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From Wolff's law to the Utah paradigmInsights about bone physiology and its clinical applications.

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THE ANATOMICAL RECORD 262:398 – 419 (2001)
Invited Review
From Wolff’s Law to the Utah
Paradigm: Insights About Bone
Physiology and Its Clinical
Applications
HAROLD M. FROST*
Department of Orthopaedic Surgery, Southern Colorado Clinic, Pueblo, Colorado 81004
ABSTRACT
Efforts to understand our anatomy and physiology can involve four often overlapping phases.
We study what occurs, then how, then ask why, and then seek clinical applications. In that
regard, in 1960 views, bone’s effector cells (osteoblasts and osteoclasts) worked chiefly to maintain homeostasis under the control of nonmechanical agents, and that physiology had little to do
with anatomy, biomechanics, tissue-level things, muscle, and other clinical applications. But it
seems later-discovered tissue-level mechanisms and functions (including biomechanical ones,
plus muscle) are the true key players in bone physiology, and homeostasis ranks below the
mechanical functions. Adding that information to earlier views led to the Utah paradigm of
skeletal physiology that combines varied anatomical, clinical, pathological, and basic science
evidence and ideas. While it explains in a general way how strong muscles make strong bones and
chronically weak muscles make weak ones, and while many anatomists know about the physiology that fact depends on, poor interdisciplinary communication left people in many other
specialties unaware of it and its applications. Those applications concern 1.) healing of fractures,
osteotomies, and arthrodeses; 2.) criteria that distinguish mechanically competent from incompetent bones; 3.) design criteria that should let load-bearing implants endure; 4.) how to increase
bone strength during growth, and how to maintain it afterwards on earth and in microgravity
situations in space; 5.) how and why healthy women only lose bone next to marrow during
menopause; 6.) why normal bone functions can cause osteopenias; 7.) why whole-bone strength
and bone health are different matters; 8.) why falls can cause metaphyseal and diaphyseal
fractures of the radius in children, but mainly metaphyseal fractures of that bone in aged adults;
9.) which methods could best evaluate whole-bone strength, “osteopenias” and “osteoporoses”; 10.)
and why most “osteoporoses” should not have bone-genetic causes and some could have extraosseous genetic causes. Clinical specialties that currently require this information include orthopaedics, endocrinology, radiology, rheumatology, pediatrics, neurology, nutrition, dentistry, and
physical, space and sports medicine. Basic science specialties include absorptiometry, anatomy,
anthropology, biochemistry, biomechanics, biophysics, genetics, histology, pathology, pharmacology, and cell and molecular biology. This article reviews our present general understanding of
this new bone physiology and some of its clinical applications and implications. It must leave to
other times, places, and people the resolution of questions about that new physiology, and to
understand the many devils that should lie in its details. (Thompson D’Arcy, 1917). Anat Rec 262:
398 – 419, 2001. © 2001 Wiley-Liss, Inc.
Key words: bone; biomechanics; endoprostheses; osteoporosis; healing; Wolff’s
law; homeostasis; muscle; microgravity
*Correspondence to: Dr. Harold M. Frost, Department of Orthopaedic Surgery, Southern Colorado Clinic, Pueblo, CO 81004.
Received 3 August 2000; Accepted 16 November 2000
Published online 28 February 2001
©
2001 WILEY-LISS, INC.
WOLFF’S LAW AND THE UTAH PARADIGM
“. . .between muscle and bone there can be no change
in the one but it is correlated with changes in the
other. . .” (Thompson, 1917)
We try to understand the anatomy and physiology of our
body’s organ systems to achieve better management of
their clinical problems. In that vein, for over 100 years
anatomists and orthopaedic surgeons looked to Wolff’s
Law (Wolff, 1892). One translation of it from German to
English reads thus (Rasche and Burke, 1962): “Every
change in the form and function of bone or of their function
alone is followed by certain definite changes in their internal architecture, and equally definite alteration in their
external conformation, in accordance with mathematical
laws.” Hindsight reveals some limitations of that Law. For
example, in 1892 it had no clinical applications; it said
mechanical influences can affect bone architecture, but
not how; and it could not predict particular effects of
specific mechanical challenges.
Later evidence began to resolve such limitations and led
to the still-evolving Utah paradigm of skeletal physiology
that sprang from a soil of multidisciplinary evidence and
ideas (Burr and Martin, 1992; Frost, 1992, 2000a; Jee and
Frost, 1992; Schönau, 1996; Takahashi, 1995, 1999). It
adds tissue-level and anatomical features and roles to
former views that emphasized cell-level features and
roles. The new paradigm has growing applications to
joints, ligaments, tendons, and fascia (Frost, 1995), but
this article concerns its applications to bone as material
and to bones as organs. Table 1 lists some of the things the
paradigm can explain. Three of its propositions concern
the purpose of load-bearing bones and how that is
achieved.
Proposition 1: Healthy, postnatal load-bearing bones
are designed to have only enough strength to keep chronically subnormal, normal or supranormal voluntary loads
(not injuries) from causing spontaneous fractures (Frost,
1997a). Achieving that “mechanical competence” should
be the ultimate test of a bone’s health and the main goal of
its biologic mechanisms. In that view, bone “health” and
“strength” differ. The former would depend on the relationship between a bone’s strength and the size of the
peak loads it usually carries. Thus mouse and horse femurs that satisfied Proposition 1 in the animals they came
from would be equally healthy, even though their
strengths differ more than 1,000 times. Likewise for the
ribs and femurs in a single human being.
Proposition 2 (in three parts): 1.) To achieve mechanical competence bone’s tissue-level biologic mechanisms
need nonmechanical factors and effector cells (osteoblasts
and osteoclasts), just as cars need motors, fuel and wheels
in order to move. 2.) In a negative feedback arrangement
bone loads and strains guide those biologic mechanisms in
time and anatomical space**, just as steering, brakes, and
accelerators guide cars. 3.) Most nonmechanical factors
can help or modulate that guidance but cannot replace
it**. In proof, such factors cannot normalize bones, joints
or tendons in paralyzed limbs. Equally, motors and fuel do
not tell cars where to go or when.
To explain, the newborn skeleton already has its basic
architecture and relationships, and the biologic mechanisms, responses, and signaling mechanisms that can
adapt it to postnatal influences (Cruess, 1982; Enlow,
1963; Hanes and Mohidden, 1965; Weinmann and Sicher,
1955). The signaling mechanisms could include osteocytes, bone lining cells, and other cells in the marrow, and
399
TABLE 1. Clinical phenomena the Utah paradigm
can explain plausibly*
Why strong muscles usually associate with strong bones.
Why too stiff and too compliant internal fixations can each
impair the healing of fractures, bone grafts, and
arthrodeses.
What makes fracture callus reshape itself.
Why some screws or external fixation pins in bone loosen or
pull out.
Why the bone supporting some endoprosthetic designs
collapses.
Why most aging adults lose bone strength and “mass.”
Why chronic muscle weakness associates with an
osteopenia.
Why chronic debilitating illness usually associates with an
osteopenia.
Why whole-bone strength and stiffness usually correlate
well.
What makes healthy bones stronger than needed for their
usual voluntary mechanical usage.
What makes net bone losses usually come from bone next to
marrow.
Why obese people have more bone strength than equally
active slender people.
Why some patients with “osteoporosis” develop spontaneous
fractures but others do not.
What causes stress fractures, “spontaneous fractures,” and
pseudofractures.
Why most men have more bone strength than most women.
The chief cause of increased bone fragility in osteogenesis
imperfecta.
Why “vigorous” exercise can help to keep but not increase
bone strength in adults.
How to distinguish mechanically competent bones from
incompetent ones.
Why osteoclasts are not essential for effective homeostasis.
Why remodeling could not cure an osteopenia but modeling
could.
The direct cause of most so-called “osteoporosis fractures.”
*While plausible need not mean correct too, as the number of
things a paradigm can explain increases, so do its credibility
and usefulness.
could depend on streaming and piezoelectric potentials,
some chemical phenomena, and fluid shear over cell membranes (Marotti et al., 1996; Martin, 2000). Chiefly gene
expression patterns in utero would predetermine those
baseline conditions (mechanical effects in the last trimester of pregnancy are ignored here; Carter and Wong,
1990). At any time after birth, the skeletal organs in
neonatally paralyzed and normal limbs show typical differences in their strength, architecture, and other features. Those differences should reveal the kinds and magnitudes of the adaptations to postnatal mechanical loads
in the normal limbs. Structures in the totally paralyzed
limbs should reveal the baseline conditions, presumably
affected by postnatal nonmechanical agents including
genes (Jaffurs and Evans, 1998), but not by normal postnatal loads (Frost, 1995).
Implication: Bones, fascia, ligaments, and tendons
should not completely disappear in total permanent disuse. Indeed, in the lower limbs of patients with congenital
complete paralysis due to myelomeningocele, some bone
and other structural tissues always remain (Frost, 1986).
The following sections demonstrate how those postnatal
bone differences develop and some clinical applications of
that physiology. A Glossary at the end defines some of the
400
FROST
Fig. 1. Bone modeling by drifts. A: An infant’s long bone with its
original size and shape in solid line. To keep its shape as it grows in
length and diameter, drifts move its surfaces in tissue space as the
dashed lines suggest. Formation drifts make and control new osteoblasts to build some surfaces up. Resorption drifts make and control
new osteoclasts to remove bone from other surfaces. B: A different drift
pattern can correct the fracture malunion in a child shown in solid line.
