Abstract
Thomason, Donald B., Otis Anderson III, and Vandana Menon.Fractal analysis of cytoskeleton rearrangement in cardiac muscle during headdown tilt. J. Appl. Physiol. 81(4): 1522–1527, 1996.—Headdown tilt by tail suspension of the rat produces a volume, but not pressure, load on the heart. One response of the heart is cytoskeleton rearrangement, a phenomenon commonly referred to as disruption. In these experiments, we used fractal analysis as a means to measure complexity of the microtubule structures at 8 and 18 h after imposition of headdown tilt. Microtubules in whole tissue cardiac myocytes were stained with fluorescein colchicine and were visualized by confocal microscopy. The fractal dimensions (D) of the structures were calculated by the dilation method, which involves successively dilating the outline perimeter of the microtubule structures and measuring the area enclosed. The headdown tilt resulted in a progressive decrease in D(decreased complexity) when measured at small dilations of the perimeter, but the maximum D (maximum complexity) of the microtubule structures did not change with treatment. Analysis of the fold change in complexity as a function of the dilation indicates an almost twofold decrease in microtubule complexity at small kernel dilations. This decrease in complexity is associated with a more Gaussian distribution of microtubule diameters, indicating a less structured microtubule cytoskeleton. We interpret these data as a microtubule rearrangement, rather than erosion, because total tubulin fluorescence was not different between groups. This conclusion is supported by Factin fluorescence data indicating a dispersed structure without loss of actin.
 microtubules
 actin filaments
 volume load
 myocyte
 colchicine
 complexity
headdown tilt and weightlessness cause a significant increase in central venous pressure with little or no increase in arterial pressure (8, 9, 14, 16). This shift of blood presents a volume load on the heart, initially increasing enddiastolic volume and stretching the myocytes. At the ultrastructural level, the myocytes exhibit alteration of their microtubule and cytoskeletal structure (3,11, 15). A quantitative analysis of cytoskeletal structural alteration is not straightforward, however, in part because of the complex structure of the cytoskeleton. Thus any alteration of the cytoskeleton has been termed “disruption,” despite the likelihood that the rearrangement represents an adaptive restructuring to the volume load.
Any macromolecular structure will have a tendency to exhibit repetition of the structure due to the limited number of interactions in which its constituent subunits can participate. This repetition suggests the possibility of fractal analysis to measure complexity. Fractal geometry provides a means for quantitatively analyzing structures in terms of their fractal dimension, a statistic describing the degree of complexity of the structure (7). Thus we can statistically test the effect of a treatment on the complexity of a macromolecular structure by calculating the fractal dimension, providing a probabilistic accounting of the effects of the treatment as support for the qualitative description.
In this paper, we apply the technique of fractal analysis to calculate a fractal dimension for the microtubule cytoskeleton within rat cardiac myocytes as the myocytes respond to the hemodynamic load of headdown tilt. We will show that the myocytes exhibit a rearrangement of their cytoskeleton within 18 h that is nearly a twofold decrease in complexity. Because the cytoskeleton is important for both structural and biochemical integrity of the myocyte, these data provide insight into the adaptive response of the heart to volume loading.
MATERIALS AND METHODS
Animal care. Female SpragueDawley rats (200–250 g) were used for all experiments. Animals were housed in light and temperaturecontrolled quarters where they received food and water ad libitum. Animals were randomly assigned to control or experimental groups. Control animals were housed and handled identically to the experimental animals. Animals in the headdown suspension group received a tailtraction bandage, as previously described (20). The experimental animals were placed in a suspension cage where they had free access to food and water but were prevented from placing their hind limbs on the floor of the cage; the angle of headdown tilt was ∼30°, depending on posture and movement of the animal. All procedures were approved by the Animal Care and Use Committee of the University of Tennessee, Memphis.
Tissue preparation. After 8 or 18 h of tail suspension, control and experimental animals were anesthetized with ketamine (40 mg/kg ip), a laparotomy was performed to expose the vena cava, and the animals were infused with icecold phosphatebuffered saline (PBS) containing 4% paraformaldehyde. After 10 min, the hearts were removed, and the right atrium and ventricle free walls were removed and postfixed in 1% glutaraldehyde in PBS. Samples were stored in sterile PBS at 4°C.
