INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

THE DEVELOPMENT OF HIGH-RESOLUTION microsphere technology has advanced the study of regional blood flow distribution within organs (1, 7). The distribution of pulmonary blood flow, for example, once believed to be primarily influenced by gravitational forces, when examined with these new techniques is found to be quite heterogeneous within isogravitational planes (11). The branching pulmonary vascular tree is fractal by nature, and, therefore, fractal methods have emerged as an effective way to describe regional blood flow distribution.

Glenny and Robertson (11) showed that regional distribution of pulmonary blood flow in dogs is fractal and can be characterized by the fractal dimension. Described first by Mandelbrot (23), fractal dimension can be determined from a log-log plot (Fig. 1) of the coefficient of variation (CV) as a function of increasing piece size. If a system is fractal, this plot will have a constant slope. Fractal dimension is equal to 1  slope of this plot, and, therefore, the more random the relationship among adjacent pieces, the higher the fractal dimension value. With this approach to data analysis, fractal dimension approaches 1 as regional perfusion becomes more spatially correlated (i.e., neighboring piece will have more similar flows), whereas a fractal dimension of 1.5 defines a totally random system. Unlike the CV, the fractal dimension does not change with changes in spatial resolution (i.e., fractal dimension is a scale-independent measure of scale-dependent heterogeneity). Values of fractal dimension have been determined for pulmonary blood flow distribution in several species (dogs 1.09 ± 0.02; sheep 1.14 ± 0.09; Refs. 4, 11) and were noted to remain constant with increasing pulmonary blood flow in an in situ, pump-perfused sheep model, despite a decrease in CV at higher flows (4). Additionally, no change in fractal dimension was observed from rest to exercise in dogs (27). We hypothesize that fractal dimension, because it is determined by a fixed vascular branching pattern, should remain constant regardless of changes in total pulmonary blood flow.

View larger version (23K): [in this window] [in a new window]   Fig. 1.   "Fractal plot" ln-ln plot of cluster size vs. coefficient of variation (CV) of pulmonary blood flow for a representative horse (horse 1) at rest (A) and with 3 levels of exercise (trot, B; canter, C; gallop, D). Fractal dimension is determined as 1  slope of regression line. Vertical bars represent two times standard error. X symbols in C represent data from two simultaneous microsphere injections. Each cluster represents n number of 1.3-cm3 core samples.

In this study we examine the effect of extremely large changes in total pulmonary blood flow on the fractal dimension, as well as local spatial correlation, of pulmonary blood flow distribution in an in vivo, unanesthetized horse model. This model is important and unique in that it provides incremental and very large increases in pulmonary blood flow via graduated exercise, allowing data to be gathered over an enormous range of pulmonary blood flow while maintaining the natural vascular milieu with its local and organwide vascular autoregulatory mechanisms intact.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

All methods and animals were approved by the University of Washington (Seattle) and Kansas State University (Manhattan) Animal Care Committees and were in accordance with the American Association for Accreditation of Laboratory Care Animals statement on the care of animals. Before the study, four Thoroughbred geldings (422-500 kg) were trained on a high-speed equine treadmill for 4 wk, and their maximal oxygen consumption (O_{2 max}) was determined. Each horse was prepared for study and monitored as previously described in detail (2, 14). Briefly, a left transverse facial artery catheter and a left internal jugular artery catheter were placed for blood-gas sampling and microsphere injection, respectively. A pulmonary artery catheter was inserted via a right internal jugular vein introducer for withdrawal of reference samples. Two additional catheters, one with a pressure transducer, the other with a thermistor, were placed in the right internal jugular vein and advanced into the pulmonary artery to measure pulmonary artery pressure and core temperature, respectively. Surface electrodes were applied for heart rate determination, and each horse was fitted with a safety harness.

Exercise protocol. Measurements were made at rest (standing quietly at a 3° incline) and at three progressively more strenuous exercise levels based on previously determined O_{2 max}. The treadmill speed was increased after resting measurements were obtained to produce a O₂ ~34% of O_{2 max} (trot). Measurements were repeated after a steady-state oxygen consumption (O₂) was achieved. Subsequent measurements were made after the treadmill speed was increased to produce a steady-state O₂ ~59% of O_{2 max} (canter) and a O₂ ~90% of O_{2 max} (gallop), in which the final set of measurements was recorded.

