
gained by the cardiocyte during the increase in stress and the
constants A and
k from Eqs. 7-9 were determined. These data are presented in
Table 2. d/d at 0.08 was 382 kN/m2, the energy gained was 5.04 × 1010 N · m, and,
using Eq. 9,
A was 295 kN/m2 and
k was 6.5.
Cardiocyte Viability in Agarose Gel
Protein synthesis rate.
The protein synthesis rate in quiescent, nonstimulated cardiocytes
embedded in agarose was 185 ± 10 nmol
[3H]Phe/g protein.
This value was not significantly different from that for cardiocytes
plated on laminin, 180 ± 12 nmol
[3H]Phe/g protein.
Mechanical response to electrical stimulation.
Cardiocytes embedded in the 2% agarose gel were responsive to
electrical stimulation. In the cardiocytes embedded in agarose, the
percentage that responded to electrical stimulation was similar to the
percentage of cardiocytes cultured on laminin-coated trays that
responded to electrical stimulation both on the day of isolation and 24 h later (75 ± 1 vs. 72 ± 1%). In addition, the threshold voltage for contraction was similar in the two groups of cardiocytes (~4 ± 0.5 vs. ~3.5 ± 0.5 V/cm). Finally, in agarose gels,
the average sarcomere shortening extent was 0.13 ± 0.01 µm. The
average shortening velocity was 1.8 ± 0.1 µm/s. These values are
less than those seen in normal cardiocytes contracting isotonically in
media in which sarcomere shortening extent was 0.20 ± 0.02 µm and
shortening velocity was 3.0 ± 0.1 µm/s. However, this small difference is expected because cells embedded in the gel were not
contracting freely or isotonically but were contracting against a load
produced by the gel.
| |
DISCUSSION |
The purposes of this study were to
1) validate a new technique for
examining cardiocyte constitutive properties,
2) prove that this technique avoids
the limitations inherent in other methods, and
3) demonstrate that this technique
is applicable to adult mammalian cardiocytes isolated from normal
animals. These data indeed show that the gel stretch method provides
accurate measurements of cardiocyte constitutive properties. With this
technique, a definable stress applied to the cardiocyte results in a
measurable change in cardiocyte and sarcomere strain. In addition to
assessing the passive elastic spring, the gel stretch method provides a measure of viscous damping. This study shows that the limitations inherent in previous methods are avoided by the gel stretch technique. Thus substantial numbers of cardiocytes from each animal can be studied; they do not need to be skinned before study; they can be
studied in the presence of physiological levels of calcium; they can be
stretched over a physiological length range and do not undergo plastic,
irreversible changes but instead return to resting length after
stretch; they remain physiologically viable while embedded in agarose
both before and during stretch; they remain responsive to electrical
stimulation with no change in threshold; and they retain normal
contraction profiles. Furthermore, while the cells are embedded in
agarose, cardiocyte protein synthesis rates are normal and cardiocyte
morphology as well as sarcomere definition and resting length are
unchanged.
Comparison of Current Data With Data From Other Investigators
Data from the current study using the gel stretch technique are
concordant with those from studies done in isolated mammalian cardiocytes with a variety of other techniques. Granzier et al. (16,
17, 46) and Brady et al. (3, 5, 6) studied the cardiocyte stress vs.
strain relationship over a range of stresses and sarcomere lengths
similar to that used in the current study. In addition, they obtained
values of A and
k that were similar to those found in
the present study. Granzier et al. (16, 17), using rodent cardiocytes
attached to glass microneedles with urethan foam, studied the
cardiocyte stress vs. strain relationship over a sarcomere length of
1.8 to 3.5 µm. As shown in Table 3, over
a physiological range of sarcomere lengths from 1.8 to 2.2 µm, stress
ranged from 0 to 40 kN/m2 and the
constants from Eq. 9 were
A = 20.6 ± 4.6 and 31.5 ± 10.2 kN/m2 and
k = 12.2 ± 0.86 and 11.6 ± 1.2 for right ventricular cardiocytes and left ventricular cardiocytes,
respectively. Brady (3, 5) found similar results in rodent
cardiocytes held between double micropipettes by suction and
barnacle cement. Over a sarcomere length range of 1.9 to 2.2 µm, stress was 0-40 kN/m2.
From Eq. 9,
A = 16.4 kN/m2 in guinea pig cardiocytes,
22.4 kN/m2 in rabbit cardiocytes,
and 25.8 kN/m2 in rodent
cardiocytes.
