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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
 
J Orthop Res. Author manuscript; available in PMC 2010 October 13.
Published in final edited form as:
PMCID: PMC2954232
NIHMSID: NIHMS236904

Age and Pattern of the Onset of Differential Growth Among Growth Plates in Rats

Abstract

Differential growth is the phenomenon whereby growth plates in the same individual at the same time all have uniquely different axial growth velocities. Differential growth is clearly present in the adolescent skeleton. In this study we ask two questions. When and by what pattern does the phenomenon of differential growth begin? Second, to what extent are the development of differential growth velocities correlated with changes in hypertrophic chondrocyte volume and/or with changes in chondrocytic production/turnover?

Four growth plates (proximal and distal radial; proximal and distal tibial) were studied at 24 different time points in Long Evans rats between the 17th gestational day (when differential growth does not exist) and postnatal day 27 (when differential growth is well established). Growth velocities were measured using fluorochrome labeling. Using stereological methodology, multiple chondrocytic kinetic parameters were measured for all growth plates.

Elongation of the proximal radial growth plate decreases relative to elongation in the other three growth plates in the late fetal phase. Differential growth is fully expressed at postnatal day 13 when the other 3 growth plates start to decrease daily elongation at different rates. Differential growth is primarily associated with differences in hypertrophic cell volume manifested when growth deceleration occurs. This study also illustrates that differential growth is superimposed on systemic regulators that affect all growth plates simultaneously. The most dramatic illustration of this is the sharp decline in growth velocity in all four growth plates that occurs perinatally.

Keywords: growth plate, physis, growth, growth velocities, hypertrophic chondrocyte

INTRODUCTION

Longitudinal bone growth is the product of discrete but linked operations carried out through chondrocytic division and differentiation. The mechanics of this process occur in all growth plates. Germinal chondrocytes pass through a series of regulated gates, enter the cell cycle, divide, and leave the cell cycle 1, 2, 3. They differentiate, swell 4, 5, 6, 7, mineralize the matrix, degrade the matrix, and finally die by apoptosis at the chondro-osseous junction. This differentiation cascade is (probably) identical in all growth plates 8, 9, 10.

It is curious, therefore, that when regulation of growth is considered at the level of the individual animal and when we alter the perspective from discrete events in the cellular maturation cascade to rates of cellular change, growth velocities are not uniform but vary from one growth plate to the next — growth plates in different locations in one individual at one moment in time: growth plates are all different. This phenomenon - differential growth - is a hallmark of growth plate biology, and was first documented 150 years ago 11, 12. Differential growth is superimposed on the well-documented phenomenon of age-related differences in growth velocity and growth plate activity where all growth plates in the body accelerate or decelerate together, and is superimposed on differences that are used to determine the ages of individuals13, 14, 15, 16, 17. Differential growth is the phenomenon whereby growth plates on opposite ends of the same bone in the same individual at the same moment in time elongate at rates that may differ by a factor of three to seven.

Preliminary studies in our lab suggested that growth plates in the fetal radius and fetal tibia were all elongating at similar rates; however, at 28 days of age in the rat, differential growth is fully expressed with proximal and distal radial and tibial growth plates are all elongating at significantly different rates. Of all the chondrocytic kinetic parameters measured, hypertrophic cell volumes (also all different) seem to be particularly significant to this process 8. Pinpointing the timing and pattern of the emergence of differential growth (between the late fetal period when growth plates have similar growth velocities and 28 days of age when they all have different growth velocities) should help identify those mechanisms and controls that are prime movers of the process.

The purpose of this study was to (1) document the emergence of differential growth by daily measurement of changes in growth velocities in four different growth plates (proximal and distal radial and proximal and distal tibial) and (2), using stereologically measured kinetic parameters of growth plate chondrocytes, determine whether it is changes in the rate of cell proliferation (turnover) or changes in chondrocytic volume during hypertrophy that are primarily responsible for effecting differential growth.

MATERIALS and METHODS

Four growth plates, the proximal and distal radial and the proximal and distal tibial growth plates from Long Evans rat pups were studied. These four growth plates were sampled daily starting at gestation day 17 (one day before the earliest visible signs of calcification in rat long bones) through the first two weeks of age. Thereafter, we sampled pups every other day for the third week and every fourth day during the fourth week. This design focused most intensively around the peripartum period, which we believed to be critical for detecting the emergence of differential growth. This study was reviewed and approved by the Institutional Animal Care and Use Committee.

