Epker, B.

Frost, H. M.

Takahashi, H.

English

Henry Ford Health System Scholarly Commons

Henry Ford Hospital Medical Journal Volume 13 Number 1 Article 5 3-1965 Relation Between Age And Size Of Osteons In Man H. Takahashi B. Epker H. M. Frost Follow this and additional works at: https://scholarlycommons.henryford.com/hfhmedjournal  Part of the Life Sciences Commons, Medical Specialties Commons, and the Public Health Commons Recommended Citation Takahashi, H.; Epker, B.; and Frost, H. M. (1965) "Relation Between Age And Size Of Osteons In Man," Henry Ford Hospital Medical Bulletin : Vol. 13 : No. 1 , 25-31. Available at: https://scholarlycommons.henryford.com/hfhmedjournal/vol13/iss1/5 This Article is brought to you for free and open access by Henry Ford Health System Scholarly Commons. It has been accepted for inclusion in Henry Ford Hospital Medical Journal by an authorized editor of Henry Ford Health System Scholarly Commons. Henry Ford Hosp. Med. Bull. Vol. 13, March, 1965 RELATION BETWEEN AGE AND SIZE OF OSTEONS IN MAN* TAKAHASHI, H . , M.D.,** EPKER, B. ,*** FROST, H . M . , M.D.**** INTRODUCTION***** I T HAS BEEN REPORTED that the rate of individual o.steon formation varies considerably in an age-dependent manner in normal people," as well as between metabolically normal and diabetic people." But in the same cases and bones the above authors reported that the quantity of bone in a finished osteon fended to remain at least approximately constant. The range of change in rate observed by these authors was as 7 is to 1 while the range of change in quantity was as .9 is to 1. It was proposed I hat this might mean that some modes of cellular behavior arc age independent, and are in effect constants. But when it is proposed that within a single cell system (such as that which makes a new osteon) there are (1) separate mechanisms for controlling the rate and total quantity of useful metabolic work done by the cells in a system, and (2) that the total quantity made when the process finishes is invariant in the face of both aging and widely varying rates, the proposition must be considered radical. It merits the most careful evaluation before being accepted, because if it were true it could seriously affect our concepts of the regulatory mechanism(s) that control the meta-bolism and aging of mammalian tissues. Partly, the reason for this is that such a phenomenon suggests strongly that a digital, either-or, dcvicet is controlling some of the dynamic aspects of the behavior of a group of cells. This is quite a different thing from having a digital device control the structure of a protein (which, in the context used here, DNA is, and does). With respect to the osteon transverse sizes discussed by Hattner et al," a moment's microscopic inspection of a cross section of the cortex of any long bone *Work aided by grant 293, Henry Ford Hospital, and AM-04186, National Institutes of Health, Bethesda, Maryland. A part of the work was presented at the Gerontological Society Meeting in Minneapolis, Minn., October 31, 1964. '•Orthopaedic Research Fellow, Orthopaedic Research Laboratory, Henry Ford Hospital. (On leave from Niigata University School of Medicine, Niigata, Japan). •••University of Detroit School of Dentistry, Detroit. Michigan. ••••Associate Orthopaedic Surgeon. Henry Ford Hospilal. Detroit 2, Michigan. •••••This paper was read to the Biological Sciences Division of the Gerontological Society al its 17lh annual meeting in Minneapolis, October, 1964. tBy which is meant that the device functions like an electrical switch: it is either on, or it is off, hut there arc no gradations in between. 25 TAKAHASHI. EPKER AND FROST will show that there arc large vari:itions in the sizes of individual osteons. Hattner et a l " circumvented this problem by determining the mean size of these osteons in any given cross section of a rib. This size is relatively constant even though the individual osteon sizes do vary widely. But these facts raise the possibilities that (1) there may be major age-related changes in the frequencv distribution which were concealed by the methods used in Ihe studies alluded to, and (2) that therefore the inteiprei.Ition ol these authors was unjustified. And in fact, they did observe an approximately \5 per cent age-ile|ieiulent change in size. In this report the size-frequency distribution of osteons in ribs from normal people of various ages is defined. In part this is done by using previously published data but some new data are added. M v i i K i A i s ANI) Mi; i i ions \/ I / / A7 l/S We obtained the middle third of the 5th. 6th or 7th rib from 130 meta-bolic:illy normal people. Their ages ranged from 10 to 70 years. The cases were obtained, some at ;iiitopsy at the county medical examiner's office, some at autopsy at Ihis hospital, and some at thoracotomy for the repair or biopsy of anatomical, nondebilitating lesions. .