The epiphyseal growth plates of the long bones and the synchondroses of the cranial base are cartilaginous growth sites with demonstrated tissue-separating capacity (Peltomaki et al., 1997), and they elongate the long bones and the neurocranium of mammals. It has been hypothesized that the nasal septum performs the same role for the facial skeleton, separating bones by its own interstitial growth, and thus elongating the facial skeleton (Scott, 1953; Koski, 1968; Roberts and Lucas, 1994), but experimental evidence has been equivocal (Stenstrom and Thilander, 1970). A long history of debate surrounds the issue of whether, and how, septal growth controls midfacial growth (for reviews, see Mooney and Siegel, 1991; Roberts and Lucas, 1994; see also Moss et al., 1968; Delaire and Precious, 1986). The nasal septum comprises a midline vertical plate of hyaline cartilage, which is continuous with the cranial base, or chondrocranial central stem. It has a dual origin as the median element of the paired nasal capsules, and as the rostral extension of the trabecular basal plate (Depew et al., 2002). In the absence of olfactory epithelial signaling by Dlx5 (Depew et al., 1999), or olfactory placode signaling by Pax6 (Kaufman et al., 1995; Quinn et al., 1997), instead of a septum there is a cartilaginous midline rod extending from the chondrocranium. If the nasal processes are abnormally positioned and outgrowth is more lateral than normal, the two capsules do not fuse in the midline, resulting in a cleft face with two widely separated nasal septa [Alx3/Alx4 double mutant and Alx4/Cart1 double mutant (Qu et al., 1999; Beverdam et al., 2001)].
Endochondral ossification is the process of replacing cartilage matrix with bone matrix and occurs at growth plates and synchondroses (Ballock and O'Keefe, 2003). The growth plate comprises four discrete zones: a resting zone, in which cells are relatively quiescent; a proliferative zone, formed by short columns of dividing cells; a hypertrophic zone, in which chondrocytes swell, mineralize the surrounding matrix, and die by apoptosis; and an ossification zone, in which blood vessels invade, and osteoblasts deposit bone matrix onto the mineralized cartilage matrix [terminology from Hunziker et al. (1987)]. Matrix synthesis occurs in all zones. During hypertrophy, cell volume increases approximately 5- to 10-fold (Buckwalter et al., 1986; Hunziker et al., 1987), and this volume increase is responsible for almost half of the increase in length of the long bone (Wilsman et al., 1996). Cranial synchondroses consist of two growth plates back-to-back, sharing a common resting zone, and are found in the cranial base. Thus, a synchondrosis connects two bones, and it pushes apart the two bones when it interstitially expands through cell division, matrix synthesis, and hypertrophy. In the midline cranial base, the spheno-occipital synchondrosis (SOS) joins the basisphenoid and occipital bones, and the presphenoidal synchondrosis (PSS) joins the presphenoid and basisphenoid. The cartilaginous postnatal septum is continuous caudally with the presphenoid and also with the perpendicular plate of the ethmoid [more properly called the mesethmoid at this stage (Rowe et al., 2005)]. Endochondral ossification has been observed at these caudal junctions (Baume, 1961; Stenstrom and Thilander, 1972; Koski, 1975) and proposed as a mechanism for lengthening the cranium. However, little is known about the rates of ossification at these sites, and without these data, the importance of these sites in facial growth cannot be evaluated.
Evidence for the role of the nasal septum in facial growth has come from two kinds of studies: surgical extirpations and in vitro growth experiments. Most extirpation experiments have shown that removal of all or part of the septal cartilage reduces facial growth, especially in the rostrocaudal direction, or lengthening of the snout (Sarnat and Wexler, 1966; Kvinnsland and Breistein, 1973). However, some extirpation experiments have shown no significant facial growth reductions (Stenstrom and Thilander, 1970; Cupero et al., 2001). These extirpation experiments have been criticized on the grounds that surgical trauma leading to altered blood supply may alter cartilage growth (Koski, 1968; Roberts and Lucas, 1994), and that the observed growth reductions are confounded by local collapse of the facial bones that appear to be mechanically supported by the nasal septum (Stenstrom and Thilander, 1970). In vitro experiments have provided evidence of the capacity of septal cartilage to expand against resistance (Copray, 1986; Copray and Duterloo, 1986), which is significant because the septum is centrally located within a framework of enclosing dermal bones (maxilla, premaxilla, nasal bones, vomer), whose periostea blend with the perichondrium of the septum. Rat nasal septal cartilage growing in culture can exert growth pressures comparable to epiphyseal growth plate, and larger than those exerted by synchondroses and the condylar cartilage. In addition, the region of the septopresphenoidal junction can also exert larger growth pressures than synchondroses (Copray and Duterloo, 1986).