Growth velocity by fluorochrome labeling

Elongation velocity was measured using calcein fluorochrome labeling. Calcein was prepared as a solution of 10 mg/ml of 1.3% sodium bicarbonate. For each prenatal day sampled, calcein was delivered to fetal pups by injection to an anaesthetized mother (30 mg/kg, IV, subclavian vein). For each gestational age, two mother rats were used and the number of fetuses in each of the ten mothers was similar, varying from 11 to 14. Twenty-four hours after receiving IV calcein, the mothers were euthanized with pentobarbital (50 mg/kg IP) and six rat fetuses were chosen for collection. After excluding the fetuses at the ends of each uterine horn to avoid sampling those that might be atypically small for gestational age, the choice of fetuses was done randomly before the uterus was opened.

For each postnatal day sampled, two pups were chosen randomly from four litters. Twenty-four hours prior to euthanasia, each rat pup was injected with calcein (5 mg/kg IP) and was euthanized 24 hours later with pentobarbital (50 mg/kg IP).

Fixation, embedment, sectioning and label detection

Following euthanasia, the right radius and tibia were collected and each growth plate (including epiphyseal cartilage/bone on one end and metaphyseal bone on the opposite end) was sectioned longitudinally into sections approximately 250um thick. The sections were mounted on slides in glycerin, cover slipped and the fluorochrome label was visualized under epi-fluorescence microscopy using a 405nm excitation filter, a 455nm dichroic mirror and a 470nm barrier filter (Figure 1).

Figure 1
Micrograph of the distal radial growth plate viewed under epifluorescence microscopy (250μm scale bar included). This micrograph illustrates the technique of fluorochrome labeling to measure growth velocity. At the time of injection the fluorochrome ...

Calcein 18, 19, 20 is a member of a family of fluorescent markers that include oxytetracycline, alizarone complexone, xylenol orange. Calcein is incorporated into all active mineralizing matrices, including a narrow band at the chondro-osseous junction. To estimate elongation per 24 hours, the distance between the leading edge of the fluorescent calcein band and the chondro-osseous junction was measured using an ocular reticle 7, 21. Measurements were taken from each growth plate for each pup (two measurements per fetal pup growth plate, three per postnatal pup growth plate) and were averaged. These averages were then averaged for each growth plate across all pups of the same age.

Left growth plates were trimmed into 1×1×2mm blocks and fixed in 2% glutaraldehyde in 0.05M cacodylate buffer (pH 7.35) with 0.7% ruthenium hexamine trichloride (RHT) 7, 22. Tissue blocks were oriented such that growth plates would be sectioned vertically 23, and blocks were embedded in Epon-araldite. For each animal and each growth plate, two tissue blocks were selected randomly from all available blocks. From each block two sets of sections 1.5μm thick were cut. The sets were spaced 15μm apart. Absolute volumes of individual growth plates are estmated from measures of the major and minor axes and the height of the growth plate 23.

Kinetics of growth plate chondrocytes – stereological framework

The details of the mathematical derivation of the stereological framework for chondrocytic kinetics of growth plate chondrocytes has been described previously 7. In brief, a growth plate is modeled as an idealized unit cylinder with diameter = 1mm (diameter is arbitrary). This method of modelling a growth plate as a unit cylinder builds on the pioneering modelling of chondrocytic kinetics by Sisson and Kember 7, 24. 25, but differes from Kembers columnar model by using entirely 3-dimensionally based parameters. As Kember pointed out when the questions of interest involve comparing different growth plates in one individual, one growth plate over time, and especially when comparing growth plates from different species where absolute volumes (in stereological terms, VT) vary extensively, for example rats and children, there needs to be a procedure for normalization 24, 25. 26.

Kember’s unit of normalization primarily was an idealized chondrocytic column in 2-dimensions. In this study we use a 3-dimensionally based unit cylinder model. Differential growth is, by definition, differences in axial growth velocity. By modelling growth plates as unit cylinders located in the central axis of a bone, we maximize the study of axial elongation and we minimize the confounding effect of lateral growth 26.

In the unit cylinder the number of chondrocytes produced per day (NNEW) is estimated by:

NNEW=[Vvproliferativezone/v(c)proliferativechondrocytes][π0.52Htproliferativezone]GF[24hrs/TotalCellCyclehrs]

where the growth fraction (GF) is the percent of chondrocytes in the proliferative zone that actually are in the cell cycle. Whenever GF has been measured 3, the result has been 100%, or GF = 1.