Physiological measurements. Complete details of the physiological measurements were outlined previously (14). Briefly, O₂ and carbon dioxide production (CO₂) were measured by using a biased-flow technique through a loose-fitting mask strapped to the horse's head. O₂ and CO₂ concentrations of expired gas were measured with a mass spectrometer (model 1100, Perkin-Elmer, Pomona, CA) after the gas passed through a mixing chamber. Exhaled airflow was measured via a pneumotachometer (model MP-45, Validyne Engineering, Northridge, CA). Arterial blood-gas determinations were made with a Nova blood-gas analyzer calibrated with standard gases and buffers and corrected to the measured temperature in the pulmonary artery with horse-specific correction factors. Oxygen content was measured from anaerobically obtained arterial and mixed venous blood samples with a Lex-O₂-Con (model TL, Hospex, Chestnut Hill, MA). Surface electrodes monitored heart rate, and a transducer-tipped catheter measured pulmonary arterial pressure. Cardiac outputs were determined by the Fick equation. Hematocrit measurements were made by using the microhematocrit method, and lactate concentration of mixed venous blood was measured with a lactate analyzer (model 23L, Yellow Springs Instruments).

Pulmonary blood flow measurements. Measurements of pulmonary blood flow distribution were made at each exercise level with 40-65 million 15-µm fluorescent microspheres (blue-green, yellow-green, orange, red, or crimson; Molecular Probes, Eugene, OR) injected via the left internal jugular vein over ~15 s. A single, different-color microsphere was used at each exercise level, and the order of colors used was picked at random for each animal. Injections occurred after a steady-state O₂ was achieved, and reference blood was simultaneously drawn during each injection from the pulmonary artery catheter at a rate of 60 ml/min, allowing blood flow calculations in milliliters per minute. A simultaneous injection during a single exercise level in each horse with a second-color microsphere (two different-colored microsphere aliquots mixed in a single syringe) was performed to estimate methodological error.

Lung processing. At the end of the experimental protocol, each horse was deeply anesthetized, and a tracheotomy was performed before exsanguination. After death, the pulmonary vasculature was flushed with normal saline, and the lungs were removed from the chest and inflated to 35 cmH₂O with warmed air and dried for 14 days. After drying, the lungs were placed in a box and surrounded with urethan foam such that in vivo isogravitational planes were parallel to the relevant box surface. Lungs were then sliced into 2.2-cm-thick coronal sections (16-21 per horse), and each section was systematically sampled by using a rigid X-Y grid. The grid was placed over each section, and core samples (1.3 cm³) were obtained at 2.3-cm intervals from the center of adjacent cores over the entirety of each lung section (Fig. 2). This produced from 1,621 to 2,503 pieces per horse after pieces consisting of >25% airway by volume (88-251 pieces per horse) were discarded. Spatial coordinates were noted for each piece, samples were soaked for 2 days in cellosolve acetate, and extracted fluorescence was measured with a fluorimeter (model LS-50B, Perkin-Elmer).

View larger version (157K): [in this window] [in a new window]   Fig. 2.   Photograph of a representative 2.2-cm-thick lung slice after all core samples were removed. Neighboring pieces are defined as those that were next to each other on sampling grid.

Fractal analysis. Fractal plots of pulmonary blood flow data for each exercise state were constructed by iteratively calculating the CV of blood flow for progressively larger piece sizes and plotting the logarithm of CV vs. the logarithm of piece size (Fig. 1). For each animal, we calculated the CV of the relative flow per piece, and then combined neighboring pieces into aggregates of size n_I and recalculated CV_I for 16 different aggregate sizes. For the larger aggregate sizes, CV_I exhibits higher variability in that the CV changes depending on which pieces are combined to form the aggregates. To reduce the variability of the CV of larger piece sizes, we estimated the CV repeatedly via a randomized algorithm to form aggregates. An aggregate center piece is chosen at random from all available lung pieces. Neighboring pieces are then combined to form an aggregate of desired size n_i around this center piece. Another center piece is then randomly chosen, and an aggregate around that center is formed in similar fashion. A graphic representation of this is shown in Fig. 3. This process is repeated until no more aggregates of the size n_i can be formed, and the CV of each aggregate is calculated. By repeating this algorithm L_I times, we obtained L_I CV measurements, which were then averaged to produce the mean CV_I used in the fractal dimension slope estimation.

View larger version (40K): [in this window] [in a new window]   Fig. 3.   Three-dimensional representation of clustering algorithm for determining fractal dimension in horse lungs (horse 1). Pieces consisting of 42 core samples (nI = 42) are shown, each represented by a different-colored sphere. A-F: progressive selection of 1-, 2-, 4-, 8-, 16-, and 32-piece clusters, respectively.