The cross-section view (right) shows the endocortical as well as the
periosteal drifts that do that. C: How the drifts in B would move the
whole segment to the right. Changing the anatomy in that way reduces
the bone’s bending moments. Drifts are created when and where they
are needed, and include capillaries, precursor and “supporting” cells,
and some wandering cells. They are multicellular entities in the same
sense as renal nephrons Reproduced from Frost (1997d) with permission
of the publisher.
terms used in the text. Note: Throughout the text, a double
asterisk (**) after a statement will mean: “While some
might consider that statement controversial and I will
respect such views, I am sure the statement is valid.”
Why not on “1” too? When compared to the big differences
in strength of our ribs and femurs, bone’s materials properties change relatively little with aging, sex, species,
bones, and most diseases, osteomalacia excepted (Martin
et al., 1998). Like bone “mass,” normally whole-bone
strength increases during growth; it plateaus in young
adults and declines afterwards (Ferretti, 1999; Garn,
1970; Schiessl et al., 1998). This article emphasizes wholebone strength, since nature seems to rank its importance
above bone “mass.”
SUMMARY OF THE NEW PHYSIOLOGY
Four Physical Features Combine to Determine
Whole-Bone Strength
(Currey, 1984; Martin et al, 1998)
1.) That strength depends on bone’s stiffness, ultimate
strength, resilience, true density, etc. (the materials property factor). 2.) It depends on the kinds of bone— woven,
plexiform and lamellar, compacta, and spongiosa— and
their amounts in a cross-section (the “mass” factor). That
amount usually increases during growth, plateaus in
young adults, and then declines, so by 80 years of age less
than 60% of the young-adult bone “mass” (and strength)
can remain (Buckwalter et al., 1993; Marcus et al., 1996;
Smith and Gilligan, 1989). 3.) Its size, shape, and the
distribution of its bony tissue in space affect a bone’s
strength (the architectural factor). Thus, doubling outside
bone diameter while keeping the same amount of bone in
the cross-section so the cortex becomes thinner, increases
bending strength about eight times. 4.) Fatigue damage or
microdamage also affects a bone’s strength (the microdamage factor) (Burr et al., 1997; Forwood and Parker,
1989; Martin 1995, 2000).
Longitudinal bone growth and the baseline conditions
excepted, normally a bone’s anatomy depends on “2” and
“3,” and whole-bone strength depends chiefly on “2,3,4.”
Two Biologic Determinants of Whole-Bone
Strength: Bone Modeling and Remodeling
In former views, independently working osteoblasts
controlled gains of bone, and independently working osteoclasts controlled bone losses (Aegerter and Kirkpatrick,
1975; Albright and Reifenstein, 1948; McLean and Urist,
1961; Snapper, 1957). But, except longitudinal bone
growth, tissue-level modeling and remodeling mechanisms chiefly control those gains and losses and help to
control a bone’s gross anatomy. Both mechanisms need
osteoblasts and osteoclasts as well as precursor, stem, and
other cells to do their work (Jee, 1989; Martin et al., 1998;
Parfitt et al., 1996; Schönau, 1996).
Modeling by resorption and formation drifts (Fig. 1) can
move bone surfaces in tissue space to determine the crosssectional size and shape and longitudinal shape of bones
and trabeculae (Jee, 1989). That seems to be nature’s
preferred way to increase a bone’s strength. Modeling
would seldom if ever reduce a bone’s strength.
WOLFF’S LAW AND THE UTAH PARADIGM
401
Fig. 2. Bone remodeling BMUs. A–C: An activation event on a bone
surface at A causes a packet of bone resorption at B, and then replacement of the resorbed bone by osteoblasts at C on the right. The BMU
makes and controls the new osteoclasts and osteoblasts that do this.
D–F: This emphasizes the amounts of bone resorbed (E) and formed
(F) by completed BMUs. G–I: In these “BMU graphs” (after Frost),
G shows a small excess of formation over resorption. H: Equalized
resorption and formation as on haversian surfaces and in “conservation-
mode” remodeling. I: Net deficit of formation, as in “disuse-mode”
remodeling of endocortical and trabecular bone. Bottom: These “stair
graphs” (after P.J. Meunier) show the effects of a series of BMUs of the
kind immediately above on the local bone “bank.” BMUs are created
when and where they are needed, and include a capillary, precursor and
“supporting” cells, and some wandering cells. They are multicellular
entities in the same sense as renal nephrons Reproduced from Frost
(1997d) with permission of the publisher.
Remodeling by BMUs (Basic Multicellular Units, Fig. 2)
turns bone over in small packets in which osteoclasts
resorb some bone and then osteoblasts fill the resulting
hole or excavation with new bone (Jee, 1989). This remodeling can work in at least two modes. In a “conservationmode,” completed BMUs resorb and make nearly equal
amounts of bone so no significant bone gain or loss ensues;
but in a “disuse-mode,” BMUs make less bone than they
resorb, but only for bone next to or close to marrow (trabecular and endocortical bone) in both children and adults
(Frost, 1998b)**. This disuse-mode remodeling should
cause all adult-acquired osteopenias on earth and in astronauts in orbit (Frost, unpublished data1)**. It should
help to explain why, in healthy human subjects, bone
“mass” can decrease over 40% between 25 and 75 years of
age (Marcus et al., 1996), and over 90% of that bone loss
comes from bone next to marrow. During that age span,
intracortical porosity increases from ⬃ 3.5% to ⬃ 7%
(Frost, 1969). BMUs seldom, if ever, increase bone
strength and “mass.” Here one should distinguish perma-
nent bone losses caused by disuse-mode remodeling, from
temporary losses from the increased remodeling space
(Heaney, 1994) that always accompanies increased remodeling-dependent bone turnover (Jaworski, 1984).
1
Frost unpublished data: Personal observations during 50
years of experience in orthopaedic surgery, education, research
and pathology, strongly supported by unpublished findings of
others.
Mechanical Control of Bone Modeling and
Remodeling
(Burr, 1998; Burr et al., 1995; Forwood and
Turner, 1995; Frost, 1990a,b; Jee and Frost, 1992;
Martin et al., 1998; Martin, 2000; Umemura et al.,
1997)
Mechanical loads on bones deform or strain them, and
larger loads cause bigger strains. Where strains exceed a
modeling threshold range, modeling slowly increases bone
strength to reduce later strains towards that range; otherwise mechanically controlled modeling turns off. Those
responses make bones strong enough to keep “typical peak
strains” (see Glossary) from exceeding that threshold**.
Since the threshold lies below bone’s ultimate strength,
those responses make healthy bones stronger than needed
for their peak voluntary loads. In young adult mammals,
that “strength-safety factor” (see Glossary) ⬇ 6 when expressed in stress terms. When strains stay below a lower
remodeling threshold range, disuse-mode remodeling permanently removes bone, but only next to or close to mar-
402
FROST
TABLE 2. Examples of nonmechanical factors that
could influence bone adaptations to mechanical
usage and strains (so they could influence bone
strength and “mass” too)
Hormones
Dietary calcium
Paracrine effects
Amino acids
Gene expression
Gender
Age
Vitamins
Other minerals
Autocrine effects
Lipids
Ethnic origin
Some diseases
Apoptosis
D metabolites
Cytokines
Cell-cell interactions
The genome
Occupation
Malnutrition
Ligands
Medications and Other Artificial Agents
row**. That causes a “disuse-pattern osteopenia” characterized by less spongiosa, an enlarged marrow cavity, and
a thinned cortex, but not a decreased outside bone diameter. When strains exceed that threshold, conservationmode remodeling begins to reduce or stop those bone
losses. That prevents an osteopenia or progression of an
existing one.
In such ways, strain indirectly but strongly influences
the postnatal strength and architecture of load-bearing
bones.
Those threshold ranges make the largest strains control
modeling and remodeling effects on whole-bone strength,
and make lesser strains have little effect on it (Lanyon,
1996; Martin et al., 1998; Rubin and McLeod, 1994; Torrance et al., 1994). The thresholds also provide natural
criteria that help to distinguish “normal” from too little or
too much bone strength**. Their existence and values
would reside as genetically determined internal standards
in some skeletal cells (we do not yet know which cells).
During mechanical usage, strain-dependent signals from
bone would be compared to those standards, and if that
reveals an error a corresponding “error signal” would arise
that made modeling or remodeling correct the error. How
aging affects these thresholds is uncertain but under
study (Raab-Culen et al., 1996). The signaling mechanisms, pathways, and cells that help to control those
things now form separate fields of study in skeletal science
(El Haj, 1990; Fukada and Yasuda, 1957; Marotti et al.,
1996; Martin, 1995, 2000; Martin et al., 1998; Skerry,
1997).
adults, and then declines (Burr, 1997; Faulkner et al.,
1990; Larsson et al., 1979).
That should help to explain why strong muscles usually
do make strong bones, and chronically weak muscles usually do make weak bones** (Doyle et al., 1970; Frost and
Schönau, 2000; Jee, 1999, 2000; Jee and Li, 1990; Jee et
al., 1991; Jee and Frost, 1992; Li et al., 1990; Li and Jee,
1991; Snow-Harter et al., 1990; Yao et al., 2000). For
example, most women have weaker muscles than most
men, so they should have less bone strength (and “mass”)
too. They do, even if gender has additional effects. As Burr
(1997) and Schönau et al. (1998) noted, neuromuscular
influences on bone strength were long misunderstood and
minimized, but they are becoming another field of study in
skeletal science. That realization led Dr. GP Lyritis in
Greece to form the new International Society for Musculoskeletal and Neuronal Interactions.
Variations in how different individuals use different
parts of their bony skeletons mechanically can cause variable differences in the strength and tissue dynamics of
different bones (Podenphant and Engel, 1987). That helps
to explain why some bones need not predict the strength of
some other bones very well. Such problems puzzled many
osteoporosis authorities who, because of the lingering
views mentioned in the Summary (Cohn et al., 1984),
sought exclusively nonmechanical explanations.