The number of chondrocytes lost per day at the chondro-osseous junction (NLOST) is estimated by:

NLOST=[Vvterminalhypertrophiczone/v(c)hypertrophicchondrocytes][π0.52][Elongationvelocity/24hrs]

In a 24 hours time frame, measuring 5 independent parameters to calculate NNEW and 3 different and independent parameters to calculate NLOST, we have shown that NNEW/24 hours = NLOST/24 hours, thus validating relatively steady state kinetics over a 24 hour period. Therefore, in this study we only measured NLOST/day as an index of NNEW/day 7. If one is interested in absolute numbers for a given growth plate (VT) all that is required is to multiply the unit cylinder value by the product of the axes of the growth plate measured at tissue collection (essentially multiply by the number of unit cyliners in the entire growth plate 23). However, data presented in this way (VT) lack a method of normalization among growth plates since changes in major and minor axes of the four growth plates and absolute total volume of a growth plate (VT) over time are a function of lateral growth 26.

Hypertrophic chondrocyte volumes and chondrocytic densities

Of the 24 different time points at which we measured growth velocities, we selected 14 time points for stereological analysis of chondrocytic kinetics. At each of these time points, we measured hypertrophic chondrocytic volumes (v(c)hypertrophic chondrocytes) using the point sampled mean linear intercept method, applying eight angles of intercept 7.

We calculated numerical densities (Nvterminal hypertrophic zone) from volume fractions (Vv) and mean cellular volumes (v (c)hypertrophic chondrocytes). Volume fraction of the hypertrophic zone (Vvterminal hypertrophic zone) was determined using an image analysis system (NIH Image). Accurate thresholding of the system was tested against volume fractions determined using point-counting techniques 27, 28, 29. Calculated numerical densities were tested against numerical densities determined using the disector technique 28. No significant differences were found in comparing these two methods. For each of these stereological parameters, a minimum of four independent measurements (2 blocks per rat pup; 2 pups per time period) were averaged to represent an independent estimate per growth plate per time period. These data were analyzed using ANOVA with Scheffe’s method of multiple comparisons (StatView 4.5 for Macintosh). Correlation coefficients were calculated directly. The basis for this analysis has been presented previously 3.

RESULTS

Differential growth may be defined as the point at which the daily growth rate in one growth plate is significantly different from that of other growth plates at the same age. The data (Figure 2) capture that portion of development when differential growth emerges: at gestation day 18 (day −4 on Figure 2), all four growth plates were elongating at approximately the same rate (~ 200um/day), while at the end of the sequence (27 days of age), differential growth is evident as all six possible pairs of growth plates demonstrate significantly different rates from each other. By the last time point, the proximal tibia is growing almost nine times faster than the proximal radius. When does this pattern first emerge? The answer has two parts. First, differential growth clearly exists in the fetal rat. The proximal radius establishes its own particular growth trajectory very early in the process while the other three growth plates remain clustered together until well after birth. Except for the first day of the study, the proximal radius has a growth rate that is significantly slower from all others for the entire sequence.

Figure 2
Rates of Growth in Four Different Growth Plates in Fetal and Neonatal Rats (μm / 24 hours)

The second part of the pattern shows that the daily growth rates for the distal radius and proximal and distal tibia remain in tandem throughout the fetal period and into the second week of life. No new developments in differential growth occur until day 13, at which time all four growth plates differ significantly from each other. After day 13, all four growth plates maintain the same order of fastest to slowest and there is an overall gradual decline in daily rates with increasingly divergent rates. Thus, the emergence of differential growth is seen in two phases: first the prenatal divergence of the proximal radius and second the later divergence in the second week by the proximal and distal tibial and the distal radial growth plates.

Additionally, there are trends that affect all growth plates in the same manner. For example, toward the end of the sequence (days 13 – 24), there is an overall gradual decline of growth rates across all growth plates (lesser in the proximal radius because of its already slow growth velocity), a trend that has been reported in several studies and across several species 30. Further, there is a dramatic perturbation in growth rates in the peripartum period. The fetal period is marked by a starting point at which all four growth plates grow at about equal rates (~200um/day), followed by a rapid acceleration to a peak that represents the fastest rates observed over the entire sequence. This acceleration is abruptly halted over the next few days, just prior to birth, but resumes during the first week of life. These changes are somewhat less pronounced in the proximal radius, but are dramatic across all four growth plates. This pattern of waxing and wanng of all growth plates simultaneously is well known and not the stubect of this study; however, what the growth velocity curves from this study is the known (waxing and waning superimposed on the pattern of the emergence of differential growth.