(1)

Spatial correlation. The spatial correlation as a function of distance over a three-dimensional space [_xyz(d)] was calculated within each lung, as previously described (6), by using Eq. 2

(2)

The parameter f represents the measured flow for a unit piece volume that varies over three-dimensional space and is defined at any region by f(x,y,z) where x  {x₁,x₂,x₃,···x_l}, y  {y₁,y₂,y₃,···y_m}, and z  {z₁,z₂,z₃,···z_n} are the Cartesian coordinates of that region. The l, m, and n are the dimensions of the space explored, and ₁ and ₂ are the mean of all values f(x, y, z) and f(x + x, y + y, z + z), respectively, that are used to determine (x,y,z). If the region (x + x, y + y, z + z) lies outside the defined space, the position (i, j, k) is not used in the calculation of (x,y,z). Thus the spatial correlation (x,y,z) is a measure of the mutual relationship between flow magnitudes at one position and a second position displaced from the first by a vector (x,y,z). Three-dimensional spatial correlations were then fit to Eq. 3

(3)

where distance d₀ = 2.3 cm. Coefficients a, b, and c were determined from the best fit to Eq. 3 at each exercise level by use of a weighted curve-fitting routine based on the number of paired regions for each distance (6)

(4)

where d_i was the distance between regions, n_i the number of pairs at distance d_i, n the total number of pairs compared in the entire data set, and r_i the sample correlation coefficient at distance d_i.

Statistical analysis. Fractal dimensions were analyzed for each horse at each exercise state via a two-way ANOVA; the two conditions of interest were exercise state and subject number. Statistical significance was set at P < 0.05 for all comparisons. A similar ANOVA model was used to compare the spatial correlations as characterized by the actual  value at the smallest realizable distance between lung pieces measured (2.3 cm) from Eq. 2 for each animal and exercise state.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Physiological measurements. All horses demonstrated comparable changes in response to exercise (2). Cardiac output increased over 10-fold with exercise, from a mean of 31 l/min at rest to a mean of 348 l/min at maximal exercise. This was accompanied by a marked increase in mean pulmonary arterial pressure (35 to 107 cmH₂O) and O₂ (4.0 to 133.9 ml · min¹ · kg¹). These and the other physiological measurements recorded are summarized in Table 1. Notably, the pulmonary artery pressure at rest did not significantly differ at the end of the experiments, after all four microsphere injections, from that seen before any microsphere administration (data not shown).

Fractal dimension. The blood flow data fit the fractal model well with an average R² value of 0.95 ± 0.032. A set of fractal plots from one horse is shown in Fig. 1. Fractal dimension values for each horse at each exercise state are shown in Fig. 4. Two-way ANOVA using subject number (i.e., identity of each horse) and exercise state as conditions of interest was conducted for the 20 fractal dimension values generated and is summarized in Table 2. Fractal dimension values varied significantly (P < 0.05) between horses and with exercise within a given horse. The interaction term (horse + exercise state) is also significant, indicating that the change in fractal dimension with exercise is different from horse to horse. This is largely due to the extreme intersubject variability of the fractal dimension at rest. These variations due to exercise and animal-to-animal comparisons are much larger than those seen in the simultaneous, duplicate microsphere injections within the same horse (Fig. 4).

View larger version (12K): [in this window] [in a new window]   Fig. 4.   Trends in fractal dimension during 4 different exercise states in each of 4 horses: , horse 1; , horse 2; , horse 3; , horse 4. Repeated measures in a given horse are represented by separate data points.

Spatial correlation. The spatial correlation of flow as a function of distance (d) was determined for each horse at each exercise state. A representative plot of the spatial correlation in one horse is shown in Fig. 5, where the line represents the weighted fit of (d) to Eq. 3. The values for the spatial correlation of flow between adjacent pieces, (2.3 cm), for each horse and exercise state are presented in Table 4.

View larger version (30K): [in this window] [in a new window]   Fig. 5.   Spatial correlation of pulmonary blood flow plotted as a function of distance between pieces. A: rest; B: trot; C: canter; D: gallop. A weighted curve was fit to data on the basis of number of pairs compared at each distance and described by Eq. 3.

Comparison of fractal dimension and spatial correlation. With increasing exercise intensity, a decrease in fractal dimension occurs, indicating more spatially organized flow distribution (fractal dimension  1.0). Conversely, correlation of flow to adjacent pieces increases under these same circumstances [(2.3 cm)  1.0]. This inverse relationship is illustrated in Fig. 6 and supports the intuitive assumption that regional blood flow will be more closely correlated as its distribution becomes more spatially organized.

View larger version (13K): [in this window] [in a new window]   Fig. 6.   Spatial correlation of adjacent pieces varies inversely with fractal dimension. , Horse 1; , horse 2; , horse 3; , horse 4. Higher local correlations occur when flow is more homogeneous. Data point for rest state in horse 1 was omitted from regression as an outlier because it falls ~5.5 standard deviations from regression line.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

The important findings from this study are 1) pulmonary blood flow distribution is fractal in exercising horses, 2) fractal dimension for pulmonary blood flow decreases when exercise intensity increases (i.e., increasing pulmonary blood flow), 3) regional pulmonary blood flow is spatially correlated, 4) the spatial correlation of flow differs among horses and exercise states, and 5) correlation of flow for adjacent pieces increases with increased pulmonary blood flow.