It has been proposed that endochondral ossification of the caudal and dorsal borders of the septum, when combined with interstitial expansion, has the effect of displacing the facial skeleton away from the neurocranium and thus enlarging the skull (Koski, 1968; Roberts and Lucas, 1994). To investigate this, we asked whether the amount of endochondral ossification at the caudal junctions is sufficient to explain the increase in size of the septum. If the septum is really “pushed” forward by endochondral growth at the caudal borders, then the observed increase in length of the septum should match the rate of growth at the junctions. If the observed length increase is larger than the rate of growth at the junctions, then interstitial growth, in the form of cell division or matrix synthesis, must be more important in septal growth. To answer this question, the rate of endochondral ossification at the two junctions of the caudal septum was measured in the postnatal mouse. The results indicate that there is significant endochondral ossification at the caudal junctions of the septum, but that the observed increase in the length of the septum is much larger than can be accounted for by growth at the junctions.
MATERIALS AND METHODS
All procedures were approved by the Institutional Animal Use and Care Committee, University of Washington. CD-1 mice (Charles River Labs, Wilmington, MA) were housed under standard conditions with a 12-hr light cycle and supplied with tap water and rodent chow (Picolab Rodent Diet 20; Purina Mills, St. Louis, MO) ad libitum. Juvenile mice were killed with an intraperitoneal injection of pentobarbital (90 mg/kg) and adult mice by CO2 inhalation.
Growth at a growth plate results from increased cell number, increased cell size, and new matrix synthesis, and this entire tissue volume is eventually mineralized and replaced by bone matrix. Therefore, mineralization rate was used as a proxy for the rate of endochondral growth and considered to reflect the rate of bone growth (Hunziker et al., 1987; Farnum et al., 2003). To measure the mineralization rate, the fluorochromes calcein and alizarin were administered at intervals of 2–5 days. These fluorochromes bind calcium and are incorporated into mineralizing tissue, which in the growth plate includes the cartilage matrix of the distal half of the hypertrophic zone, and the osteoid of the ossification zone. The incorporated fluorochrome is visible as a fluorescent band, the leading edge of which represents mineralized cartilage matrix of the hypertrophic layer (Farnum et al., 2003). The distance between the leading edges of the two fluorescent bands is the amount of mineralization that occurred during the interval and indicates the amount of growth at the growth plate. The mineralization rate was calculated by measuring the distance between the leading edges of the two fluorescent bands and dividing this distance by the number of days between fluorochrome injections.
To measure the mineralization rate at synchondroses and the septum, mice from three litters were divided into four groups. One group (P0–P2) was injected as soon as possible after birth (P0) with calcein (Sigma C0875, St. Louis, MO; 10 μg/g body weight, dissolved in sterile phosphate-buffered saline, intraperitoneal injection). Alizarin was injected 2 days later at the same time of day as the calcein administration (Sigma A3882; 10 μg/g body weight, dissolved in sterile phosphate-buffered saline, intraperitoneal injection). The second group of mice (P2–P5) was given the same fluorochromes on days 2 and 5, the third group (P5–P10) on days 5 and 10, and the fourth group (P10–P15) on days 10 and 15. Sample sizes were eight mice in the P0–P2 group, seven in the P2–P5 group, six in the P5–P10 group, and six in the P10–P15 group (grand total 27 mice). Mice were not sexed and were randomly assigned to groups. Mice were sacrificed 2 hr after the alizarin injection, and the midline basicranium and right third metatarsal were isolated and fixed in 70% ethanol. The midline basicranium included the occipital, basisphenoid, presphenoid, and ethmoid bones and the intervening synchondroses (Fig. 1).