Garnier et al. (15, 24) and Fish et al. (12) studied cardiocytes over a
range of sarcomere lengths similar to that used in the current study;
however, these investigators required significantly lower stress values
to obtain these sarcomere lengths. Consequently, measured values of
k were also lower than those in the
present study. Garnier et al. (15, 24) examined cardiocytes impaled with glass microneedles, and Fish et al. (12) attached cardiocytes to
carbon fibers. Although these studies operated over a sarcomere length
of 1.8-2.2 µm, stress values approximated 0-1
kN/m2. When Eq. 7 is used to examine their cardiocyte stress vs. strain data, Garnier et al. (15, 24) and Fish et al. (12) found values of
k = 13.5 ± 1.2 and 10.07 ± 2.14, respectively. Both stress and values of
k obtained from Eq. 7 were significantly lower than those found in the
current study. In fact, these values were similar to those obtained by
Tarr et al. (39-44) using frog atrial cells, which are far more
compliant than mammalian cardiocytes. Although there are no obvious
explanations for these differences, Fish et al. (12) did not report
values of active force, and the active force values reported in the
experiments of Garnier et al. (15, 24) were very low. Furthermore,
Brady and Granzier (personal communications) have each speculated that
these differences may be based in part on the state of intracellular
titin in these preparations. The titin filament system is highly
sensitive both to chemical and to mechanical denaturation. For example,
cells may appear to have a normal sarcomere length at rest, but if they have been stretched beyond the yield point during preparation they can
be abnormally compliant. This may occur either because of the
cardiocyte isolation method or because of methods such as mechanical
skinning used subsequently to prepare the cardiocytes for study. In
addition, in mechanically or chemically skinned preparations there may
be substantial loss of cardiocyte mitochondria, leaving an ambiguous
cross section of stress-bearing elements, and thereby altering the
constitutive properties of the cell. Brady (personal communication)
also speculates that this difference may be related to variations
around the length of the PEVK region in the titin
filaments. As an example of the potential importance of
such variability, it is possible that frog atrial titin has a longer
PEVK section than mammalian cardiocytes, so that in terms of its
constitutive properties it resembles skeletal muscle.
Taken as a whole, the cardiocyte stiffness data presented in the
current study have many parallels with data from other studies using
very different techniques. Furthermore, as shown in Table 3, there are
fascinating parallels between the current data and those from studies
examining myocardial stiffness in isolated muscle strips and in intact
left ventricular myocardium. Cardiac muscle is a composite material
consisting of cardiac muscle cells surrounded by a matrix containing
collagen fibrils, elastin, aminoglycans, and other proteins. In the
current study, we examined a composite material consisting of
cardiocytes surrounded by a carbohydrate agarose matrix. Studies in
isolated myocardium (8, 13) showed that the muscle can be stretched
sufficiently to produce sarcomere stretch within the cardiocyte over a
physiological range of sarcomere lengths from 1.8 to 2.2 µm by
applying stress to the myocardium over a range of 0 to 10 kN/m2. When myocardial stress vs.
strain data obtained from such experiments were fit to
Eq. 8,
k 
10 (8, 13). Studies examining
myocardial stress vs. strain in intact left ventricular myocardium
yielded similar results (10, 21, 23, 31, 35, 45, 50, 56, 57). In these
studies of the intact left ventricle, myocardial strain ranged from 0 to 6% during diastole, a time during which myocardial stress ranged
from 0 to 5 kN/m2, and when these
myocardial stress vs. strain data are fit to Eq. 8, k = 10-15.
In the current study, the composite consisting of cardiocytes
surrounded by a carbohydrate agarose gel matrix had characteristics similar to those of the myocardial composites of isolated muscle and
intact ventricle, in that cardiocytes within the agarose gel were
stretched over similar sarcomere lengths as those seen in muscle by
applying comparable levels of stress to the gel. As shown in Fig. 7,
when the gel was stretched 10-15%, cardiocytes within the gel
increased their sarcomere lengths from 1.8 to 2.2 µm. The stress
applied to the gel required to produce this cardiocyte stretch was
0-10 kN/m2, a range similar
to that used in isolated muscle or intact myocardium to produce a
similar range of cardiocyte sarcomere stretch. These parallels between
the agarose gel and myocardial data suggest that both within the muscle
and within the agarose gel the cardiocyte may be stiffer than the
matrix in which it is embedded. That is, during a protocol that
resulted in an increase in sarcomere length from 1.8 to 2.2 µm, the
stress on the cardiocyte was 0-40
kN/m2, whereas the stress on the
gel was one-fourth this value, i.e., 0-10
kN/m2. Thus, for any given stress,
the strain on the agarose gel was two to three times greater than the
strain in the cardiocyte. The data presented in the current study are
by no means definitive, and the issue of relative stiffness of the
cardiocyte and of its surrounding extracellular matrix remains
controversial. Furthermore, it is clear that the extracellular matrix
contributes to myocardial stiffness both in normal and in pathological
myocardium. However, whether and to what extent the extracellular
matrix selectively alters the passive elastic spring or the viscous
damping properties of the myocardium has not been adequately defined.
In addition, the relative contribution either of the extracellular
matrix or of the cardiocyte to myocardial constitutive properties must
await future studies.