Fluorescent microscopy. The right atrial samples were permeabilized for 30 s in acetone at −20°C and stained 30 min with 10 μM fluorescein colchicine (Molecular Probes, Eugene, OR) in PBS for microtubules and in a 1:40 dilution of rhodamine phalloidin (Molecular Probes) in PBS for Factin, washed with PBS, and placed in a hanging drop well slide such that the plane of focus was perpendicular to the transmural axis. Confocal fluorescent images from random locations in the tissue were taken on a BioRad MRC 1000 microscope (BioRad, Hercules, CA) using a ×20 objective and plane thicknesses of 2.5 μm; a twofold variation in optical magnification was obtained by changing image magnification at the ocular. Images measured 768 × 512 pixels. Single focal planes were chosen for analysis in which ∼75–80% of the field of view was occupied by microtubules. The data were stored for analysis with the NIH Image program. Representative images are shown in Fig.1.
Image analysis. The confocal images were analyzed by using the dilation method of capacity fractal dimension analysis; the NIH Image package provides a macro for this analysis and the necessary software (available at ftp://zippy.nimh.nih.gov/pub/nihimage) to prepare the image for analysis as follows. Single focal planes of the confocal images were first inverted to provide a dark image of the microtubules on a light background (Fig. 2 A,left). This image was converted to a binary image (black and white, no gray) containing only the outlines of the microtubules by first convolving the image with the 13 × 13 pixel “hat filter” (provided with NIH Image) to detect the edges of the microtubule filaments and then converting the image to a binary outlined image (Fig.2 A,middle). The macro for fractal analysis by the dilation method calculated the area (A) and perimeter for successively larger kernel sizes (k) used to define the outline of the microtubules (shown for the first three dilations in Fig. 2 A,right). From these data, the slope (S_{k}) of log(A) vs. log(k) for each successive pair of kernel sizes was calculated, and the fractal dimension isD_{k} = 2 − S_{k}. The fold change in microtubule complexity of each sample with headdown tilt is the ratio of the fractional portions of D. Thus, for eachD _{k} in control and treatment groups, the fold change is the ratio calculated from the fractional portions of each sampleD _{k} and the control mean D_{k} .
To explore the significance of “edge effects” arising from finite image size and the variable degree to which microtubule images may occupy the field, we tested the dilation method on the Koch “box” (Fig. 2 B), a purely fractal structure having a theoretical fractal dimension of log(7)/log(3) (∼1.771) (7). Owing to the finite pixel structure of the image, the calculated dimension using the dilation method is 1.88; an alternative method of calculating the fractal dimension by box counting (6) also yields a fractal dimension of 1.88. When the Koch box is partially moved out of the image so that the remaining portion is touching the edge (Fig. 2 B,right), there is a small increase in the calculated fractal dimension to 1.89.
Both the mean and the distribution of the fluorescence intensity from microtubule bundles or actin filaments was measured in a 100 × 100 pixel area containing structures in the plane of focus. The distribution of the fluorescence intensity was obtained by averaging the sample distributions in the 10,000 square pixel area. The mean intensity was obtained from the weighted averages (the product of the number of pixels and the intensity of the pixels) for each of the samples.
Statistical analyses. Differences between groups for fractal dimension in the region of selfsimilarity [i.e., linearity of log(A) vs. log(k)] were determined by regression analysis. Differences between groups in fractal dimension over the entire range of k and in the fold change in complexity were determined by twoway analysis of variance and the KolmogorovSmirnov test for differences in distributions. Differences between groups in microtubule diameter distribution statistics (median, kurtosis, skewness) were determined by calculating the tstatistic (18). Differences were considered significant ifP < 0.05.
RESULTS
The confocal microscope images of Fig. 1 show the typical alteration of the microtubule cytoskeleton observed within the first 18 h of headdown tilt. Multiple planes of focus were combined into single images in Fig. 1, so that the depth of the tissue was visualized (single focal planes were used for the quantitative analysis). There are two immediate observations of the microtubule organization: less distinct branching and a restructuring of the large microtubule bundles from the long axis of the myocytes to a more evenly distributed orientation. The total amount of tubulin detectable by the fluorescein colchicine was not different between treatment groups [70 ± 70 vs. 80 ± 33 (SE) fluorescence units, on a scale of 0–256, for control and 18h headdown tilt, respectively;n = 6].