The intact basicrania and metatarsal bones were photographed as whole-mount preparations using a fluorescent microscope. ImageJ 1.34 (W. Rasband, National Institutes of Health) was used to measure the mineralization rate from the fluorescent images. A grid was superimposed on each image, and the distance between the two fluorescent labels in the rostrocaudal direction was measured at each grid point. The average of these distances was divided by the number of days between labels to give the mineralization rate per day. Within the SOS, these distances were calculated for the rostral edge of the occipital bone (SOS-occ) and the caudal edge of the basisphenoid bone (SOS-sph). Within the presphenoidal synchondrosis (PSS), distances were calculated for the rostral edge of the basisphenoid (PSS-sph) and the caudal edge of the presphenoid (PSS-pre). Distances were also calculated for the rostral edge of the presphenoid, where it joined the septum (PS-sept), the distal end of the metatarsal (Met), and the nasal half of the nasofrontal suture (NF). The metatarsal and nasofrontal suture were used as additional comparisons. The metatarsal growth plate represents a postcranial endochondral ossification site, while the nasofrontal suture represents an area of the facial skeleton that grows by intramembranous ossification and is adjacent to, and possibly influenced by, the nasal septum.
Measurement of the mineralization rate of the ethmoid at the septoethmoidal junction was more complicated, because unlike the synchondroses, the ethmoid is approximately semicircular in shape and grows radially. In addition, the shape changes during the observed growth period. The distance measured was the horizontal component of the diagonal interlabel distance, taken at the midpoint of the ethmoid arc (Fig. 1).
Statistical analyses were performed using JMP 5.1 (SAS, Cary, NC). One-way analysis of variance of all measured mineralization rates was carried out for each age group. Significant ANOVAs were followed by pairwise comparisons using Tukey's HSD tests. When standard deviations were not equal (Levene's test), Welch ANOVA was used.
To measure the growth of the ethmoidal and cartilaginous portions of the septum, mice were sacrificed soon after birth (P0 group, six mice), and at 2 days of age (P2, four mice), 5 days (P5, seven mice), 10 days (P10, six mice), 15 days (P15, five mice), and as adults (two female breeder mice). The complete septal cartilage extending from the presphenoid to the nasal tip was isolated. The nasal bones and vomer were removed to expose the dorsal and ventral edges of the septum, and the lateral cartilages at the rostral tip were removed to expose the rostral edge of the septum in the midline. The septum was fixed in 70% ethanol for a minimum of 2 days, stained with alcian blue solution (8GX, 0.015% in 70% ethanol) for 2 days, macerated with 1% KOH, and then cleared and stored in glycerol. Septa were photographed and measurements made using ImageJ. Images were oriented to correspond with the palate in the horizontal plane, and the perimeter of the septum, including the perpendicular plate of the ethmoid, was outlined to record the maximum length and height.
Histology and Immunostaining
To examine the distribution of dividing cells, bromodeoxyuridine (BrdU solution, 00-0103; Zymed, San Francisco, CA) was injected intraperitoneally at 1 ml/100 g body weight into mice at P0 (four mice), P2 (four mice), P5 (three mice), P10 (three mice), or P15 (three mice). Two hours later, the mice were sacrificed, and the complete basicrania were isolated. To preserve endogenous alkaline phosphatase, the basicrania were processed according to a previously described method (Miao and Scutt, 2002). Briefly, tissues were fixed for 24 hr in 2% paraformaldehyde containing 0.01 M lysine and 0.01 M sodium periodate, decalcified in EDTA for 2 weeks, dehydrated, and embedded in paraffin. Five micron thick sections were cut in the sagittal plane, dewaxed, hydrated, and stained with hematoxylin and eosin or 0.1% Safranin O.
To visualize BrdU, sections were treated with 0.1% trypsin containing 0.1% calcium chloride for 30 min at 37°C, then treated with 2 N HCl for 30 min at 37°C and washed in 0.1 M sodium borate. Sections were incubated in biotinylated monoclonal anti-BrdU antibody (Zymed) diluted 1/100 in phosphate-buffered saline for 1 hr at room temperature. Sections were washed and incubated with streptavidin-conjugated alkaline phosphatase for 1 hr at room temperature. They were then incubated in BCIP/NBT substrate solution (Vector Laboratories, Burlingame, CA) for 5 min in the dark and counterstained with nuclear fast red (Vector) or 0.1% Safranin O.
