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Am J Physiol Heart Circ Physiol 274: H2188-H2202, 1998;
0363-6135/98 $5.00
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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

    ABSTRACT
Top
Abstract
Introduction
Methods
Results
Discussion
References

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 [sigma  = A/k(ekepsilon  - 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

    INTRODUCTION
Top
Abstract
Introduction
Methods
Results
Discussion
References

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.

    METHODS
Top
Abstract
Introduction
Methods
Results
Discussion
References

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.


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  		Fig. 1.   Schematic drawing of mold used to form agarose gel (top) and agarose gel itself (bottom).

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.

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 (sigma ) = force/area
&sfgr; = (L) (gf) (<IT>g</IT>) (kg/1,000 g)/(G-CSA) (233.57) (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 (epsilon ) was calculated as nominal or engineering strain
&egr; = (<IT>L</IT><SUB>n</SUB> − <IT>L</IT><SUB>i</SUB>)/<IT>L</IT><SUB>i</SUB> (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 · min-1 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
&sfgr; = <IT>C</IT><SUB>1</SUB>&egr; + <IT>C</IT><SUB>2</SUB>&egr;<SUP>2</SUP> (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 [sigma  = (51 kN/m2)epsilon  + (343 kN/m2)epsilon 2] and the cardiocyte (sigma  = C1epsilon  + C2epsilon 2). 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 (sigma ) vs. cardiocyte strain (epsilon ) predicted by FEM. With each iteration, constants C1 and C2 were adjusted until epsilon  values from model matched epsilon  values from experiment. Note that both here and in Figs. 5-8, epsilon  is by definition a unitless value (µm/µm), whereas sigma  is expressed as kN/m2.

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 (dsigma /depsilon ) was calculated at a specific cardiocyte strain. At strains of 1, 5, and 8%, dsigma /depsilon 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 (sigma ) is equal to the force per cross-sectional area of the cell (C-CSA)
&sfgr; = F/ (C-CSA) (4)
Strain (epsilon ) is equal to the distance moved by the cell divided by the initial length of the cell
&egr; = <IT>D</IT>/<IT>L</IT><SUB>i</SUB> (5)
Thus energy imparted to the cardiocyte during an increase in force can be calculated as (Fig. 4D)
E (N · m) = area (N/m<SUP>2</SUP>) × C-CSA (m<SUP>2</SUP>) × <IT>L</IT><SUB>i</SUB> (m) (6)
The average C-CSA was 2,865 µm2, or 2.865 × 10-9 m2. The average distance was 10.88 µm, or 1.08 × 10-5 m. The average initial length was 1.36 × 10-4 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 (dsigma /depsilon ). 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.

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
&sfgr; = <IT>Ae</IT><SUP><IT>k</IT>&egr;</SUP> (7)
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
&sfgr; = <IT>A</IT>(<IT>e</IT><SUP><IT>k</IT>&egr;</SUP> − 1) (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
&sfgr; = <IT>A</IT><SUP><IT>k</IT></SUP>/<IT>k</IT>(<IT>e</IT><SUP><IT>k</IT>&egr;</SUP> − 1) (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.

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 protein-1 · h-1) was calculated by dividing the incorporation of Phe into protein [disintegrations/min (dpm) · mg protein-1 · h-1] 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.

    RESULTS
Top
Abstract
Introduction
Methods
Results
Discussion
References

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 sigma  = (51 kN/m2)epsilon  + (343 kN/m2)epsilon 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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  		Table 1.   Constitutive properties of agarose gel

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, dsigma /depsilon 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, dsigma /depsilon was 464 kN/m2, the energy gained was 5.4 × 10-10 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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  		Table 2.   Constitutive properties of normal cardiocytes

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.

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 × 10-10 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 × 10-10 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.

From the cardiocyte stress vs. strain relationship shown in Fig. 9B, dsigma /depsilon 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. dsigma /depsilon at 0.08 was 382 kN/m2, the energy gained was 5.04 × 10-10 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
Top
Abstract
Introduction
Methods
Results
Discussion
References

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.

                              
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  		Table 3.   Cardiocyte stress, strain, and stiffness: Comparison with other investigators

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 approx  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 stress measurement required the use of the FEM. Nonetheless, the gel stretch method provides an accurate and definable force. In addition, length errors did not occur using the gel stretch technique because the entire cell was visible throughout the procedure. Finally, use of protocols A-C allowed viscous damping to be measured and to be differentiated from passive elastic stiffness and myofilament activation.

The presence of viscous damping in normal cells is supported indirectly by Brady (5) and Granzier and Wang (17). Although no attempt was made to differentiate viscous or velocity-dependent parameters from passive stiffness, these studies clearly suggested the presence of viscous damping. Brady (5) and Granzier and Wang (17) showed that a sequence of length increases and decreases generated an open loop in the stiffness-length relationship, reflecting the presence of mechanical hysteresis in these cells. The presence of this loop clearly demonstrated that the cardiocyte has viscous properties. These data are concordant with those in the current study.

Finally, one technical difference that favors the use of the gel stretch method is that this technique can be applied to a large number of cells from a given cell isolation or animal. In other techniques the mechanical properties of only small numbers of cells can be studied (3-7, 9, 15-17, 24, 25, 29, 33, 36, 39-44, 46-48). Therefore, these techniques cannot be used to correlate mechanical properties with biochemical or biosynthetic properties of normal or abnormal cells. With the use of the gel stretch technique, larger numbers of cells can be studied and it might be possible to correlate mechanical and biochemical or biosynthetic properties. Once cardiocytes are embedded in an agarose matrix, the cells are very stable. Cardiocytes remain responsive to electrical stimulation, protein synthesis rates are normal, morphometry and sarcomere definition are unchanged, and the cells tolerate physiological calcium concentrations while remaining quiescent.

In conclusion, this study shows that the gel stretch technique provides accurate measurements of cardiocyte constitutive properties. With the use of this technique, a definable stress can be applied to the cardiocyte, resulting in a measurable change in cellular strain. These measurements allow quantitative assessment of the passive elastic spring and viscous damping. The gel stretch method should be useful in determining whether and by what mechanisms pathological processes alter the constitutive properties of isolated cardiocytes.

    ACKNOWLEDGEMENTS

The authors thank Mary Barnes and Valerie Young for technical assistance and Bev Ksenzak for help in preparing this manuscript.

    FOOTNOTES

This study was supported by the research service of the Department of Veterans Affairs (G. Cooper IV and M. R. Zile), by National Heart, Lung, and Blood Institute Grant P01-HL-48788 (G. Cooper IV and M. R. Zile), by the National Aeronautics and Space Administration (M. R. Zile), and by the Bioengineering Alliance of South Carolina (V. Gharpuray and M. R. Zile).

Address for reprint requests: M. R. Zile, Div. of Cardiology, Medical Univ. of South Carolina, 171 Ashley Ave., Charleston, SC 29425-5799 (E-mail: zilem{at}musc.edu).

Received 12 August 1997; accepted in final form 24 February 1998.

    REFERENCES
Top
Abstract
Introduction
Methods
Results
Discussion
References

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