Nonmechanical Control of Bone Modeling and
Remodeling
(Frost and Schönau, 2000; Kannus et al., 1996;
Pauwels, 1986; Rittweger et al., 1999; Schiessl et
al., 1998; Schiessl and Willnecker, 1999; Schönau
et al., 1998)
In former views, factors like those in Table 2 dominated
control of the postnatal strength of load-bearing bones
(Bilezikian et al., 1996; Canalis, 1993; Duncan and
Turner, 1995; Favus, 1999; Huffer, 1988; Parfitt, 1993,
1995; Parfitt et al., 1996). However the omissions of such
views make them suspect.
In fact, most such factors can help or modulate but
cannot replace the mechanical control of postnatal bone
modeling and remodeling**. As examples, by direct actions on bone cells things like hormones, calcium, vitamin
D, and genes might determine 3% to as much as 10% of a
bone’s postnatal strength, but mechanical usage effects on
modeling and remodeling determine over 40% of it**. In
proof, years after a paraplegia bones in lower but not
upper extremities can lose over 40% of their original bone
“mass” (Kiratli, 1996). Similar events occur after total
lower extremity paralysis from anterior poliomyelitis
(Frost, unpublished results), while lower limb bones of
patients paralyzed by a myelomeningocele show even
larger deficits (Frost, unpublished observations).
Figure 3 indicates some combined effects of modeling,
remodeling, and their strain thresholds on a bone’s
strength.
Muscles work against such bad lever arms that it takes
well over 2 kg of muscle force on bones to move each
kilogram of body weight around on earth (Crowninshield
et al., 1978; English and Kilvington, 1979; Lu et al., 1997;
Martin et al., 1998). Ergo, the largest voluntary bone loads
and bone strains come from muscles, not body weight as
formerly thought (Koch, 1917). Since those strains help to
control modeling and remodeling effects on bone strength,
momentary muscle strength (see the Glossary) indirectly
but strongly affects the strength of load-bearing bones. Or:
muscle forces 3 bones 3 strains 3 control of modeling
and remodeling. Like bone strength, usually muscle
strength also increases during growth, plateaus in young
2
Jee WSS: Hard Tissue Workshops organized annually since
1965 by Professor Jee provide a uniquely seminal and multidisciplinary forum for presenting and discussing new methods, evidence and ideas about human skeletal disease. These workshops
are attended by hundreds of international authorities and fellows
in many disciplines, sponsored by the University of Utah and
supported by private and federal funds. They have had a more
profound effect on how people think about and study skeletal
disease than any other meetings in this century. The Utah paradigm had its genesis at these Workshops; hence its name.
Role of Momentary Muscle Strength in WholeBone Strength
WOLFF’S LAW AND THE UTAH PARADIGM
403
Fig. 3. Combined modeling and remodeling effects on bone strength
and “mass.” The horizontal line at the bottom suggests typical peak
bone strains from zero on the left, to the fracture strain on the right (Fx),
plus the locations of the remodeling, modeling, and microdamage
thresholds (MESr, MESm, MESp, respectively). The horizontal axis represents no net gains or losses of bone strength. The lower dotted line
curve suggests how remodeling would remove bone where strains stay
below the MESr range, but otherwise would tend to keep existing bone
and its strength. The upper dashed line curve suggests how modeling
drifts would begin to increase bone strength where strains enter or
exceed the MESm range. The dashed outlines suggest the combined
modeling and remodeling effects on a bone’s strength. D.H. Carter
originally suggested such a curve (Carter, 1984). At and beyond the
MESp range, woven bone formation usually replaces lamellar bone
formation. Fx ⫽ the fracture strain range centered near 25,000 microstrain. At the top, DW ⫽ disuse window; AW ⫽ adapted window as in
normally adapted young adults; MOW ⫽ mild overload window as in
healthy-growing mammals; POW ⫽ pathologic overload window (Frost,
1992a). In the nearly flat region between the MESr and MESm, bone
strength and “mass” change little as typical strains change. Reproduced
from Frost (1997d) with permission of the publisher.
Putative Marrow Mediator Mechanism
Microdamage (MDx)
A still-enigmatic mechanism in marrow should help
to control modeling and remodeling of bone next to or
close to it, but not of intracortical (haversian) and subperiosteal bone (Chow et al., 1993; Erben, 1996; Frost,
1998b)**. This could explain why endocortical bone
losses expand the cross-section area of the marrow cavity in human ribs by more than 50% between 20 and 75
years of age. During normal and supranormal mechanical usage, as well as under the influence of estrogen
(Fig. 4), this mediator mechanism would make conservation-mode remodeling keep existing bone and thus
prevent an osteopenia or progression of an existing one.
In acute disuse, or in acute loss of estrogen (Wronski et
al., 1993) or androgen (Christiansen et al., 1981; Erben
et al., 2000, Yao et al., 2000), or during treatment with
adrenalcortical steroid analogs like Prednisone, this
mechanism would help to make disuse-mode remodeling
cause a disuse-pattern osteopenia**. That should explain the usual loss of bone next to marrow in women
going through menopause. Figure 4 shows how those
responses to estrogen and muscle can affect bone “mass”
and, by implication, whole-bone strength.
(Burr and Stafford, 1990; Burr et al., 1997; Kimmel, 1993; Mori and Burr, 1993; Pattin et al., 1996)
Repeated strains cause microscopic fatigue damage
(MDx) that weakens bones. Normally remodeling BMUs
replace the damaged bone with new bone, and strains
below an operational MDx threshold range cause so
little MDx that remodeling can repair it. When larger
strains cause too much to repair, the resulting accumulated MDx causes or helps to cause all “spontaneous”
and stress fractures (so “spontaneous” fractures are not
really spontaneous) (Devas, 1975; Frost, 1989a; Markey, 1987), as well as pseudofractures in osteomalacia
and pathologic fractures**. Such accumulations can
also allow pull-outs or loosening of pedicle and other
screws, or make a bone weak enough to let a minor
incident (low energy trauma; Freeman et al., 1974;
Greenspan et al., 1994) fracture it.
Apparently this threshold lies above bone’s modeling
threshold but below its ultimate strength. That arrangement would minimize MDx, and it has been argued that bone design does minimize fatigue failures
(Alexander, 1984; Frost, 2000b). Controversial when
first described (Frost, 1960), MDx in bone now forms
404
FROST
Fig. 4. A bone-muscle mass comparison. H. Schiessl constructed
this graph from an Argentine study of 345 healthy boys and 443 healthy
girls between 2 and 20 years of age (Zanchetta et al., 1995). It plots the
grams of total body bone mineral content (TBMC, an indicator of wholebone strength) on the vertical axis that correspond to the grams of lean
body mass (LBM, an indicator of muscle strength) on the horizontal axis,
as determined by a Norland DEXA machine. Crosses: girls. Open circles:
boys. Each data point stands for an age one year older than the data
point on its left, and it shows the means for all subjects in that one-year
age group. Around 11 years of age TBMC began increasing faster than
before in girls. By ⬇ 15 years of age, their TBMC and LBM both
plateaued. Since both indices were still increasing in 20-year-old males,
they ended up with more muscle and bone than the 20-year-old girls.
This evidence supports the roles of muscle and estrogen discussed in
the main text. It has been suggested that the extra bone stored during a
woman’s fertile years could serve needs of lactation more than to
increase whole-bone strength. Reproduced from Schiessl et al. (1998)
with permission of the publisher.
another field of study in skeletal science (Fazzalari et
al., 1998; Martin, 1995, 2000; Schaffler et al., 1995;
Verborgt et al., 2000).
transections or in the lower extremities of patients with
diabetic neuropathy (Frost, 1986). Interestingly, motor
denervation alone, as in post-polio states, does not impair
development of an RAP (Frost, unpublished observations).
A, RAP usually responds to local need (Hernandez et al.,
1995). It causes three of the classical signs of inflammation: Edema, erythema, and increased warmth. Pathological RAPs known as algodystrophies or migratory osteoporoses also occur (Duncan et al., 1973; Langloh et al.,
1973; Mailis et al., 1992; Schiano et al., 1976). They usually respond well to prostaglandin inhibitors but poorly to
physical therapy (Frost, unpublished data)**.
Regional Acceleratory Phenomenon (RAP)
(Frost, 1983, 1986, 1995; Kelly, 1990; Kozin, 1993;
Martin, 1987; Martin et al., 1998; Shih and Norrdin, 1985)
This ubiquitous phenomenon is a necessary factor in the
normal healing of all hard and soft tissues. Injuries and
other noxious stimuli usually increase all ongoing biologic
activities in the affected body region. The increases include local perfusion, cell metabolism and turnover, and
any ongoing growth (Ring and Ward, 1958), modeling,
remodeling, healing, maintenance, and inflammatory activities. In combination, those things comprise the RAP**.
A RAP can last from a week when caused by a small
pimple to over 2 years when caused by a complex largebone fracture or a spinal fusion. Presumably it causes the
long bone overgrowth that occurs after some fractures in
children (Blount, 1955; Cozen, 1990; Frost, 1997b). Failure to develop a RAP can retard healing of all tissues.