-Ml of the C.ISCS were felt to be met.ibolic;illy normal up to the time of skeletal sampling. ;ind records were sufficient in all e;ises to suhstanti:ite this claim. \l1.1 ll<IDS I ush. mineralized, imeinbedded. 50-75 micron thick cross sections of the ribs were made by methods previously reported.'''" They were oriented within 5 degrees of perpendicularity to the long axes of the bones. While the sections were stained by 1 per cent IMSIC tiKlisin 111 .1 so ,.^.ni cili.inol solution, the staining method is not critical in this work. .An average of three sections per ease were available for this study. MEASUREMENTS: The cross section areas of secondary osteons were measured by a prcvioiislv ilescribed point count method, utilizing the Zeiss integrating eyepiece I . " " Mc.isiiring precision was arbitrarily set at - .005 mm'. In the //r.v/ .series of measurements, \'.c nu-.isiiieil the lot.il ;irea inside Ihc cement line, using as the criterion of an osteon that VI .is sclecicil for me;isurement. th:it il be any iinrcmodcleil secondary osteon^ in the section. I here were 1.155 such structures. In the .second .series, we made this same measurement, hut changed the selection criterion so that only actively forming osteons were measured. .•\n osieoiil se.im was taken as the criterion of the state of being in active formation. ' ' "" I here were 604 such striictiiics Ihe data were then arrayed by age decades, the total frequencies norm.ilized and the si/e increments standardized. Ilu- il.ii.i .ire shown in tabular form in Table I and Table I I . Figures 1 and 2 are iipieseni.iiivc lusiograms. constructed from columns 2-6, Table I , and columns 2-6, Table I I . RESULTS XNithin the limit of precision of the measuring method, no significant change w.is found in ihe distribution of the various sizes of total osteon cross section areas across the M) ye.ir span of life that was studied, as long as the selection criterion was an actively lorming osteon. I here is a sy stematic, age related change in the size distribution when the selection criterion was ;inv iinremodeled sccondarv osteon. •We wish to thank Drs. E. S. Zawadski, R. H. Hom and G. Fine for their generosity in donating this material and for making the records and autopsy rcporls available lo us. .^•\ setondarv osteon is anv osteon lormed iif ifr the formation of the cortical bone in which it is deposited. 26 AGE AND SIZE OF OSTEONS Table I THE SIZE-FREQUENCY DISTRIBUTION OF CROSS-SECTION AREAS OF OSTEONS WITH OSTEOID SII.VM Range of Normalized Size of Nonimlizetl Fieiiiwiicks Osteons (%) 10s 20s 30s 40s 50s D- 10.3 2.4 3.9 12.7 6.9 6,3 10.4- 21.5 15.6 16.4 lO.I 20.7 23.6 21.6- 32.7 24.1 18.0 21.5 16.3 27.5 32.8- 43.9 20.5 27.3 26.6 21.6 13.7 44.0- 55.1 21.8 14.9 12.7 13.8 16.3 55.2- 66.4 12.0 11.7 8.9 6.9 7.4 66.5- 77.6 3.6 7.0 2.5 3.5 4.7 77.7- 88.8 0 0.8 5.0 6.0 0.5 88.9-100.0 0 (1 0 4.3 0 Over 100.0% 0 1.6 0 3.4 l . l Total osteons 83 130 79 120 192 A selection of the cross section areas within the cement line of 604 actively forming osteons in 90 subjects, arranged by age decades. Their differences are not fell to be f ignificanl. Both the sizes. and the frequencies. are given as per cents of the maximum or total. respeelively. In the first column, 100 per cent corresponds lo .107 mm' in both this "able and in table I I . Table I I THE SIZE-FREQUENCY DISTRIBUTION OF CROSS-SECTION AREAS OF UNREMODELED SECONDARY OSTEONS Range of Normalized Size of h'ormiiltzoil Frci/iii'iit it s Osteons (%) 10s 20s 30s 40s 60s 0- 10.3 6.8 15.0 12.8 13.0 17.6 10.4- 21.5 15.8 19.8 29.2 31.0 20.7 21.6- 32.7 22.3 19.0 27.3 20.6 25.0 32.8- 43.9 21.0 22.6 16.2 17.6 18.7 44.0- 55.1 17.2 11.6 8.1 7.4 7.7 55.2- 66.4 7.1 6.4 4.6 3.0 5.6 66.5- 77.6 5.8 4.0 1.5 4.4 3.0 77.7- 88.8 2.7 0.8 0 2.7 1.0 88.9-100.0 1.3 0.8 0.3 0.3 0.7 Over 100.0% 2.4 0.8 0.3 0.7 0 Total osteons 303 250 400 302 300 Similar to Table I . but constructed from measurements of any unremodeled secondary osteon. The accumulated excess of small, unremodeled osteons described in the text can be seen by comparing 'he tops of columns 2 and 6. 27 TAKAHASHI. EPKER AND FROST A C T I V E L Y F O R M I N G O S T E O N S ( R l B S ) N : 604 A G E : 1 0 - 5 9 0 0 0 Figure 1 A liisio'ji.im of the cross seclion areas of actively forming osteons. There is no significant difference in their distribution according to age. U N R E M O D E L E D O S T E O N S ( R I B S ) N ; 1155 AGE: 10-65 n I ooc Figure 2 V histogram made from all secondary osteons, whether they were actively forming or not. Whereas the average age of Ihe structures in Figure 1 is 45 days, for those in this figure i l is on the order of 10 years. There is a definite relative increase in the smaller size osteons in this figure. Both the X and Y axes in these figures have been normalized so that the total frequency is 1.00, and the maximum si/e is LOU: Ihis device makes different sized groups of data comparable. 