Is differential growth best explained by changes/differences in the rate of cell production (comparing Figure 2 with Figure 4) or by changes/differences in hypertrophic cell volume (Figure 2 with Figure 3)? Visual inspection of these three graphs demonstrate that we need to consider the prenatal period separately from the postnatal period.

Figure 3
Volumes of Hypertrophic Chondrocytes in Four Different Growth Plates in Fetal and Neonatal Rats (μm3)
Figure 4
Chondrocytes Produced / Turned Over in Four Different Growth Plates in Fetal and Neonatal Rats (chondrocytes / 24 hours)

Prenatal Period

In the prenatal period, volumes of hypertrophic chondrocytes did not vary significantly among time periods or among different growth plates at any one time period (Figure 3). On average, regardless of growth plate or prenatal time period, fetal hypertrophic chondrocytic volume was 11,400μm3 ± 2,350. In the prenatal period there was no correlation (or even a slight negative correlation (r = − 0.01)) between rate of growth and hypertrophic cell volume.

In this study NLOST was measured. However, in the short time frame of 24 hours, we previously demonstrated that NLOST = NNEW 7. In the prenatal period the number of chondrocytes produced/lost varied day-to-day, and fluctuations of number of chondrocytes lost/day paralleled each other in each of the four growth plates in a pattern similar to changes in growth velocity. For example in the prenatal period, in the distal tibial growth plate, the number of chondrocytes turned over per day varied from a low of 8,600 cells/day in the slowest growing 18th gestational day to a high of 23,000 cells/day just two-days later on the 20th gestational day. In the prenatal period, number of chondrocytes lost/day correlated (r = 0.79 p<0.001) with growth velocity (Figure 4).

Postnatal Period

Postnatally, hypertrophic chondrocytic volume varied with time period and with growth plate (P < 0.01). The fluctuations of hypertrophic cell volumes paralleled each other in each of the four growth plates and fluctuated in a pattern similar to the fluctuations in rate of growth. For example, the smallest hypertrophic chondrocytes (~4,000μm3) were found in the slowly growing proximal radial growth plate at 24 to 28 days of age. The largest hypertrophic chondrocytes (~20,000μm3) were found in the rapidly growing proximal tibial growth plate at 7 to 13 days of age. In the postnatal period, hypertrophic cell volume correlated significantly (r = 0.70; 0.01>p>0.001) with rate of growth (Figure 3).

Alternatively, in the postnatal period, the number of chondrocytes lost/day remained relatively constant (Figure 4). Within a given growth plate and even among growth plates, the number of new cells produced per day varied but not significantly. For example at the time of the emergence of differential growth at 13 days of age the number of new chondrocytes produced per day was about 10,500 ± 1,500 cells per day in all four growth plates.

DISCUSSION

A complex array of factors, both genetic and epigenetic, are involved in the mechanisms by which growth plate cellular activity during endochondral ossification results in bone elongation. (recent reviews 8, 9, 10, 31, 32). While mechanisms regulating the differentiation cascade of growth plate chondrocytes can be studied by the reductionist and transgenic approaches of molecular biology31, stereological approaches to understanding the kinetics of chondrocytic performance parameters in growth plates growing at different rates have been a valuable approach for the analysis of how the chondrocytic differentiation cascade is converted quantitatively into incremental bone elongation through time 5, 7, 31. Interstitial growth contributes to elongation during both the proliferative phase (through changes in cellular numbers) and the hypertrophic phase (through changes in cellular size). Matrix synthesis contributes during both phases. Although the relative magnitude of contributions made during the proliferative and hypertrophic phases vary in growth plates growing at different rates, even over an eight-fold range of growth from approximately 50um a day to 400um days, it has been demonstrated that the single biggest contribution to differential growth results from cellular swelling and associated shape change during hypertrophy 4, 5, 7, 9. Therefore, for a study in which multiple time points and multiple growth plates are analyzed, chondrocytic volume increase and elongation velocity are the two variables most likely to yield significant comparative information.