Methods of Measuring Cardiocyte Stiffness
As discussed above, a number of investigators (3-7, 9, 12,
15-17, 24, 25, 29, 33, 36, 39-44, 46-48) have
successfully attached cardiocytes to an apparatus capable both of
controlling force or length and of assessing stress, strain, and
stiffness. However, although each of these methods provides useful
information, each has specific limitations that make them difficult to
apply to the issues we wanted to address both in this and in future studies, i.e., defining the constitutive properties of normal and
abnormal cardiocytes. In addition to avoiding some of these limitations, the gel stretch method allowed selective assessment of the
passive elastic spring, viscous damping, and the effects of calcium
that were not possible with previous techniques. Thus, although there
was concordance between previous and current studies in some portions
of the data, there were differences in other respects. For example, a
major limitation in attaching an intact cardiocyte to a force or length
transducer is that the sarcolemma is extremely sensitive to applied
stress (4). Cardiocytes can be held between concentric double
micropipettes using suction and barnacle cement; however, the forces
used to attach the cardiocyte to the double micropipettes (10-15
mg) may be enough to alter cardiocyte integrity, biosynthetic function,
and the viscoelastic properties of the cell. This may be especially
true in abnormal cells. Cardiocytes can also be attached to glass
microneedles using urethan foam insulant (16, 17, 36, 46); however, as
many as 75% of the cell attachments using this method are of poor
quality, or the cardiocytes are damaged during attachment such that
these cells must be excluded from study. Some of these experimental
models require the use of detergent-skinned preparations, a process
that in and of itself could alter the constitutive viscoelastic properties of cardiocytes. These facts make it difficult to compare normal vs. abnormal cardiocytes and to detect, in an in vitro setting,
those abnormalities that were present in vivo. These limitations led us
to develop the gel stretch method wherein cardiocytes are embedded in
an agarose matrix that protects the sarcolemma from potentially harmful
effects of direct cardiocyte attachment. The gel stretch method does
not require direct cardiocyte attachment to a force or length
transducer, and the force is applied along the entire cardiocyte
length. Our data show that cardiocytes embedded in agarose remain
electrically, mechanically, physiologically, and morphologically intact
and retain normal biosynthetic properties. Mechanical response to
electrical stimulation is a complex physiological process that requires
many cellular properties, including the sarcolemmal membrane, the
transmembrane receptors and channels, the sarcoplasmic reticulum, and
the myofilaments, to be intact and functioning normally. This is true
to an even greater extent when biosynthetic processes such as protein
synthesis are considered.
To define the constitutive properties of normal and abnormal
cardiocytes, methods that mimic the in vivo environment of the cardiocyte must be used. We believe that there are a number of advantages to the gel stretch method not shared by other techniques, which allow it to reproduce the in vivo setting more closely. Studies
have shown that the constitutive properties of cells are contact
dependent (52, 53). Cardiocytes embedded in agarose are surrounded by a
matrix that influences the entire surface of the cardiocyte rather then
just the portion of the cardiocyte attached at two ends. Within the
agarose gel force is applied throughout the cell length, cardiocytes
are calcium tolerant, and sarcolemmal membranes remain intact, all of
which recreates more closely the environment under which the cardiocyte
lengthens in vivo. In life, the cardiocyte is embedded within the
myocardium. As the length, diameter, and thickness of this tissue
changes, so does the cardiocyte shape change in a parallel fashion.
Similarly, a cardiocyte embedded within a gel will change in shape in
parallel with the gel itself. There is evidence that intracellular
calcium concentration and calcium homeostasis may alter viscoelastic
properties of isolated cardiocytes (20, 37, 38). This may be true to an
even greater degree in an abnormal cardiocyte, in which many components
of calcium homeostasis may be altered and which may in turn alter
myofilament activation and the rate of cross-bridge cycling (1, 2, 30,
34). The active state of the myofilaments contributes significantly to
the viscoelastic properties of the cardiocyte (20, 37, 38). Therefore,
the ability to study cardiocytes in medium containing physiological
calcium concentrations is a major advantage of the gel stretch method.
There are other technical differences that favor the use of the gel
stretch method. In some techniques the measurement of stress and strain
and the differentiation between passive spring and viscous damping
properties present certain difficulties. When highly sensitive force
transducers with a surface tension of ~10 mN are used, the force
transducer produces substantial noise levels because the cardiocyte
forces of interest are one to two orders of magnitude below this level
(4). To obtain accurate mechanical data, the cardiocyte was driven with
sinusoidal length perturbations, and the dynamic stiffness was measured
as a function of length (5). Therefore, to obtain cardiocyte stiffness,
the stiffness-sarcomere data were fit by an exponential relationship,
and then the conversion to stress was made. In addition, some methods
were subject to errors made in length measurements. During length or
force perturbations, the cell may move within the mounting pipettes,
making accurate assessment of cell length difficult (3-6). Other
methods (16, 17, 36, 46) raised similar concerns. In contrast, the gel stretch method allowed direct measurement of force applied to the gel.
It is true, however, that our cardiocyte stres
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Abstract
Introduction