28 AGE AND SIZE OF OSTEONS DISCUSSION Effect of Size on Remodeling of Osteons: The distribution of sizes in actively forming osteons remained unchanged by any amount that could he detected by our methods, i.e., it was less than ± .01 mm'. Because these structures are actively lorming. they are relatively young, and it can be shown that their average age is 42 days.* This means that these measurements indie;ite the relative incidence of formation tas distinguished from relative prevalence) of the various sizes of osteons. Then what was the origin of the small, age related changes in mean osteon cross section area ( ± .006 mm') that were found bv Hattner et al," as well as bv Fanderos and Frost." and as well as of the changes in osteon diameters loiind independently bv Currcv' and Frost'."^ These changes proved to be an illustration of the ilifference in meaning of incidence and prevalence, and were created by the criteria for selecting osteons for measurement. None of the authors mentioned above measured an osteon it ll had been parti;illy remodeled, ;ind there seemed to be sound reasons lor this procedure. But large osteons are more likely to be partially remodeled by newer remodeling processes than are small ones, given equal periods ot time afler iheir completion. Thus, with increasing time, there is an accumulated excess ot unremodeled smaller osteons th;it is out of proportion to that of unremodeled large ones. For this reason the arithemeiic means, both of diameters and of cross section areas, of all secondary osteons, (i.e., both completed and actively forming) tend to decline with aiiviincing age. This effect can be very convincingly shown by comparing Figure I to Figure 2. The first is the histogram obtained Irom the cases in the age 10-59 decade, the selection criterion being that the osteons were actively lorming, i.e., had an osteoid seam lining their central canal. T his portrays the relative incidence of the lormation of the various osteon sizes*. The second figure is a histogram of the same sections, but using the selection criterion that any unremodeled secondary osteon was measured. This portrays the relative prevalence of the various osteon sizest. Invariance in Osteon Size: A Markov Property: The meaning of ihis study then is that, whenever a new osteon is about to be made in human ribs, there is a definite probability that it will have a given cross section area, and this probability is invariant (i.e., changes less than : t 10 per cent) over the span of life, and in the bone, we studied. This is true in spite of independent evidence that during this same span of life the rate at which this amount of bone is made declines to some 40 per cent of its original value' At the macroscopic level, the amount of proteinaceous matrix in a cubic millimeter of bone (absolute bone volume)' changes less than 7 per cent across the span of life that was studied.' •By substituting in equation 6.f)9, p. 53, (Frost)" the data in the cited references ( » " ) and dividing by two. The assumption of linear radial rate of osteon closure involved in this procedure has been shown to be approximately true by Epker, Hallncr and Frost.' + lncidence means how often something happens in unil time. Relative incidence is how often il happens compared to other happenings. For example, the statement thai male births are 52 per cent of all births is a statement of relative incidence. Prevalence is Ihe composition of a population or sample al any instant. For example, the prevalence of males in the nurses residence is around .03. although the'rclauve incidence of male births (outside of this residence!) is around .52. 29 / \KMIASIII. EPKER AND FROSI Ihe Basu .Meiaholizing Cellular Unit: Thus, a special kind of invariance has been shown to be present in a system of cells (i.e., that making new osteons). This is an invariance in the distrihiition of transition prohahiUties in a matrix of available choices of action. This embraces the fact that the distribution of sizes of osteons made this \c.ir SCLIIIS to be unaffected by what happened last year or earlier, a situation which has the pr. pviiies ot the probabililv chain described by Markov,' and can be repre-sented as an ergodic probability matrix.' The property we have unearthed in this study could nol be seen in cell-free homogenate systems, nor in studies of macroscopic portions of any organ such as ilie