The perimeters of the microtubule structures in the images were dilated with kernels of successively larger size to outline the structures (analogous to drawing the outline with pens of increasingly broader tips); the area enclosed by the successively dilated outline was measured as a function of the kernel size, as demonstrated in Fig.2 A. The region of greatest linearity (indicative of greatest selfsimilarity) occurs at perimeter kernel diameters between 5 and 20 μm, yielding a relatively constant fractal dimension (Fig. 3). Regression analysis of the region of linearity between kernel diameter and the area enclosed detects significant regression but does not indicate a significant difference between the slopes (D) in this region. As it happens, this is the region of greatest fractal dimension. Therefore, we conclude that the maximum complexity is not different between groups. However, the distribution of fractal dimension as a function of kernel diameter was significantly different between groups, as outlined further in the following paragraph.
Twoway analysis of variance of the fractal dimension statistic (kernel diameter vs. group) indicated a significant difference between groups and a significant interaction between kernel diameter and the groups. The nature of the difference is easily observed from the plots of the fold change in complexity shown in Fig. 4. The fold change in microtubule complexity is the ratio of the fractional portions of fractal dimension (seediscussion). A significant difference in the distribution of the fold change in complexity vs. kernel diameter was detected. The majority of the difference between groups appeared as a timeprogressing decrease in complexity at small kernel diameters (Fig. 4). Possible causes of decreased complexity may be the changes in microtubule diameter and changes in branching. Analysis of microtubule diameter in control and 18h headdown tilt hearts indicates a significant change in diameter distribution (Fig.5). Although there is no difference between groups in the median diameter, the microtubule diameter distribution in 18h headdown tilt hearts exhibits a significant decrease in kurtosis and skewness (P < 0.05), indicating a shift toward a more Gaussian distribution.
As a second indicator of cytoskeleton rearrangement, rhodamine phalloidin staining of the hearts provides a measure of Factin structure (both cytoskeletal and sarcomeric). As shown in Fig.6, there is less intense fluorescence spread over more pixels in the hearts from the 8h headdown tilt group of animals (P < 0.05). Although this measure cannot distinguish sarcomeric from cytoskeletal actin, this decrease in Factin fluorescence intensity occurs despite a lack of change in total Factin fluorescence (Fig. 6) and actin protein during this short time period (unpublished observation; Ref. 20).
DISCUSSION
The fact that a change in cardiac functional demand is accompanied by changes in myocyte cytoskeletal organization indicates that the cardiac cytoskeleton is dynamic, adapting to conditions in an attempt to maintain a viable cell (1, 3, 5, 11, 15). This dynamic and presumably adaptive restructuring is commonly termed “disruption” and its description is usually limited to qualitative terms. In this paper, we have provided a quantitative fractal analysis of cardiac myocyte cytoskeleton restructuring in a model known to cause cytoskeleton rearrangement.
At the lightmicroscopic level, it is easy to discern a rearrangement of the cardiac myocyte microtubule cytoskeleton in response to the volume load of headdown tilt (Fig. 1). That this is a dynamic process is evidenced by the fractal analysis indicating progression of changes over at least an 18h period (Figs. 3 and 4). We hesitate to call this rearrangement a disruption because of the following observation. In many sections, chosen at random, it appeared as if a very rapid reorientation of the microtubules takes place such that the normally distinct preferential orientation of the microtubule bundles along the long axis of the myocytes becomes less distinct, as does the microtubule branching. The altered orientation of the microtubules may be either a dynamic rearrangement of the bundles or an erosion of the existing bundles without replacement. Because there is no change in the amount of detectable tubulin and the area encompassed by the image of the microtubule structure does not decrease in the volumeloaded hearts (as determined from the dilation measurements used to calculate the fractal dimension), we conclude that the change in structure represents a dynamic rearrangement rather than erosion. This is supported by the analysis of the Factin structure: a significant decrease in Factin structure occurs (more pixels of less intensity; Fig. 5) despite the lack of a change in total Factin fluorescence and actin protein during the period of headdown tilt (12, 13, 20).