Inadequate regional blood supply can cause that, but so
can sensory denervation after major peripheral nerve
Mechanostat Hypothesis
For over 75 million years (Romer, 1966) it seems all
load-bearing bones satisfied Propositions 1 and 2 in all
healthy amphibians, birds, mammals, and reptiles of any
size, age, and sex**. Whatever orchestrates such a universal effect was called the mechanostat (Frost, 1987b; Jee,
2000; Martin et al., 1998). As currently viewed it would
combine some of the above-mentioned features to form a
negative feedback system that makes modeling, remodeling, and their thresholds increase bone strength where
necessary, or remove bone when it is not needed mechan-
WOLFF’S LAW AND THE UTAH PARADIGM
ically (Frost, 1996)**. The marrow mediator, estrogen,
growth hormone, androgens, drugs, and other factors
might modulate how the mechanostat affects whole-bone
strength, in part by modulating the above thresholds or
internal standards (Burr and Martin, 1992; Slemenda et
al., 1994). A car can provide a useful analogy. Its steering,
brakes, accelerator, and ignition switch would be like the
features mentioned above; its wheels would be like effector cells. and its fuel and engine would be like the nonmechanical things in Table 2. Its driver would be like voluntary mechanical usage.
Implications. Just as studying only its wheels could
not explain why a car drove to Berlin instead of Paris,
studying only bone’s effector cells could seldom explain the
cause of an osteopenia, osteoporosis, impaired bone healing or other bone disorder**. Aided by the modeling and
remodeling thresholds, this mechanostat could tell exactly
where and when a bone or trabecula needs more strength
or has too much, and then make modeling or remodeling
correct the local error. No hormone, other humoral agent
or gene can do such things (Ferretti, personal communication, 1999). The strain range between the modeling and
remodeling thresholds in Figure 3 would provide a natural
definition of “normal” whole-bone strength relative to the
size of a bone’s peak voluntary loads. The strength and
architecture of some weakly-loaded cranial bones may
depend more on their baseline conditions than on the
mechanostat. They include the turbinates, nasal bones,
ethmoids, wing of the sphenoid, frontal and parietal
bones, and inner ear ossicles.
Summation
Muscle strength and anatomy combined with neuromuscular physiology determine the size and orientation of
the voluntary muscle forces on bones. Because of that and
the physiology summarized above, voluntary neuromuscular activities strongly influence and could even dominate control of the major fraction of the postnatal strength
of our load-bearing bones**. That should help to make
bones satisfy Proposition 1. The physiology supporting
those sentences could represent a kind of “quantum jump”
in our understanding of Wolff’s Law when it is compared
to earlier views, including some of my own (Brand and
Claes, 1989; Chamay and Tschantz, 1972; Evans, 1957;
Frost, 1964; Jansson, 1920; Muller, 1926; Roesler, 1987;
Roux, 1895; Treharne, 1981; Vico et al., 1987; Welten et
al., 1994; Whedon, 1984; Woo et al., 1981; Wunder et al.,
1979).
The above summary concerns some of the “what, how,
and why” of our 300⫹-year effort to understand bone
anatomy and physiology. That makes this question pertinent: Does that understanding have clinical applications?
Yes, it does.
SOME CLINICAL IMPLICATIONS OF THE
ABOVE PHYSIOLOGY
Two Meanings of “Vigorous” Exercise and Their
Effects on Whole-Bone Strength
(Frost, 1998a, 1999b)
These meanings could have special importance in space,
sports, and physical medicine, and in rehabilitation, geriatrics, biomechanics, and pharmacology.
To explain, muscle power and neuromuscular coordination help to achieve excellence in many sports, but at
405
present it seems whole-bone strength adapts chiefly to
peak momentary muscle forces. Thus, low-force muscle
contractions repeated to exhaustion, as in marathon or
treadmill running, or in long distance walking, swimming,
and bicycling, can increase muscle endurance but not momentary muscle strength or whole-bone strength (Micklesfield et al., 1995). However, maximal-force muscle contractions, as in weight lifting or sports like soccer (Wittich
et al., 1998) that involve violent accelerations of the
body— “supranormal” has that meaning here— can increase momentary muscle strength and put much larger
loads on bones than low-force exercises like those above.
Note that muscle strength can increase faster than wholebone strength (Heinonen et al., 1995).
Implications.Weight lifters and soccer players should
have greater bone strength than devotees of low-force
exercises and they do (Frost, 1990a; Karlsson et al., 1993;
Marcus et al., 1996; Riggs and Melton, 1995; Smith and
Gilligan, 1989; Taafe et al., 1995). Because the remodeling
threshold lies well below the modeling threshold (Fig. 3),
low-force exercises could still cause large enough strains
to make or help to make conservation-mode remodeling
keep the existing bone strength. It seems they do (Frost,
1999b, 2000a; Smith et al., 1989)**.
Physical Exercise and Whole-Bone Strength in
Children, Adults, and Young Athletes
(Frost, 1999b; Nilsson et al., 1978; Sumner and
Andriacchi, 1996)
These matters could have special importance in pediatrics, in space, sports, and physical medicine, and in anthropology, pharmacology, geriatrics, and biomechanics.
Besides aging effects on those matters (Stanulis-Praeger,
1989), biomechanical effects would occur too.
Increasing body weight and muscle strength keep increasing the size of the loads on a child’s bones, so the
sluggish modeling could lag behind in making bones
strong enough to keep strains from exceeding the modeling threshold (Frost and Jee, 1994). That was called the
adaptational lag (Frost, 1997c). When body weight and
muscle strength plateau in young adults, modeling could
“catch up,” reduce strains below that threshold and turn
off. Declining muscle strength in most aging adults should
put bones adapted to young-adult muscle strength into
gradual partial disuse. That could downshift bone strains
to the remodeling threshold and cause slow losses of bone
next to marrow.
Implications. More vigorous exercise should more
readily increase bone strength in children and young athletes than in aged subjects. That is true (Tsuji et al., 1996).
Also, in aged subjects such exercise could cause large
enough strains to limit further bone losses but not large
enough strains to make modeling increase bone strength.
That does happen (Marcus et al., 1996; Smith and Gilligan, 1989; Smith et al., 1989). That emphasizes the value
of regular exercise to increase bone strength during
growth, and hopefully help to maintain it in order to
minimize fractures in aging adults (Schönau et al., 1998).
The above “adaptational lag” should increase fractures
during our adolescent growth spurt but let them decrease
in young adults. Both of these things occur (Frost, 1997c;
Rockwood and Green, 1991; Wiley and McIntyre, 1980). In
microgravity conditions in orbit, exercising against maximal resistance might minimize bone losses more effec-
406
FROST
tively than treadmill running or riding a stationary bicycle (Rittweger et al., 1999), although this idea has not been
tested yet.
Fracture Patterns of the Radius
This “natural experiment” offers insight into fracture
patterns in general. It could hold special interest for pediatricians, gerontologists, orthopaedic surgeons, osteoporosis experts, biomechanicians, and physiologists.
In children, radius fractures from falls can affect both
the diaphysis (shaft) and the metaphyseal region, but in
aged adults falls usually only fracture the metaphyseal
region (the wrist) (Rockwood and Green, 1991, 1997).
While nonmechanical explanations were suggested for
that difference (Deng et al., 2000), the above physiology
offers a plausible biomechanical explanation too (granted:
“plausible” does not automatically mean “correct”).
Consider that in children the radius would adapt its
strength to increasing loads from growing voluntary muscle forces. Its diaphysis would adapt to combined uniaxial
compression, bending, and torsional loads from muscles**,
but the very low friction of the radiocarpal joint would
make the metaphyseal region of the radius carry and
adapt mainly to uniaxial compression muscle loads**. In
young adults both parts of the radius would have adapted
to such loads.
Falls on the outstretched hand can put momentarily
large combined bending, torsional, and compression loads
on the whole radius. In aged adults, its diaphysis would
have adapted to such loads, but its metaphysis would have
adapted mainly to compression loads. As a result, the
bending forces from such falls would more likely fracture
the metaphysis than the diaphysis. Hence the common
Colle’s fracture in aging adults.
Implication. Similar things could help to explain why
falls in aging adults seldom fracture the femoral, humeral
or tibial diaphyses**. Instead, they usually fracture the
metaphyseal regions of those bones (which include the hip
[femoral neck, greater and lesser trochanters, and intertrochanteric region], surgical neck of the humerus, and
malleolar regions of the ankle) (Ferretti et al., 1995).
Whole-Bone Strength in Obesity
This matter would have special importance for internists, endocrinologists, metabolic bone disease, nutrition
authorities, and anthropologists (Nishizawa et al., 1991).
To explain, body weight provides a resistance muscles
must overcome to let us work and play on earth (Ferretti
et al., 1998a; Martin et al., 1998). Ergo, to pursue similar
physical activities obese people would need stronger muscles than less heavy slender people. The stronger muscles
would put larger loads on bones, to which the above physiology should respond by increasing bone strength**, even
if nonmechanical factors help to do it. That seems to be the
case (Riggs and Melton, 1995; Nishizawa et al., 1991). Presumably for such reasons most bed-ridden or otherwise
chronically very inactive obese people lose bone, even when
their obesity increases (Frost, unpublished observations).
Table 4 lists conversion factors for English and metric
units of measure, and some stress-strain conversions for
healthy lamellar bone.
Some Clinical Features That Depend on Bone
Modeling (Frost, 1995; Jee, 1989; Schönau, 1996)
These matters could have special importance for physiologists, anatomists, anthropologists, pediatricians, geneticists, internists, dentists, pathologists, histologists,
pharmacologists, cell and molecular biologists, and histomorphometrists.