At birth, the synchondroses and the basic shape of the intervening skeletal elements were already established. Fluorochrome labeling showed that mineralization occurred parallel to the existing surface, and evenly along the surface, at the synchondroses, the septopresphenoidal junction, the metatarsal, and the nasofrontal suture (Fig. 2). In contrast, the pattern of mineralization at the septoethmoidal junction was more complex (Fig. 3). Mineralization of the ethmoid was established at around the time of birth, as some P0 mice had a mineralized zone within the cartilaginous septum, while other P0 mice had completely cartilaginous septa. Once the center of mineralization was established, the mineralized zone expanded rapidly along the dorsocaudal edge of the septum, elongating the ethmoid (Fig. 3A–C). In addition, mineralization occurred evenly along the junction with the cartilaginous septum, thus achieving growth in the radial direction, to give a semicircular shape. By P10–P15, however, the rate of mineralization became uneven along the septal junction, with rapid mineralization being maintained rostrally but slowing ventrally and caudally (Fig. 3D).
In general, the rate of mineralization at synchondroses was 60–80 μm/day around birth (P0–P2; Fig. 4A), remained the same at P2–P5, decreased during P5–P10, and further decreased during P10–P15 to approximately 40–50 μm/day (Fig. 4B).
At the septoethmoidal junction, the rate of mineralization at P0–P2 was 66 μm/day (Fig. 4A), and this decreased to 46 μm/day by P10–P15 (Fig. 4B). These rates were not significantly different from any of the synchondroses (SOS-occ, SOS-sph, PSS-sph, PSS-pre) or the septopresphenoidal junction (PS-sept).
At the septopresphenoidal junction, the mean mineralization rate at birth was 70 μm/day, which was not significantly different from any other location (Fig. 4A). By P10–P15, the mineralization rate had declined to the low value of 26 μm/day, which was significantly less than the spheno-occipital synchondrosis (SOS-occ and SOS-sph), but not significantly different from the presphenoidal synchondrosis (PSS-sph and PSS-pre) or the septoethmoidal junction (Esept; Fig. 4B).
The nasofrontal suture and metatarsal mineralized rapidly at birth (91 and 95 μm/day respectively) and were significantly faster than the spheno-occipital synchondrosis, sphenoidal half of the presphenoidal synchondrosis, and septoethmoidal junction (Fig. 4A). By P10–P15, they were significantly faster than all other growth sites, at 151 and 331 μm/day, respectively (Fig. 4B).
In summary, mineralization occurred at the septoethmoidal junction at the same rate as that of the synchondroses at all ages. At the septopresphenoidal junction, the mineralization rate was similar to that of the synchondroses at birth, but decreased by P10–P15.
The septum steadily increased in length and height between birth and day 15, with length increasing slightly faster than height (Fig. 4C). Least-squares regression slopes fitted to the data gave increases of 273 μm/day for septal length and 151 μm/day for height (R2 of 0.94 and 0.92, respectively). When compared with the P15 septum, the adult septum was considerably longer, but was not larger in height (Fig. 4C).
Histology and Cell Proliferation
At birth, there was a small region of hypertrophic chondrocytes located at the dorsocaudal boundary of the septum, approximately halfway between the cranial base and the frontal bones (Fig. 5A). This region represents the center of ossification of the perpendicular plate of the ethmoid within the cartilaginous septum. At 2 days, this hypertrophic zone had expanded rostrally and caudally and extended further into the cartilaginous septum (Fig. 5B). A few small spicules of bone matrix were present on the very edge of the septal border, indicating the initiation of ossification. At 5 days, blood vessels had invaded the hypertrophic zone and osteoblasts were laying down bone matrix (Fig. 5C). The hypertrophic zone had narrowed to a distinct strip between the ossification zone and the cartilaginous septum, and a discrete zone of proliferative columns was visible next to the hypertrophic zone. These proliferative cells appeared to be smaller than the interstitial chondrocytes of the main cartilage. At 10 days, the histological appearance was similar to that at 5 days (Fig. 5D). At 15 days, the hypertrophic zone had narrowed (Fig. 5E) and remained narrow at P20 (data not shown).
At the junction of the presphenoid and the nasal septum, the ossification of the presphenoid was already established at birth (Fig. 6). The junction had the characteristic appearance of a growth plate, with zones of proliferating and hypertrophying chondrocytes, and an adjacent ossifying zone (Fig. 6). The hypertrophic zone narrowed considerably from P0 to P10, and by P15 it had essentially disappeared (Fig. 6).