A particularly interesting aspect of growth plate biology is that each individual growth plate of the body can be considered to have a biological life span. For the purposes of this study, the ontogeny of an individual growth plate can be considered to start with formation of the primary center of ossification of the bone prenatally. From this perspective, the proximal and distal growth plates of a given bone begin their formation simultaneously. The timing of formation of the secondary center of ossification postnatally is a second key biological time point, and this differs for the two ends of a given long bone. For the radius, the secondary center forms earlier distally than proximally, and for the tibia it is the reverse – the proximal secondary center forms prior to the distal one. A third critical time point when considering biological age of a given growth plate is the timing of closure. The proximal radial growth plate closes earlier than the distal radial growth plate; the distal tibial growth plate closes earlier than the proximal one. Differential contributions to overall length of a bone from the proximal and distal growth plates results from their relative rates of growth while both growth plates are open, as well as from the relative differences in overall length of the growth period for the two growth plates.

The timing of formation of the primary center of ossification is different in the radius than in the tibia, and thus the growth plates associated with these two bones are formed initially at different stages of development. The timing of formation of the secondary centers in the four growth plates studied also differs, as do their times of closure. If changes in growth velocity are a function of biological age, one would predict to see the same form to the curve of growth velocity for all four growth plates, but offset from each other depending upon the biological age of each specific growth plate. However, the data generated in this study demonstrate a trajectory of changing velocity that is essentially identical in form and in active acceleration for three of the four growth plates (distal radial, and proximal and distal tibial) from birth until day 10 – 13 postnatally. Growth velocities in these three growth plates track each other up to this point as a function of chronological age, rather than biological age. It is interesting to note that differential growth for these three growth plates emerges as differences in rate of elongation when all growth plates begin to slow their rates of elongation. Thus, these three growth plates accelerated at the same velocity, but decelerated at different velocities. Unlike the other three, the velocity curve for the proximal radial growth plate essentially is one of decreasing velocity throughout the period of growth plate activity, including the prenatal period. The degree of separation of growth velocities seen in this study at 27 days contuniues through 35 and 42 days33.

One could hypothesize that epigenetic factors are significant for the timing of the start of differential elongation in these three growth plates, but that hypothesis was not directly tested in this study. One possibility is the emergence of differential biomechanical (compressive, tensile, and strain) forces as significant contributors to the timing of the onset of differential growth in specific growth plates. These biomechanical signals in the fetal period could originate from in-utero skeletal muscle contractions 34. Prenatally ossification of the primary diaphyseal center could change the forces seen by the growth plate chondrocytes. Postnatally, while the timing of the ossification of primary and secondary centers of ossification is primarily a developmental phenomenon (radius before tibia), the subsequent effect of differential growth velocity of the growth plate might be mediated through biomechanical signals 35, 36, 37. Such signals then would be accentuated through gravity, especially as pups begin rigorous ambulation at two-weeks of age.

This leads to the generalization that regulation of growth velocities is a function of 1) regulating the number of cells produced multiplied by 2) regulating the amount that each cell increases its volume, with normal modulation of cell shape 5, 6, 7, 38. Both functions exist in all growth plates. All functions can be regulated independently. One function or the other may dominate over the other functions. Which of these fundamental processes accounts for the emergence of differential growth? The answer appears to be differential regulation of hypertrophy. Late gestation through birth and the early neonatal period are periods without fully expressed differential growth, even though growth velocities in all four growth plates rise, fall, and rise again. The primarily factor associated with these changes in velocity of all growth plates are changes in cell production kinetics (compare Figure 2 with Figure 4; r=0.79). After the second week of age to adolescence, while growth velocities all slowly decrease, all four growth plates have unique and significantly different velocities from each other. During this period significant differences of hypertrophic cell volume emerge (compare Figure 2 and Figure 3; r = 0.70). In the postnatal period while differences in cell production kinetics have a positive correlation with growth velocities (r = 0.35) this correlation is not statistically significant. When we consider velocity of growth as the variable of interest, this study demonstrates that at any one time in any one growth plate, regulation of the kinetics of proliferation and regulation of the kinetics of hypertrophy occur simultaneously. Regulation of either the kinetics of proliferation or hypertrophy or both determine final growth velocity.