lemur, lung or kiilney. The reason is that this appetirs as a property of the b.isic. b me-lormiiig unit inside of cortical bone, the seconilarv osteon. I his structure is made by a collection of cells of dilferent kinds, and involves several different kinds ot ceil behavior a :il function which have varying ilcgrees of synchrony with K | H : I to ilieir generation, ;ind metabolic activity. The collection of cells and their liinei.ins appear to merit recognition as being a system, which is the smallest ana-I 1U1..1I unit ilisphiving the full range of behavior which is required to produce the phen. men.i known to occur in all cortical bone lemodeling. (Elsewhere this system will ie calleil .1 ll.isie Mei.ibolic Unit, or BMLI.) When intact organs or slices of them are s'lulied that are made up of such units, the dvnamic idiosyncrasies of i;nlividu.il BMU tend to be •"drowned out" by the similar but asvnchronous contribu-tions ol thous.;nds of others in all ililterent (i.e.. :isvnchronousI stages ot function. Ihe kill s\ ncr.isics ol the inilividual units may thus appear ;is "noise", and tend to be i::nored bv observers. I • • I t of tins Invariance nn Mclahoiii Regulation: It is natural to suspect that the t .1.11.lime controls ol some soil tissue svsiems may possess properties analogous to those we h.ive shown here in bone. If so. this knowleilge would be of crucial import.ince 111 le.irning how to regulate their metabolic activities on an a priori b.isis.t One re.ison lor this is quite simple: Given: a tissue system whose total work I. I I Is divided up into .1 luimbei ol phvsically. temporally and functionally discrete units 1 he .imount of "work" that each of these units had produced when finished woulil be inv.iri.int in the sense just described. Given further: that the function of these units cm be turned on b\ some suitable stimulus. There is only one way i f pro,till tm: a peimuiic' t change in the rate of metaholic output of such a system, and thill is hv chani:ing the numher of units that are functionally activated, or ' turned < n". in a unit period of time, tin bone we have called this the mesenchvmal cell .iciiv.Ition lunction.)" Changing the rale at which individual units function can Whivh , as vie will show later. i>roMde.s n.t wuh a sYnchronouslv sencrated culture or system of cells 1 osieiKl.isis .111.1 osieobl.isis I . provided the svstem is studied in cross section. Moreover this culture I . in t>c oh<<rved as i l functions in its in \ i \ o stale, completely unaffected by Ihe observing act, hecausr the cells leave a record of what they do. The record is permanent, and il is read afler its I I . iiis^npii.'ii this mav be the only human situation in which synchronous cell culture can be s l i i d i e d I ' l w i l l ' Bv .1 piiori IS inc.inl ihal .1 svstem is well enough understood to manipulate its functions intelligently and vnth a high degree of sonlulensc ih.ii .1 ei^en manipulation or change will produce exactly the effccl dcMied. The opposite of this would be "cut-and-try", or shooting in the dark, or purely empirical. 30 AGE AND SIZE OF OSTEONS only cause temporary changes in the rate at which metaholic work is produced (i.e., system transients), which must always return to normal levels, given time enough and when the output of the entire tissue or organ is considered. The theoretical rate at which systems of cells can produce metabolic work is a function of the maximum, limiting ;imouRt of work per unit, the rate at which this work is produced by the unit, and the numher of units that are active at any moment. One degree of freedom is removed Irom this system when the limiting amount is set constant. When the time parameters of such a system are known, the duration of the transient (or temporary change) caused by disturbing the rate of evolution of individual units can easily be calculated. S U M M.VRV The distribution of osteon cross section sizes in human rib is constant over the age span of 10-70 years, in spite of a more than two-fold change in the rates at which they are made over this same time. It is suggested ( I ) that similar dynamic invariants occur in other tissues, (2) and that analytical accuracy and comprehension ot metabolic and aging processes would be improved in the luture by recognizing and separating invariant from variable dynamic properties of experimental biological svstems. This is a new concept in the study of the dynamics of multicellular systems. Relerences for this and the following two papers will be found on pages 49-50. 31 

Relation Between Age And Size Of Osteons In Man

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Relation Between Age And Size Of Osteons In Man

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