Some modeling functions. Modeling formation
drifts create our initial supplies of cortical bone (Jee,
1989). Modeling can slowly increase bone strength by increasing bone “mass” and reshaping a bone as in Figure
1B. Aided by the modeling threshold it sets the upper limit
on a bone’s strength relative to the size of the loads the
bone carries. Over time periods of months or, in large
bones, even years, it reshapes and strengthens an initial
fracture callus or a healing bone graft to provide enough
strength to endure voluntary activities (where “enough
strength” means keeping strains from exceeding the modeling threshold, and satisfying Proposition 1). In such
ways, modeling helps to provide the greatest strength
with the least amount of material (Currey, 1984), and it
affects whole bones and individual trabeculae. It might
strengthen the bone supporting load-bearing implants, if
the bone is alive and if its strains exceed its modeling
threshold but stay below its microdamage threshold
(Frost, 1992b)**. Normal modeling makes bones strong
enough to minimize microdamage, fatigue failures, and
the true osteoporoses described in Classifying “Osteopenias” and “Osteoporoses.”
Some modeling disorders. These can make bones
fail to satisfy Proposition 1. That failure helps to increase
bone fragility in osteogenesis imperfecta** (Damjanov and
Linder, 1996; Frost, 1987a; Seeforf, 1949; Sillence et al.,
1979). Curiously, so far no research studied how an abnormal Type I collagen could cause the modeling and
remodeling disorders that chiefly reduce bone strength,
increase bone fragility and let spontaneous fractures occur
in this disease (Frost, 1987a; Jaffe, 1972)**. An analogous
modeling malfunction should help to cause the true osteoporoses described in Classifying “Osteopenias” and “Osteoporoses”** in which the affected bones do not satisfy
Proposition 1 (Frost, 1997a; Marcus et al., 1996). Decreases or failures of modeling to make healing fractures,
bone grafts, osteotomies, and arthrodeses strong enough
to carry voluntary loads can cause late but uncommon
failures of that healing (Frost, 1998c). A clinical clue to
such a late failure: Initially the bone heals well enough to
let function resume, but later the healed region develops a
stress fracture or begins to angulate (Frost, unpublished
observations). Excessive periosteal formation drifts in
Paget’s disease and congenital lues cause many of the
bone deformities associated with those disorders (Jaffe,
1972; Luck 1950). Inability to form woven bone is lethal
for mammals (Dickman, 1997), but not for elasmobranchs
like sharks and skates, which only have cartilage in their
skeletons. Most laminar periosteal reactions called “periostitis” by radiologists represent new formation drifts of
woven bone, in reaction to some local pathology such as a
stress fracture, an inflammatory process or a neoplasm in
the bone. Sometimes humoral agents can cause them, as
in pulmonary hypertrophic osteoarthropathy and scurvy
(Damjanov and Linder, 1996; Jaffe, 1972; Luck 1950), and
WOLFF’S LAW AND THE UTAH PARADIGM
in the formation drifts incited by systemically administered prostaglandin E-2 (High, 1988; Tang et al., 1997).
Some Clinical Features That Depend on Bone
Remodeling
These matters could also have special importance for
physiologists, anatomists, anthropologists, pediatricians,
internists, geneticists, dentists, pathologists, histologists,
pharmacologists, cell and molecular biologists, and histomorphometrists.
Some remodeling functions. Remodeling replaces
primary spongiosa beneath growth plates with the secondary spongiosa made of lamellar bone (Frost and Jee, 1994;
Jee, 1989). It helps to replace mineralized cartilage in
osteochondromas with a normal secondary spongiosa
(Jaffe, 1958). Aided by the remodeling threshold, remodeling sets the lower limit on whole-bone strength, and
thereby helps to determine the width of a bone’s adapted
window (AW) in Figure 3. It replaces fracture callus with
lamellar bone. It repairs limited amounts of microdamage
(Mori and Burr, 1993). In its disuse mode, it removes
mechanically unneeded bone next to marrow (Frost,
1998b). Presumably that explains the nearly total lack of
spongiosa in postnatal diaphyseal marrow cavities, and
the loss of spongiosa and expansion of the marrow cavity
diameter in all adult-acquired osteopenias**. Disusemode remodeling of bone next to marrow causes a woman’s normal postmenopausal bone loss**. Where woven
bone carries postnatal loads, remodeling usually replaces
it with lesser amounts of lamellar bone. Remodeling has a
minor role in homeostasis (see Homeostasis and Bone).
Acute disuse increases BMU creations and bone turnover
by remodeling, while increased mechanical usage tends to
depress those creations and turnover**. Still, it seems
increased microdamage during suddenly increased mechanical usage can override the latter effect and independently increase BMU creations and bone turnover (Frost,
1992a; Martin, 2000; Martin et al., 1998).
Some remodeling disorders. These can fail to replace fracture callus with lamellar bone to cause some
healing problems of fractures, autografts, allografts, xenografts, osteotomies, and arthrodeses (Frost, 1998c)**.
That same failure impairs bone healing in osteopetrosis
(Bollerslev, 1989; De Palma et al., 1994). Failure to replace primary spongiosa with secondary spongiosa causes
one kind of osteopetrosis (Jaffe, 1972). Combined with
modeling malfunctions, disuse-mode remodeling would
help to cause all true osteoporoses including osteogenesis
imperfecta**, and it (not osteoclasts alone) seems to cause
all adult-acquired osteopenias on earth and in orbit**.
Disuse-mode remodeling helps to cause loss of femoral
calcar bone after some total hip replacement arthroplasties (Frost, 1992b; Pritchett, 1995), and it (not osteoclasts
alone) causes the bone loss associated with treatment with
adrenalcortical steroid analogs like Prednisone**. It helps
to cause subchondral cysts in osteoarthritis, and may help
to cause some lytic bone lesions associated with things like
sarcoid, multiple myeloma, some kinds of bony metastases, unicameral bone cysts, and giant cell tumors of bone
(Jaffe, 1958, 1972). Antiremodeling agents like estrogen
and the bisphosphonates depress disuse-mode remodeling
(not just osteoclasts) and help to retard local and generalized bone losses (Fleisch, 1995; Frost, 1997a). Impaired
microdamage repair by BMUs causes or helps to cause
407
osteochondritis dissecans, aseptic necroses of bone, and
spontaneous fractures of irradiated bone (Frost, 1986), as
well as stress fractures in athletes and military trainees,
pathologic fractures, pseudofractures in osteomalacia, and
spontaneous fractures in true osteoporoses (Frost,
1989a)**. That impaired repair also helps to explain the
loosening of some internal fixation implants and some
load-bearing endoprostheses (Frost, 1992b).
Addenda. Modeling and remodeling may have other as
yet unrecognized functions and disorders. A special bone
resorption mechanism that remained unstudied after its
original report may also participate in some bone disorders (Jaworski et al., 1972). While woven bone can form de
novo, meaning where no bone of any kind existed before,
lamellar bone only forms on preexisting bone of any kind
(Frost, 1986).
Classifying “Osteopenias” and “Osteoporoses”
This could have special importance in metabolic bone
disease, absorptiometry, radiology, internal medicine, endocrinology, geriatrics, genetics, anthropology, nutrition,
pathology, space medicine, pharmacology, and histomorphometry.
In the 1990s, participants in WSS Jee’s seminal Hard
Tissue Workshops (Jee, unpublished data2) suggested the
physiology summarized in Summary of the New Physiology above could cause four kinds of “osteoporosis” that
could have similar bone “mass” deficits, and thus similar Z
scores (Frost, 1997a). They do occur and some of their
clinical features were known for over 40 years (Riggs and
Melton, 1995; Snapper, 1957; Urist, 1960). Those participants suggested the following names.
In physiologic osteopenias, chronic muscle weakness
and physical inactivity would make normal modeling and
remodeling cause a corresponding disuse-pattern osteopenia in which voluntary activities and loads on bones do not
cause spontaneous fractures. Here bones would satisfy
Proposition 1, and only injuries like falls cause fractures,
usually of extremity bones like the hip and wrist (Lauritzen, 1996). As Runge et al. (2000) and Overstall et al.
(1997) noted, impairments of muscle strength, coordination, balance, and vision help to increase falls and fractures in aging adults. These osteopenias can affect children, women, men, most aged adults, and most persons
with chronic muscle weakness and/or debilitating illnesses (Table 3)**.Presumably the loss of bone in women
going through menopause also causes such an osteopenia
(Christiansen et al., 1981), since over two-thirds of such
women never develop spontaneous fractures. In former
times and in older people, these osteopenias were often
called “senile osteoporoses.”
In true osteoporoses, still-enigmatic modeling and remodeling malfunctions cause a disuse-pattern osteopenia
in which voluntary activities and muscle forces do cause
spontaneous fractures. Here the affected bones do not
satisfy Proposition 1. Much less common than physiologic
osteopenias, these osteoporoses include in part osteogenesis imperfecta, hyperphosphatasia, and idiopathic juvenile osteoporosis, in which the spontaneous fractures can
affect both the spine and extremity bones (Dimar et al.,
1995; Marcus et al., 1996). A more widely discussed kind
affects women more than men and seldom affects children
(Riggs and Melton, 1995). Its spontaneous fractures affect
thoracic and lumbar vertebrae but, curiously, rarely affect
the pelvis and extremity bones (the still-debated issue of
408
FROST
TABLE 3. Some conditions that cause chronic disuse and muscle weakness in humans
(and related osteopenias)*
Asthma
Renal failure
Malnutrition
Metastatic cancer
Muscular dystrophy
Organic brain syndrome
Lou Gehrig disease
Cystic fibrosis
Drug addiction
Emphysema
Hepatic failure
Anemia
Depression
Multiple sclerosis
Huntington’s chorea
Paralyses
Still’s disease
Nursing home residence
Aging
Pulmonary fibrosis
Cardiac failure
Polyarthritis
Stroke
Alzheimer’s disease
Myelomeningocele
Leukemia
Alcoholism
Juvenile RA
*In causing an osteopenia, the relative importance of the mechanical disuse and muscle weakness,
and of the biochemical-endocrinologic abnormalities accompanying some of these entries, is still
uncertain. So far, few studies tried to quantify the muscle and mechanical usage effects. The Utah
paradigm suggests the mechanical effects would dominate most biochemical-endocrinologic ones.