One candidate for the dramatic suppression of growth in the peripartum period is the fetal cortisol surge, released by the maturing adrenal glands to initiate the birth process. The growth retarding effects of corticosteroid therapy on children are well known and experimental animals receiving synthetic cortisone have been shown to experience a dramatic deceleration or total cessation of bone elongation at their growth plates 39, 40. IGF’s are widely accepted to be the primary modulators of growth hormone (GH) on skeletal tissues 41. Fetal cortisol may act directly to suppress local expression of IGF-1 by chondrocytes or may act indirectly by suppressing the synthesis or release of GH. In an interesting parallel, human neonate IGF-1 levels are known to drop precipitously the first day after birth and remain low for three days, returning to prebirth levels by the end of the first week of life 42. Therefore, maternal fluctuations of estrogens or progesterones may be another contributor to the decrease in growth at birth.

As we consider the array of locally produced molecules known to influence growth plate chondrocytes, it is useful to think about their differential role in regulating cell production, hypertrophic chondrocyte volume, cell shape and integrating these cellular activities across these regulatory gates 43, 44. This is what has made the discovery of the hedgehog protein and its internal negative feedback loop Ihh — PTHrP — (alternatively TGF-β 45) such a fascinating discovery 46, 47. If, as many studies suggest, Ihh is inducible by biomechanical signals 48, 49, 50, and if different growth plates are exposed to differential biomechanical environments 35, 36, 37, then the negative Ihh —PTHrP — TGF-β feedback loop could be applied differentially. Consistent with this argument is the report that the lamb tibia elongates only when the lamb is recumbent and by inference relatively unloaded. During standing/ambulation the lamb tibias’ length is static. Although most regulatory inputs are continuous regardless of whether the tibia is loaded or unloaded, at the level of the individual lamb the tibia only elongates when unloaded 51.

Clinically, these concepts can be taken to the level of the whole animal for consideration of how all regulatory inputs integrate to create the clinically relevant variable, which is velocity of elongation. Growth velocity is a classical example of an emergent property of a complex system. It is analogous to the concept that behavior cannot be studied at the level of the neuron. Only when multiple neurons are included in the system does behavior emerge as a property of the system. Regulatory inputs to growth plate chondrocyte differentiation occur at all levels of biological organization. Growth velocity is a variable that plays out at the level of the individual animal. The clinical relevance of understanding differential growth is that sometimes corrections need to be made that have the potential to affect all growth plates in the body. In contrast, in other scenarios what is needed is for the clinician to be able to influence growth velocity of a single growth plate differentially or even differentially on the different sides of the same growth plate as in angular deformities 52.

Figure 5
The three micrographs are of 1.5um thick plastic-embedded sections stained with methylene blue/azure II/ basic fuchsin of the distal radial growth plate (scale bar = 200um). Three time points for illustration where chosen by referring to Figure 2 and ...

Acknowledgments

This project was supported by the National Institute of Health (NIH), National Institute of Arthritis, Musculoskeletal & Skin Disease (NIAMS): AR 35155-18, and a Merck-Merial Research Fellowship to Dr. Bernardini. We would also like to acknowledge and thank Dr. Ian Stokes for his leadership, and his willingness to share software code, as a part of our collaborative effort to develop Matlab compatible software to greatly facilitate point-sampled, mean cubic intercept measures of mean cell volumes. None of the authors received financial support for this study.