At the sutural junctions between the septum and the vomer and nasal bones, the bone and cartilage compartments were separated by a fibrous layer composed of blended periostea and perichondria, and no zones of hypertrophy or proliferation were apparent. This fibrous layer was never observed at the septoethmoidal and septopresphenoidal junctions.
BrdU labeling showed that from birth to 5 days, cellular proliferation occurred throughout the septum, excluding the hypertrophic zone (Fig. 7). There were no marked regional variations in cell density. By day 10, proliferation was focused at the septoethmoidal junction, and few chondrocytes were replicating interstitially (Fig. 7). Higher-magnification images of the septoethmoidal junction (Fig. 8) showed that by P15, dividing chondrocytes were only found adjacent to the hypertrophic zone. The same trend was evident at the junction between the presphenoid and the septum (Fig. 8), except that by P15, BrdU-positive cells were rare. In the synchondroses, this pattern was repeated; cell division was found throughout the resting and proliferative zones between P0 and P5, but by P10–P15 it was limited to a narrow proliferative layer (Fig. 8).
Endochondral ossification at the caudal junctions of the nasal septum has been reported (Scott, 1953; Baume, 1961; Koski, 1968; Stenstrom and Thilander, 1972), but not thoroughly investigated. In this study, we examined these junctions in postnatal mice and found that the junctions are true growth plates, that they mineralize as rapidly as the synchondroses and have similar patterns of cell proliferation. The significance of endochondral ossification of the caudal and dorsal borders of the septum is that when combined with interstitial expansion, it should have the effect of displacing the facial skeleton away from the neurocranium, and thus enlarging the skull.
Cellular proliferation decreased with age in the septal cartilage, which is consistent with other studies of rodent septa (Searles, 1977; Ma and Lozanoff, 1999). BrdU labeling showed that cell division was extensive throughout the septum, at least until P5. Presumably, this cell division would by itself cause significant interstitial growth of the septum. However, the septum continued to increase in size at approximately the same rate during the first 15 days of life (Fig. 4C), even after proliferation decreased, implying that the interstitial expansion is not primarily due to cell division. It is possible that cell division contributes to septal expansion in the earlier growth period (P0–P5), whereas matrix synthesis or increase in chondrocyte volume plays a greater role in the later growth phase (P5–P15). The importance of cell division of the nasal septum is shown by the Brachyrrhine mouse (Br/+) (Lozanoff et al., 1994; Ma and Lozanoff, 1999, 2002), which has a significantly shorter snout due to reduced cell division in the sphenoethmoidal and presphenoidal regions of the anterior cranial base (these regions correspond with the septoethmoidal and septopresphenoidal junctions as defined in this article). In addition, the presphenoidal synchondrosis and presphenoid are malformed (McBratney et al., 2003), so other factors may also be involved.
The pattern of mineralization of the perpendicular plate of the ethmoid has not been described before in the mouse, nor, to our knowledge, in other species. The center of ossification appeared at the caudal border of the cartilaginous septum, at a position approximately midway between the palate and the frontal/nasal bones. The timing is difficult to establish, but would seem to be around birth, because some newborns had the ossification center and others did not. At birth, the center of ossification consisted of hypertrophic chondrocytes with some mineralization of the surrounding cartilage matrix, but by postnatal day 5, osteoblasts were laying down bone matrix. The shape of the mineralized zone was semicircular at P0 and remained so up to P10 as matrix was mineralized evenly along the junction, but during P10–P15 mineralization was faster rostrally than ventrally, creating a more irregularly shaped ethmoid.
The septoethmoidal and septopresphenoidal junctions had the characteristic morphology of a growth plate, complete with hypertrophic zone and mineralization. The width of the hypertrophic zone at the midpoint of the ethmoid decreased with age, which agrees with the observed decrease in mineralization rate with age at that site. At all ages, the rate of mineralization at the septoethmoidal junction fell within the range of the synchondrosal rates, with the exception of P5–P10, in which the rate was slightly higher than synchondrosal rates, although not significantly so. This indicates that considerable endochondral ossification occurs at the septoethmoidal junction. At the septopresphenoidal junction, hypertrophy ceased by P15, proliferative cells became rare, and the mineralization rate was slower (although not statistically significantly so) than the synchondroses. This implies a reduced growth capacity for the septopresphenoidal junction, at least in the later growth phase observed. This is consistent with studies of mineralization and matrix synthesis at the septopresphenoidal junction and synchondroses in rats (Roberts and Blackwood, 1983, 1991), in which the mineralization rate at P4–P8 was similar to the synchondroses, but had declined to zero by P32, unlike the synchondroses.