RA: rheumatoid arthritis.
how to classify spontaneous vertebral “fractures” is not
discussed here; Eastell et al., 1991; Marcus et al., 1996).
Presumably, it also involves excessive microdamage accumulations (Heaney, 1993; Vernon-Roberts and Pirie,
1997). Here too the osteopenia facilitates extremity-bone
fractures from falls. In former times these were often
called “symptomatic osteoporoses.”
In combined states features of those two affections seem
to combine in various ways**.
In transient osteopenias, a regional disuse-pattern osteopenia occurs after a fracture, burn, or other severe
injury. Two or more years after the injury heals and physical activities resume, the affected bones regain the
strength needed to endure voluntary activities for the rest
of life**. In proof, late refractures of such fractures are
rare (Frost, unpublished data). It seems the associated
mechanical disuse and an accompanying regional acceleratory phenomenon cause this “naturally reversible osteopenia”** as Z.F.G. Jaworski dubbed it (Jaworski,
1984). Since spontaneous fractures do not occur in it, it
should constitute a physiologic bone response to an injury
(Garland et al., 1994). In former times these were sometimes called “posttraumatic osteodystrophies.”
Implications. X-ray absorptiometry cannot distinguish those four conditions from each other, nor can it
alone evaluate bone health**. Defining “osteoporosis” by
BMD-derived Z scores (Kanis, 1994; Marcus et al., 1996)
could need revision or supplementation, since that could
suggest that “osteoporoses” and “osteopenias” are only
different severities of the same thing, like the hemoglobin
in mild and severe pernicious anemias**. Yet as defined
above, they differ biologically, pathologically, and pathogenetically. We need new standards for the muscle
strength– bone strength relationship** (Ferretti et al.,
1998b; Schiessl et al., 1998; Schönau et al., 1998), and will
need to learn more about muscle itself (Dickinson et al.,
2000; Worton, 1995). Muscle weakness plus impairments
of balance (Schroll et al., 1999), neuromuscular coordination, and vision cause most of the falls that, in turn, cause
most extremity bone fractures (so-called “osteoporotic
fractures”) in aging and aged humans. The literature
shows growing recognition of that fact (Lauritzen, 1996;
Nguyen and Eisman, 2000; Runge et al., 2000; Tinetti et
al., 1994), so future “risk of fracture” studies might try to
account for it. Increased exercise and/or increased muscle
strength [perhaps due to exercise, androgens (Bhasin et
al., 1996) or growth hormone (Ogle et al., 1994; Ullman
and Oldfors, 1989)] should help physiologic osteopenias,
but they could make true osteoporoses worse (Frost, unpublished data). If so, it would be imperative to distinguish
between those disorders before prescribing or advising
such things. Agents that could turn modeling on, could
normalize and cure an osteopenia**, while agents that
could turn disuse-mode remodeling off could prevent one
or progression of an existing one**. Yet we need better
agents to do such things than the currently available
bisphosphonates, parathyroid hormone, prostaglandins,
and estrogens (Harris et al., 1996; Ma et al., 1994; Takahashi et al., 1991; Wronski et al., 1989). Searches for
intrinsic bone disorders, including genetic disorders in
bone cells, that could cause physiologic and transient osteopenias should be futile, since the chief cause of the
former would be muscle weakness (which of course could
depend on genetic factors), and of the latter, trauma. In
my experience, physiologic osteopenias outnumbered true
osteoporoses by more than five to one. In the past, did we
exaggerate the need for abundant dietary calcium to minimize or prevent osteopenias, osteoporoses and fractures
(Bronner, 1994; Gallagher, 1990; Nordin and Heaney,
1990; Recker and Heaney, 1985)? The bone loss in microgravity situations should exemplify a disuse-pattern osteopenia caused by greatly reduced muscle loads on bones.
At least in my view, the nonmechanical explanations proposed are erroneous. Searches for genetic errors in bone
that might explain “osteoporosis” as diagnosed by Z scores
(Kanis, 1994) should be futile in the cases of physiologic
osteopenias (since their cause would usually lie in muscle)
and transient osteopenias (which should represent normal
responses to trauma). Seeking other bone effector-cell disorders that would cause physiologic osteopenias should be
futile too, and so should seeking the cause of spontaneous
fractures only in the spine by studying unaffected bones
like the ilium and tibia. Physiologic osteopenias should
only affect hollow bones with marrow cavities, which
seems to be true (Frost, unpublished data).
Noninvasive Absorptiometric Evaluation of
Whole-Bone Strength
This matter could have special importance in metabolic
bone disease, in absorptiometry by X-ray, magnetic reso-
WOLFF’S LAW AND THE UTAH PARADIGM
nance imaging, and/or ultrasound, in radiology, and in
“osteoporosis”-related research.
To explain, material in classifying “Osteopenias” and
“Osteoporoses” indicates the need to evaluate whole-bone
strength noninvasively in patients. Yet no current absorptiometric method can reliably evaluate a bone’s materials
properties or its microdamage burden. As for the other two
factors in whole-bone strength (see Four Physcial Features Combine to Determine Whole-Bone Strength,
above), bone mineral “density” (BMD) and content (BMC)
measured by dual energy X-ray absorptiometry (DEXA)
became popular ways to evaluate the “mass” factor, but
they cannot distinguish between woven, plexiform, and
lamellar bone (Jiang et al., 1999; Kanis, 1994). Also,
“mass” factors alone do not indicate whole-bone strength
reliably (Banu et al., 1999)**, and neither do current ultrasound methods** (Ferretti et al., 1998b; Nielsen, 2000;
van der Perre and Lowet, 1996).
However, Bone Strength Indices (BSIs) obtained by peripheral quantitative computed tomography (pQCT) that
account for both the “mass” and architectural factors can
provide much better estimates of a bone’s true strength
(Banu et al., 1999; Ferretti, 1997, 1999; Ferretti et al.,
1998a,b; Jiang et al., 1999; Schiessl and Willnecker, 1999;
Wilhelm et al., 1999), so they should see increasing use in
the future. Please note that the major issue in life seems
to be bone health, which in my view would constitute the
relationship between a bone’s strength and the size of the
voluntary loads it carries and would normally adapt to.
Implications. Evaluating bone health would require
comparing a bone’s strength to the usual loads on it, and
then comparing that relationship to suitable norms. Because the largest voluntary loads come from muscles, that
would require comparing bone strength to muscle
strength.
Ferretti et al. (1989), Schiessl and Willnecker (1999),
and Schönau et al. (1998) have begun to obtain such “bone
strength-muscle strength” norms. No current method of
bone absorptiometry can by itself evaluate a bone’s health
as Proposition 1 defines it. Nor can any such method
distinguish the four conditions described in Classfying
“Osteopenias” and “Osteoporoses” from each other, nor
can the T and Z scores currently used in such work (Kanis,
1994). Such distinctions would require adding to bone
strength data, further information obtained from X-rays,
clinical facts, and muscle strength data.
Design and Use of Load-Bearing Implants
This matter would have special importance for orthopaedic surgeons, dental and maxillofacial surgeons, biomedical engineers, biomechanicians, and implant manufacturers. The following paragraphs concern only one of
the problems such implants have (Bauer and Hirokawa,
1995; Doyle, 1993; Hamilton and Gorczyca, 1995; Jasty et
al., 1994).
To explain, the above physiology suggests the design of
load-bearing endoprostheses should 1.) keep typical peak
strains in the supporting bone below its microdamage
threshold, but 2.) let them exceed its remodeling threshold
(Frost, 1992b)**. Strains in the mild overload window
(Frost, 1992a) in Figure 3 might help modeling to
strengthen the supporting bone, and should keep disusemode remodeling from removing it. These criteria should
apply to load-bearing artificial joints, partial bone replace-
409
ment endoprostheses, dental implants, and some spinal
instrumentation.
While a bone microdamage threshold was suggested in
1983 (Burr et al., 1983) and verified later (Carter, 1984;
Pattin et al., 1996), even in 2000 AD no marketed loadbearing skeletal implant intentionally tried to satisfy
those two criteria. Yet it seems Branemark’s dental implant system does it unintentionally, which should prove
it can be done (Branemark, 1988).
As for other kinds of implants, including ones used for
internal and external fixation, very osteopenic bones with
thin cortices and reduced amounts of spongiosa would
need more and/or larger screws, pins, and other devices to
provide larger load-bearing bone-implant interfaces
(Okuyama et al., 1995). Combined with suitable postoperative management, that could help to keep the unit loads
on those interfaces below bone’s microdamage threshold,
which in stress terms seems to lie in the region of ⬇ 60
megapascals. Otherwise, accumulating fatigue damage in
the bone supporting the implants could and often does
loosen them before satisfactory healing occurred.
Implications for Bone Healing in Fractures,
Bone Grafts, Osteotomies, and Arthrodeses
These implications could have special importance for
orthopaedic surgeons, pathologists, and pharmacologists,
for cell and molecular biologists who study hard tissue
healing, and for the designers of internal and external
fixation devices. Of course, this healing poses other clinical and basic science problems, too.
To explain, in earlier views bone healing comprised a
single indivisible process, and its supposed key players,
osteoblasts, were aided by things like angiogenesis, apoptosis, chondroblasts, and stem cells (Aho et al., 1994;
Burchardt, 1983; Brand and Rubin, 1987; Habal and
Reddi, 1992; Hall, 1991; Luck, 1950; Rahn, 1982; Rhinelander and Wilson, 1982; Sherman and Phemister, 1947).