Microsphere method. The microsphere method for measuring regional organ blood flow distribution has been previously validated in dogs (7), and the justifications for its use in these experiment have been discussed in prior reports (1, 13, 24). Flow to each lung piece was normalized to the mean flow to all pieces in a given animal. The coring method used to sample the lungs in this study yielded pieces of virtually identical volume; therefore, we did not report blood flow normalized to piece weight, as has been the case for previous studies from this laboratory (8, 10, 11). Weight normalization has been used as a surrogate for the painstaking process of ensuring that each lung piece sampled is of equal volume. The core samples in this study were weighed, and, when weight-normalized relative flows were analyzed, CVs were routinely increased by 2 to 3%, suggesting that additional noise is added by weight normalization.

View larger version (150K): [in this window] [in a new window]   Fig. 7.   Fluorophotomicrograph (×40 magnification) from a core sample of horse lung. Microspheres are clearly seen in alveolar capillaries, and their numbers are very small relative to number of alveoli present.

Horse 2. Significant differences were seen in the results obtained from analysis of the blood flow data from horse 2 compared with the other animals in this study. As we have previously shown, this horse had an unusual bimodal distribution of pulmonary blood flow at rest, which markedly differed from the unimodal distribution seen in the other horses (14). A significant number of low-flow pieces were seen in the dorsocaudal lung regions of this horse at rest, and, on removal of the lungs, reddened areas were seen in these same regions, compatible with exercise-induced pulmonary hemorrhage. Although no diagnostic procedure was performed to confirm this, horse 2 is clearly an outlier in the Thoroughbred population, but these differences only slightly impacted the findings of this study when the rest data were included in the analysis of fractal dimension.

Fractal dimension. We found statistically significant decreases in fractal dimension with increasing total pulmonary blood flow induced by exercise. This finding conflicts with prior results reported in open chest, pump-perfused sheep in which relative distribution decreased but fractal dimension remained constant with increases in pulmonary blood flow from 1.5 to 5.0 l/m (4). Parker and colleagues found no significant change in fractal dimension from rest (1.132 ± 0.006) to exercise (1.149 ± 0.01) in dogs, despite a two- to fourfold increase in cardiac output (27). Differences in study design may account for some of these discrepancies. We employed an awake, unanesthetized horse model, which not only provided a much larger (10-fold) increase in total pulmonary blood flow but did so in the intact animal in which normal autoregulatory mechanisms continued to influence regional vascular tone. It has recently been shown that, in horses, vasoactive substances evoke different responses as a function of the vessel's spatial location (28). Specifically, 6-mm arteries from the dorsocaudal lung relaxed when exposed to methacholine, whereas cranioventral arteries constricted. This phenomenon was endothelium dependent and nitric oxide mediated, a mechanism similar to that which is thought to mediate flow-dependent vasodilation (20, 21). It was postulated that similar mechanisms might account for the preferential perfusion of dorsal-caudal lung regions seen when using microsphere techniques (8, 14). Indeed, in our prior paper (2), we reported an increase in dorsal distribution of pulmonary blood flow with increasing exercise. Similar alterations in regional vascular tone may be responsible for the change in fractal dimension seen in this study. Regional variation in vascular tone will change the distribution of flow to the lung distal to the affected vessel(s) as well as the proportion of flow to its sister vessel(s) in a dichotomously branching system. Although only described to date in 6-mm OD vessels, if a flow-mediated vasodilatory signal affects larger, more proximal parent vessels, the proportion of flow to these areas could be significantly increased, thereby altering the effective "geometry" of the vascular tree and the fractal dimension that describes it.

Spatial correlation. Glenny (6) has previously found that regional pulmonary perfusion is highly correlated over large spatial distances in dogs. The present study found a similar strong correlation of blood flow but across even larger distances (up to ~60 cm) and further supports the theory that a dichotomously branching vascular tree is the primary factor influencing the distribution of regional pulmonary blood flow. As has been previously observed, correlation was highest among pieces in the closest spatial proximity and lower as distance between pieces increased, becoming negative at extremes of distance. This can be explained by the concept of conservation of flow, in which, given a fixed amount of blood flow to a vascular tree, high flow in one region can only occur at the expense of flow to another region.

Summary. We have shown that pulmonary blood flow in horses at rest and at three levels of exercise is fractal in nature and spatially correlated. Additionally, this is the first study to document a change in fractal dimension as a result of increasing pulmonary blood flow. A recent study from this institution has also documented a reduction in fractal dimension with isovolemic hemodilution in rabbits (5). This phenomenon may be at least partially explained by spatial differences in response to vasoregulatory mediators, but further study is needed to better elucidate the mechanism(s) responsible.