The growth patterns are summarized in Figure 9, which shows the mean mineralization rates during P0–P15 at the measured growth sites. Mineralization was relatively slow at the synchondroses and septal junctions, and rapid at the nasofrontal suture. The horizontal component of growth at the septoethmoidal junction was similar to the (horizontal) growth measured at the synchondroses. The most rapid growth occurred within the cartilaginous septum.
The presence of growth plates at the caudal and dorsal margins of the septum implies that growth at these junctions might act to “push” the septum rostrally and ventrally and thus enlarge the facial skeleton. Nevertheless, interstitial growth would appear to be more important in septal expansion for two reasons. First, the cartilaginous septum is expanding at a rate well beyond that needed to maintain endochondral ossification. For example, at the spheno-occipital synchondrosis, the width of the cartilage stays roughly constant between P0 and P15, yet on average 120 μm/day is mineralized, implying that proliferation, hypertrophy, and new matrix together account for 120 μm/day (120 μm/day was calculated by averaging the total amount of mineralization on each side of the SOS per day). Essentially, cartilage is synthesized as fast as it is replaced by bone matrix. In comparison, the cartilaginous septum increases in length by some 273 μm/day on average, while only approximately 50 μm/day of cartilage matrix is mineralized at the junction with the presphenoid (51 μm/day is the average rate during P0–P15). Thus, the cartilaginous septum must be increasing in length by approximately 325 μm/day to account for that lost via mineralization at the septopresphenoidal junction. These growth rates show that the septum is being “pushed” from its caudal borders, but this occurs slowly in comparison to the rapid interstitial expansion of the cartilaginous septum.
The second reason that interstitial expansion is more important in septal growth than caudal growth plates is that mineralization rates are out of phase with septal growth curves, implying independent regulation. During P10–P15, the mineralization rate declines at the septoethmoidal and septopresphenoidal junctions, and the growth plates either narrow (septoethmoidal) or become quiescent (septopresphenoidal). But at the same time, the cartilaginous septum is still expanding rapidly. The time at which the growth rate of the cartilaginous septum begins to decline is unknown, but it is clearly after P15. Continued interstitial growth of the septum is also suggested by the rate of mineralization of the nasofrontal suture, which is actually higher at P10–P15 than at P0–P2.
This view of the septum as an interstitial expansive force is consistent with the septopremaxillary traction hypothesis (Latham, 1970; Siegel et al., 1985). In this model of mid-facial growth, the growing septum pulls the premaxilla forward, away from the maxilla, thus lengthening the facial skeleton. This traction is achieved by a ligament that runs posteriorly from the rostral tip of the septum to attach to the premaxilla. Resection of this ligament results in reduced facial growth in rats (Gange and Johnston, 1974) and nasal capsule shape changes in chimpanzees (Siegel et al., 1992). The septopremaxillary traction hypothesis requires that the septum grow anteriorly and does not predict how that growth is achieved. Thus, either endochondral ossification at the caudal junctions or interstitial expansion is compatible with the hypothesis. In mice, an additional ligament runs from the septum to the rostral tip of the nasal bones, and severing of this ligament results in reduced growth at the nasofrontal suture in mice aged P4–P7, although not in older mice (Long, 1985). This finding implies that traction of the nasal bone from the frontal bone by the expanding septum contributes to nasofrontal sutural growth, at least in younger mice. The septal traction model also provides a possible explanation for our data showing comparable rates of growth at the nasofrontal suture and the septum (Fig. 9).
We conclude that endochondral ossification lengthens the presphenoid and ethmoid and displaces the septum forward and downward. However, the magnitude of this displacement by endochondral ossification is small in proportion to that achieved by interstitial growth of the main body of the cartilaginous septum. Thus, insofar as the septum contributes to enlarging the facial skeleton by displacing facial bones, our results suggest that the primary mechanism is septal interstitial growth and that endochondral ossification of the caudal septum plays a lesser role.
The authors thank Drs. Martha M. Bosma, Lynn M. Riddiford, and James W. Truman for helpful advice.