However, its omissions make that view suspect. The
true key players in that healing include four tissue-level
phases, the callus, remodeling, and modeling phases, accompanied by a regional acceleratory phenomenon
(RAP)** (Frost, 1998c; Woodard, 1991). Each phase can
malfunction independently of the others**, so many different kinds of healing problems could and do occur that
do not stem from known treatment errors. While former
anatomists, histologists, and pathologists described the
light-microscopic tell-tales of those things quite well (Gegenbaur, 1867; Lewis, 1906; Putschar, 1960; Weinmann
and Sicher, 1955), their functional significance in this
matter remained unknown until the Utah paradigm
gelled.
Initially a soft fracture callus forms with new vessels,
supporting and precursor cells, osteoblasts making woven
bone, and often chondroblasts making hyaline cartilage. It
fills the gaps and surrounds, embeds, and welds to the
fragments of the fracture or graft, and it lacks a general
“grain” (Weinmann and Sicher, 1955). After the callus
mineralizes remodeling BMUs begin to replace it and/or
any graft material with packets of new lamellar bone, the
“grain” of which usually parallels the largest local compression and tension strains. Presumably guided by those
strains and partly overlapping “2,” modeling begins to
modify the shape and size of the callus to make it strong
enough to satisfy Proposition 1. Those three phases last
longer in adults, large bones, and diaphyses than in children, small bones, and metaphyses. A fracture, arthrode-
410
FROST
sis, osteotomy, or grafting operation normally incites a
RAP (Garland et al., 1994) that lasts throughout the healing process and accelerates the “1,2,3” phases**. Otherwise, a delayed union or a “biologic failure” of healing can
ensue (Frost, 1989b). Besides impaired regional blood supply, sensory denervation as in some diabetics increases
the likelihood of an inadequate RAP, which nevertheless
seldom happens in children (Frost, 1986). The possibility
that cigarette smoking might impair a RAP, and thus bone
healing too, seems to deserve study (Cook et al., 1997).
The osteoclast defect that causes osteopetrosis impairs
replacement of fracture callus with lamellar bone (“B”
above) (de Palma et al., 1994), which should help to explain impaired bone healing in that disease**.
In my experience, most impairments of bone healing not
due to treatment errors stemmed from disorders in the “1”
and “4” phases, the “4” disorder being the most common.
Role of Strain. Mounting evidence indicates that
small strains help to guide the remodeling and modeling
phases of bone healing (Blenman et al., 1989; Carter et al.,
1988; Claes et al., 1994; Frost, 1989b; Hanafusa et al.,
1995; Kenwright and Goodship, 19889; Mosely and
Lanyon, 1988; Wolff et al., 1981). Lacking any strains,
disuse-mode remodeling tends to remove the callus, modeling stays off, and healing can retard or fail** (see “disuse” in the Glossary). All orthopaedists know that excessive strains (gross motion) can prevent healing. The
“permissible” strains might lie in the 100 –2,000 microstrain region. For comparison, bone’s fracture strain is a
range centered near ⬇ 25,000 microstrain (Currey, 1984;
Reilly and Burstein, 1991). The 100 –2,000 microstrain
span includes the adapted and mild overload windows in
Figure 3 (Frost, 1992a). In compliant (i.e., not yet rigid
and strong) healing fractures, bone grafts, or arthrodeses
including spinal fusions, very small loads could cause
harmfully large strains.
Cell and Molecular Biology on Which “1– 4”
Should Depend. Bone healing should also depend on
the growing numbers of known humoral and molecularbiologic influences on bone cells. The humoral influences
include in part hormones, vitamins, minerals, and drugs
(Bak et al., 1991). The molecular-biologic influences include in part cytokines, growth factors, other ligands,
angiogenesis, apoptosis, stem cell hierarchies, “supporting
cell” functions, cell proliferation and differentiation, and
gene expression mechanisms and patterns (Barnes et al.,
1999; Caplan and Dennis, 1998; Goldring and Goldring,
1996; Gowen, 1992; Manolagas and Jilka, 1995; Ridley,
2000; Urist, 1995). One might add electrical treatment to
that list (Lavine and Grodzinski, 1987). So far, a lack of
appropriate studies leaves us uncertain about how such
things would affect the true key players in this healing,
the tissue-level “1– 4” phases.
According to the Utah paradigm, very similar observations would apply to the healing of fascia, ligaments, tendons, and articular cartilage (Frost, 1995).
Homeostasis and Bone
This matter would have special importance for physiologists, internists, endocrinologists, and specialists in nutrition.
In early views, the responses of osteoclasts and BMUs to
parathyroid hormone, calcitonin, and other humoral
agents were viewed as essential for calcium homeostasis
(Albright and Reifenstein, 1948; Barzel, 1970; Favus,
1999; Rasmussen and Bordier, 1974; Snapper, 1957).
Some people even viewed that as their chief function.
Yet bone can handle most homeostatic challenges without BMUs or osteoclasts (Frost, 1986)**. In proof, problems with homeostasis, tetany, and acid-base physiology
seldom occur in osteopetrosis, where osteoclasts function
poorly or not at all (Bollerslev, 1989; Key and Ries, 1996).
Also, in dogs large doses of a bisphosphonate suppressed
osteoclastic and osteoblastic activities for 9 months without causing hyper- or hypocalcemia, tetany, or disturbed
acid-base physiology (Flora et al., 1981). Since those doses
did cause spontaneous fractures that did not heal until the
treatment stopped, it became necessary to ensure such
agents do not do similar things in humans (Fleisch, 1995).
Parenthetically, while preclinical studies of some bisphosphonates claimed they did not increase microdamage in
bone, a later study could suggest otherwise (Mashiba et
al., 2000).
At least three other mechanisms that do not involve
osteoclasts help in the homeostatic function of bone and
handle most homeostatic challenges very well (Frost,
1986; Norimatsu et al., 1979)**. One of them could involve
an osteocyte-based mechanism originally proposed by Arnold et al. (1971) and later supported by studies by, among
others, Borgens (1984), Tate et al. (1998), and Rubinacci et
al. (2000). However, in prolonged calcium deprivation or
malabsorption, disuse-mode remodeling probably can help
to maintain homeostasis.
Role of Nutrition
In former views, adequate nutrition dominated the development of healthy and strong bones (Bronner, 1994;
Heaney, 1990; McLean and Urist, 1961; Kuhlencordt and
Bartelheimer, 1981; Tylavsky and Anderson, 1988;
Vaughn et al., 1975). While serious malnutrition certainly
can affect bone strength adversely, and muscle strength
too (Shires et al., 1980), in the Utah paradigm most things
like protein, calcium, vitamins, and calories would act
mainly like the fuel and engine in a car. Without them a
car cannot move, but they do not drive it. Instead, the car’s
driver does that. For the bone “car,” the “driver” seems to
be mechanical usage, muscle strength, and the related
bone strains instead of nutritional factors**. In proof, no
nutritional supplements can make sedentary people develop the strong bones of weight lifters, nor can they
normalize whole-bone strength in paralyzed limbs (Frost,
unpublished data). Furthermore, supplemental dietary
calcium seems to have little effect on bone “mass” in normal children (Lee et al., 1996).
CONCLUSION
Three Caveats
Besides dynamic longitudinal bone strains, other things
could help to control modeling and remodeling. They include shear, strain gradients (Frost, 1993; Gross et al.,
1979; Judex et al., 1997), and strain rates, frequencies and
repetitions, and other things too (Evans, 1957; Lanyon,
1996; Martin et al., 1998; Mosely and Lanyon, 1988;
O’Connor et al., 1982; Rubin and McLeod, 1995). Until
those things are resolved, longitudinal strains can provide
reliable indicators of the loads on bones. Ergo, where this
text mentions strain as a control of a biologic activity, “or
equivalent stimulus” is always understood.
Bone physiology combines anatomical and biomechanical concerns with subjects like endocrinology, biochemis-
WOLFF’S LAW AND THE UTAH PARADIGM
try, cell biology, and homeostasis. The resulting amalgam
has important mechanical functions, but poor interdisciplinary communication left people in many fields unaware
of that amalgam and its applications (Brown and Haglund, 1995; Parfitt, 1997). As one result, they tried to
explain bone’s anatomy, physiology, and clinical disorders
with generally accepted earlier views about independently
working effector cells. In retrospect, they may have tried
to explain too much with too little.
As another result, when those early views met the
newer ones in this text, controversies began that only time
and help from many people can resolve. But controversies
fuel progress in all science, so why not air, instead of
discourage, any about issues raised by the newer physiology?
On the Cartilage-Bone Relationship
On What Cellular, Molecular-Biologic, Genetic,
and Pharmacologic Roots Does the Above
Physiology Depend?
Past, Present, Future
It must depend on such roots, but the post-1950 rush to
study bone’s effector cells pretty much overlooked that.
For recent reviews about those cells see Caplan and Dennis (1996), Goldring and Goldring (1996), Duncan and
Turner (1995), Mundy (1996), Parfitt and colleagues
(1993, 1995, 1996), Raisz (1988), Rodan (1997), and
Turner et al. (1994).
Yet growth hormone and somatomedins (Inzucchi and
Robbins, 1994; Kalu et al., 2000), androgens (Bhasin et al.,
1996), cortisone analogs, vitamin D, calcium, and genes all
affect muscle strength and could indirectly affect bone
strength in that way (Dickinson et al., 2000). These and
other factors might also potentiate the mechanostat’s responsiveness to mechanical and other influences to affect
whole-bone strength in that way too (Frost and Schönau,
2000); recent studies support that idea (Gasser, 1999;
Halioua and Anderson, 1989; Jee, 1999; Tang et al., 1997;
Yao et al., 2000). Some factors might even affect the impaired balance and neuromuscular coordination that help
to cause the falls that, in turn, cause most extremity bone
fractures in aged adults (Guralnik et al., 1995; Runge,
1997; Steinhagen-Thiessen and Borchelt, 1996). While few
if any efforts to find genetic causes for so-called “osteoporosis fractures” studied the associated problems with balance, neuromuscular coordination, muscle strength and
vision, simple, effective ways to study such things in outpatient settings do exist (Runge et al., 2000).