References

1. Beier F. Cell-cycle control and the cartilage growth plate. J Cell Phys. 2005;202:1–8. [PubMed]
2. Farnum CE, Wilsman NJ. Determination of proliferative characteristics of growth plate chondrocytes by labeling with bromodeoxyuridine. Calcif Tiss Int. 1993;52:110–119. [PubMed]
3. Wilsman NJ, Farnum CE, Green EM, et al. Cell cycle analysis of proliferative zone chondrocytes in growth plates elongating at different rates. J Orthop Res. 1996;14:562–572. [PubMed]
4. Buckwalter JA, Mower D, Ungar R, et al. Morphometric analysis of chondrocyte hypertrophy. J Bone Jt Surg Am. 1986;68:243–255. [PubMed]
5. Hunziker EB, Schenk RK. Physiological mechanisms adopted by chondrocytes in regulating longitudinal bone growth in rats. J Physio. 1989;414:55–71. [PubMed]
6. Buckwalter JA, Sjolund RD. Growth of Cornstalks and Long Bones: Does Longitudinal Bone Growth Depend on a Matrix Directed Hydraulic Mechanism? Iowa Ortho J. 1990;9:25–31.
7. Wilsman NJ, Farnum CE, Leiferman EM, et al. Differential growth by growth plates as a function of multiple parameters of chondrocytic kinetics. J Orthop Res. 1996;14:927–936. [PubMed]
8. Ballock RT, O’Keefe RJ. Current Concepts Review: The biology of the growth plate. J Bone Jt Surg Am. 2003;85:715–726. [PubMed]
9. Kronenberg HM. Insight Review Articles: Developmental regulation of the gowth plate. Nature. 2003;423:332–336. [PubMed]
10. Wilsman NJ, Farnum CE, Leiferman EM, et al. Growth plate biology in the context of growth by saltations and stasis. In: Lampl M, editor. Saltation Stasis and Human Growth and Development: Evidence, Methods, and Theory. Philadelphia: Smith-Gordon; 1999. pp. 71–87.
11. Digby KH. The measurement of diaphysial growth in proximal and distal directions. J Anat Physio. 1916;50:187–188. [PubMed]
12. Payton CG. The growth in length of the long bones in the madder-fed pig. J Anat. 1932;66:414–425. [PubMed]
13. Maresh MM. Linear growth of long bones of extremities from infancy through adolescence continuing studies. Amer J Dis Child. 1955;89:725–742. [PubMed]
14. Greulich WW, Pyle SI. Radiographic Atlas of Skeletal Development of the Hand and Wrist. 2. Stanford: Stanford University Press; 1959.
15. Shapiro F. Developmental patterns in lower-extremity length discrepancies. J Bone Joint Surg Am. 1982;64:639–51. [PubMed]
16. Pritchett JW. Growth plate activity in the upper extremity. Clin Orthop Rel Res. 1991;268:235–42. [PubMed]
17. Smith SL, Buschang PH. Longitudinal models of long bone growth during adolescence. Am J Hum Bio. 2005;17:731–745. [PubMed]
18. Rahn BA, Perren SM. Calcein blue as a fluorescent label in bone. Experientia. 1970;26:519. [PubMed]
19. Rahn BA. Polychrome fluorescent labeling of bone formation-instrumental aspects and experimental use. Zeiss Information Booklet #85. 1977;22:36–39.
20. Begu S, Devoisselle JM, Mordon S. Noninvasive fluorescent study in situ and in real time of glucose effects on the pharmacokinetic of calcein. J Biomedical Optics. 2002;7:609–612. [PubMed]
21. Hunziker EB, Schenk RK, Cruz-Orive L-M. Quantitation of chondrocytic performance in growth-plate cartilage during longitudinal bone growth. J Bone Jt Surg Am. 1987;69:162–173. [PubMed]
22. Hunziker EB, Herrmann W, Schenk RK. Improved cartilage fixation by ruthenium hexamine trichloride (RHT) J Ultrastruct Res. 1982;81:1–12. [PubMed]
23. Cruz-Orive LM, Hunziker EB. Stereology for anisotrophic cells: application to growth plate cartilage. J Micros. 1986;143:47–80. [PubMed]
24. Kember NF. Comparative patterns of cell division in epiphyseal cartilage plates in the rat. J Anat. 1972;111:137–142. [PubMed]
25. Kember NF. Cell kinetics and the control of growth in long bones. Cell Tissue Kinet. 1978;11:477–485. [PubMed]
26. Kember NF. Cell kinetics of cartilage. In: Hall BK, editor. Cartilage Vol 1, Structure, Function and Biochemistry. New York: Academic Press; 1983. p. 164.
27. Sterio DC. (nom de plume of HJG Gundersen) The unbiased estimation of the number and sizes of arbitrary particles using the disector. J Micros. 1984;134:127–136. [PubMed]
28. Gundersen HJG, Bendtsen TF, Korbo L, et al. The new stereological tools. APMIS. 1988;96:379–394. 857–881. [PubMed]
29. Noonan KJ, Hunziker EB, Nessler J, et al. Changes in cell, matrix compartment, and fibrillar collagen volumes between growth-plate zones. J Orthop Res. 1998;16:500–508. [PubMed]