A selfsimilar structure, i.e., a structure possessing a scale invariance of complexity over a range of kernel sizes used to dilate the perimeter (analogous to changing magnification), is determined by a linear region of the log(A) vs. log(kernel diameter). In our experiments, the region of greatest linearity (constant fractal dimension) occurs at the larger kernel sizes (Fig. 3). Although the similarity of the microtubule structure is expressed over this range of kernel diameters, the volumeloaded hearts do not exhibit a significant difference in fractal dimension in this range, and thus the fractal dimension of the structure is statistically the same in this range of kernel diameters. Nonetheless, when we consider the fractal dimensions calculated for each successive pair of kernel diameters, there is a significant pattern difference in the volumeloaded hearts (Fig. 3). The nature of this difference is easily seen from the calculation of the fold change in fractal dimension (Fig.4). The fractional part of the fractal dimension is calculated from the slope of log(A) vs. log(kernel diameter), and thus is the ratio of two logarithms. As a result, the ratio of the fractional parts of the fractal dimensions (i.e., the ratio of the slopes) is the fold change in complexity (17). From the data of Fig. 4, we conclude that there is a significant decrease in the complexity of microtubule structure in the myocytes from volumeloaded hearts when the outline of the microtubules is described by kernels of small diameter. Roughness of the microtubule outline may be caused by variation in microtubule bundle thickness, e.g., microtubules that appear thick in some control regions (Fig. 1) may thin in other regions and thus appear mathematically rough; microtubule bundles of more uniform thickness would exhibit less of this roughness. Such a possibility is supported by the analysis presented in Fig. 5. Although microtubule median thickness is not different between the control and 18h volumeloaded hearts, the latter exhibit significantly less deviation from a Gaussian distribution of microtubule thicknesses. These data indicate a less structured, more random distribution of microtubule thicknesses in the volumeloaded hearts that may be indicative of the rearrangement. Another way that decreased complexity could occur is through decreased branching, although at present we do not have evidence supporting this mechanism. Both mechanisms likely occur, however. Regardless, the microtubules from the volumeloaded hearts exhibit an apparent timedependent decrease in complexity when the width of the outline border is small.
What is the physiological significance of the cytoskeleton rearrangement? We believe that one effect of the cytoskeleton rearrangement may be alteration of protein synthesis. There is an emerging body of evidence indicating an integral role of the cytoskeleton in protein synthesis (2, 4, 10). We have previously reported that the volumeloaded heart exhibits a rapid decrease in protein synthesis rate (12, 13, 19). It is possible, therefore, that part of the protein synthesis adaptation to the volume load, possibly as an energyconserving mechanism to the increased oxygen consumption of stretch, is mediated through cytoskeleton rearrangement. In addition to providing an intracellular framework to which organelles and macromolecular complexes may attach, the cytoskeleton also provides mechanical support to the cell. We observed a rearrangement of the cytoskeleton such that it appeared to be a more evenly distributed network in response to the stretch of volume load. A putative reason for this rearrangement may be to evenly distribute the mechanical stress from the increased stretch associated with the volume loading. Indeed, failing myocardia also show “disruption” of the cytoskeleton (5). Therefore, although cytoskeleton rearrangement has been termed “disruption” and carries with it the connotation of damage, the rearrangement is probably more significant as a biochemical and mechanical adaptive response.
In summary, we present data indicating myocardial cytoskeleton rearrangement with the volume loading of headdown tilt. The qualitative observation of the rearrangement is supported statistically by calculating the fractal dimension of the microtubule network as a measure of complexity.
Acknowledgments
The authors are grateful to Laura Malinick for her assistance with graphics and to Sharon Frase and Dr. Andrea Elberger for their assistance with the confocal microscopy.
Footnotes

Address for reprint requests: D. B. Thomason, Dept. of Physiology and Biophysics, Univ. of Tennessee Health Science Center, Memphis, 894 Union Ave., Memphis, TN 38163 (Email: thomason{at}physio1.utmem.edu).

This work was supported by National Institutes of Health Grants AR40901 (to D. B. Thomason), AHA92–013800 (to D. B. Thomason), and HL0774601.
 Copyright © 1996 the American Physiological Society