30. Stockwell RA. Biology of Cartilage Cells. Cambridge: Cambridge University Press; 1979. pp. 213–230.
31. Farnum CE, Wilsman NJ. Converting a differentiation cascade into longitudinal growth: stereology and analysis of transgenic animals as tools for understanding growth plate function. Current Opinion in Orthopaedics. 2001;12:428–433.
32. Farnum CE, Wilsman NJ. Chondrocyte Kinetics in the Growth Plate. In: Shapiro IM, Boyan B, Anderson HC, editors. The Growth Plate. Washington: IOS Press; 2002. pp. 245–257.
33. Breur GJ, VanEnkevort BA, Farnum CE, et al. Linear relationship between the volume of hypertrophic chondrocytes and the rate of longitudinal bone growth in growth plates. J Ortho Res. 1991;9:348–359. [PubMed]
34. Germiller JA, Goldstein SA. Structure and function of embryonic growth plate in the absence of functioning skeletal muscle. J Orthop Res. 1997;15:362–370. [PubMed]
35. Arriola F, Forriol F, Canadell J. Histomorphometric study of growth plate subjected to different mechanical conditions (compression, tension and neutralization): An experimental study in lambs. J Ped Orthop. 2001;10:334–338. [PubMed]
36. Carter DR, Wong M. Modelling cartilage mechanobiology. Phil Trans Royal Soc of London. 2003;358:1461–1471. [PMC free article] [PubMed]
37. Henderson JH, Carter DR. Mechanical induction in limb morphogenesis: The role of growth-generated strains and pressures. Bone. 2002;31:645–653. [PubMed]
38. Breur GJ, Farnum CE, Padgett GA, et al. Cellular basis of decreased rate of longitudinal bone growth in pseudoachondroplastic dogs. J Bone Jt Surg Am. 1992;74:516–528. [PubMed]
39. Baron J, Huang Z, Oerter K, et al. Dexamethasone acts locally to inhibit longitudinal bone growth in rabbits. Am J Physio. 1992;263:E489–492. [PubMed]
40. Silbermann M. Hormones and cartilage. In: Hall BK, editor. Cartilage development, differentiation and growth. Vol. 2. New York: Academic Press; 1983. pp. 327–368.
41. Trippel SB. IGF-1 and IGF-2 in growth plate regulation. In: Buckwalter JA, Ehrlich MG, Sandell LJ, et al., editors. Skeletal growth and development: Clinical issues and basic science advances. Rosemont: American Academy of Orthopaedic Surgeons; 1998. pp. 263–283.
42. Giudice LC, deZegher F, Gargosky SE, et al. Insulin-like growth factors and their binding proteins in the term and preterm human fetus and neonate with normal and extremes of intrauterine growth. J Clin Endo Met. 1995;80:1548–1555. [PubMed]
43. Colnot C, de la Fuente L, Huang S, et al. Indian hedgehog synchronizes skeletal angiogenesis and perichondrial maturation with cartilage development. Dev. 2005;132:1057–1067. [PubMed]
44. van Donkelaar CC, Huiskes R. The PTHrP Ihh feedback loop in the embryonic growth plate allows PTHrP to control hypertrophy and Ihh to regulate proliferation. Biomech Model Mechanobiol. 2007;6:55–62. [PubMed]
45. Li TF, O’Keefe RJ, Chen D. TGF-beta signaling in chondrocytes. Front Biosci. 2005;10:681–688. [PMC free article] [PubMed]
46. Lanske B, Karaplis AC, Lee K, et al. PTH/PTHrP receptor in early development and Indian hedgehog – regulated bone growth. Science. 1996;273:663–666. [PubMed]
47. Vortkamp A, Lee K, Lanske B, et al. Regulation of rate of cartilage differentiation by Indian hedgehog and PTH-related protein. Science. 1996;273:613–622. [PubMed]
48. Sundaramurthy S, Mao JJ. Modulation of endochondral development of the distal femoral condyle by mechanical loading. J Orthop Res. 2006;24:229–241. [PMC free article] [PubMed]
49. Wong M, Siegrist M, Goodwin K. Cyclin tensile strain and cyclic hydrostatic pressure differentially regulate expression of hypertrophic markers in primary chondrocytes. Bone. 2003;33:685–693. [PubMed]
50. Wu Qq, Zhang Y, Chen Q. Indian hedgehog is an essential component of mechanotransduction complex to stimulate chondrocyte proliferation. J Biol Chem. 2001;276:35290–35296. [PubMed]
51. Noonan KJ, Farnum CE, Leiferman EM, et al. Growing Pains: Are they due to increased growth during recumbency as documented in a lamb model? Ped Orthop. 2004;24:726–731. [PubMed]
52. Stevens PM, Brown N, Mast N, et al. A rabbit model for hemi-epiphysiodesis: Staples vs. plates. Ped Orthop Soc North Am. 2006;14:46.