Consequently future studies must find how such roots
support the above physiology. That may depend heavily on
live-animal research, because as Parfitt (1995) and Gasser
(1999) also note, bone’s tissue-level mechanisms do not
function normally in vitro (Frost, 1986). W.S.S. Jee’s laboratory at the University of Utah pioneered ways to do
such in vivo work (Jee, 1995).
Role for Controlled Vibration?
High loading rates of frequent loads with small amplitudes (including but not limited to ultrasound) may have
useful effects in treating “osteoporoses,” some hard and
soft tissue healing problems, and other matters (Abendroth et al., 1998; Flieger et al., 1998; Heckman et al.,
1994; Wood, 1987). Among others, H. Schiessl in Germany
and H. Sievanen (Sievanen et al., 1996) in Finland study
the effects of such vibration on human bones, joints, muscles, and neuromuscular physiology (personal communications, 1998).
411
Question: Are things like congenital hip dysplasia
(Stanisaljevic, 1964), genu varum, scoliosis, club foot,
metatarsus varus, achondroplastic dwarfism, Madelung’s
deformity, Marfan’s syndrome (Joseph et al., 1992), and
hallux rigidus examples of bone disorders? They are not.
Instead they stem from modeling disorders of the cartilage
in joints and growth plates (Frost, 1995, 1999a; Frost and
Jee, 1994). Usually cartilage conducts and bone plays first
violin in the skeletal “orchestra” (Frost, unpublished observations), and far more often than not the statistical
abnormalities in bone architecture in such conditions represent effective adaptations to loading changes caused by
the cartilage problems (Frost, 1995). In proof, spontaneous
fractures of such bones are rare (Frost, unpublished data).
As a young man, my “bibles” for bone physiology included books by Jaffe (1958, 1972), McLean and Urist
(1961), and Weinmann and Sicher (1955), and a chapter
by Putschar (1960). Comparing their content to the above
material suggests how much progress occurred in understanding bone, bones, and Wolff’s Law. History suggests
more progress will come (Maddox, 1999; Mayr, 1961,
2000), and many devils will show up in the details too. But
the above physiology’s parent, the Utah paradigm, keeps
evolving to account for new evidence and ideas (and “devils”), so it could provide a kind of gold standard in such
matters for years to come.
ACKNOWLEDGMENTS
The author thanks the staffs of Pueblo’s Southern Colorado Clinic, Parkview Episcopal Hospital, and St. Mary
Corwin Hospital for their time producing this and related
articles, and David Gavin and Ralph Scott for the drawings. Thanks also to the orthopaedic surgeons trained at
Henry Ford Hospital between 1957–1973 for their spontaneous assistance in a time of great troubles. Other colleagues who have offered perceptive comments and advice
regarding matters discussed in this article include: J.S.
Arnold, D.B. Burr, Z.F.G. Jaworski, W.S.S. Jee, R.B. Martin, A.M. Parfitt, E.L. Radin, R.R. Recker, H.E. Takahashi, M.R. Urist, and C. Woodard.
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APPENDIX
Glossary
As some terms have vague or even different meanings in
the medical literature, the intended meaning of some
terms in this article are listed below. (*: The scientifically
correct meaning in 2000 AD.)
architecture: the size, shape, and orientation of a
bone, the amounts of bone tissue in it, and the arrangement of that tissue in anatomical space.
BMU: the Basic Multicellular Unit of bone remodeling
(Jee, 1989)*. In 3 or more months and in a stereotyped,
biologically-coupled Activation 3 Resorption 3 Formation or “ARF” sequence, it turns over ⬇ 0.05 mm3 of
bone. The resulting new packet of bone was called a
bone structural unit (BSU) by Jaworski (1984). When a
BMU makes less bone than it resorbs, that “disuse
mode” tends to remove bone permanently, but only for
bone next to or close to marrow. When it resorbs and
makes equal amounts of bone, that “conservation mode”
turns bone over without net gains or losses. Completed
BMUs do not seem to make more bone than they resorb
so they do not increase bone “mass.” Healthy adult
humans may create and complete about 3 million BMUs
annually, but in disease and other circumstances that
can change more than five times (Frost, 1995).
bone “density”: since the true physical density of bone
as a material varies little with age, sex, and species,
“density” as absorptiometrists use the term only provides an estimate of the amount of bone in the path of
one or more X-ray beams as a bone-mineral equivalent
(here one can assume gamma rays and X-rays are the
same). While many still think otherwise, true bone density is normal in most osteoporoses and osteopenias
(Seeman, 1997). When in quotes in this article, “density”
has its meaning in absorptiometry.
bone “mass”: the amount of bone tissue in a bone or
skeleton, preferably viewed as a volume minus the volume of the soft tissues in the marrow cavity. In absorptiometry, it does not mean mass as used in physics.
When in quotes in this article, it has the absorptiometric meaning.
DEXA: dual energy X-ray absorptiometry. Often also
written as “DXA.”
disuse: bones need some criterion to recognize this.
When a bone’s peak strains down-shift into or below the
remodeling threshold region in Figure 3, for that bone
that would signal the existence of disuse, no matter how
small or big the bone (Frost, 2000a). In such situations,
disuse-mode remodeling usually removes bone next to
marrow. “Disuse” would be the relationship between a
bone’s strength and the size of its usual peak loads and
the strains they cause. The relationship between those
418
FROST
TABLE 4. Conversion factors and symbols for units
Symbols for units
N ⫽ Newton
kg ⫽ kilogram
cm ⫽ centimeter
mpa ⫽ megapascal
M ⫽ meter
in ⫽ inch
psi ⫽ pounds per square inch
mm ⫽ millimeter
lb ⫽ pound
Approximate strain-stress equivalents for normal lamellar cortical bonea (loaded in compression parallel to
the grain)
50–100 microstrain corresponds to ⬇ 1–2 mpa, ⬇ 140–280 psi, 0.2 kg/mm2
1,000 microstrain corresponds to ⬇ 20 mpa, ⬇ 2,800 psi, ⬇ 2 kg/mm2
3,000 microstrain corresponds to ⬇ 60 mpa, ⬇ 8,500 psi, ⬇ 6.1 kg/mm2
25,000 microstrain corresponds to ⬇ 120 mpa, ⬇ 17,000 psi, ⬇ 12.2 kg/mm2
Bone’s ultimate strength is a range centered near 25,000 microstrain, 120 mpa, or 17,000 psi
Some English-metric conversionsa
1 kg ⫽ 2.2 lb ⫽ 9.8 N. 1 N ⫽ 0.225 lb ⫽ 0.102 kg. 1 million N ⫽ 224,000 lb.
1 mpa ⫽ 1 million N/M2 ⫽ 145 psi ⫽ 1 N/mm2 ⫽ 0.102 kg/mm2. 1 kg/cm2 ⫽ 14.2 psi.
1 kg/mm2 ⫽ 9.8 mpa ⫽ 1,420 psi. 120 mpa ⫽ 17,400 psi ⫽ 12.2 kg/mm2. 60 mpa ⫽ 8,700 psi ⫽ 6.1 kg/mm2. 20 mpa ⫽
2,800 psi ⫽ 2.04 kg/mm2. 1 M2 ⫽ 1,550 in2.
1 in2 ⫽ 6.45 cm2.
a
Values to two or three place accuracy. Taken from Frost (1998a), Yamada (1970), and The Merck Index, 11th ed. (1989).
strains and the remodeling threshold would provide a
natural criterion for “recognizing” disuse.
disuse-pattern osteopenia: as a steady state, an osteopenia in which endocortical bone loss expanded the
marrow cavity, loss of trabecular bone reduced its
amount, cortical porosity remains essentially normal,
and outside bone diameter does not decrease, or may
even increase a bit. The reduced outside bone diameter
in some children’s osteopenias usually reflects failure of
modeling to increase it instead of an effect of periosteal
bone loss. In steady-state osteopenias, surface-referent
bone tissue dynamics tend to be normal for the subject’s
age (Recker, 1983).
drifts: see “modeling” below, and Figure 1.
effector cells: here, differentiated osteoblasts and osteoclasts but not their precursor or other cells. The
effector cells directly make or resorb bone, so by that
definition osteocytes would not be effector cells.
mechanical competence: the state in which bones
endure voluntary physical activities for life without developing spontaneous fractures. Sometimes called “biomechanical competence.” The antonym, “mechanical incompetence,” means the state in which voluntary
physical activities (not injuries) do cause spontaneous
fractures; modeling and/or remodeling disorders would
usually cause it.
microdamage: microscopic physical damage in a structural material due to materials fatigue (Martin et al.,
1989)*. To increase the fatigue life of inanimate structures, engineers usually add more structural material.
But skeletons can detect and repair limited amounts of
fatigue damage to keep it from accumulating, so they only
need enough strength to keep strains below the level that
could cause larger amounts. Presumably they could carry
loads that cause smaller amounts indefinitely.
microdamage threshold: the strain range above
which new microdamage begins to escape repair and
accumulate (MESp in Fig. 3). It seems to center near
3,000 microstrain, which corresponds to a stress of
about 60 megapascals. Pattin et al. (1996) found that as
the loads that originally cause strains in the 2,000 microstrain range only double to cause 4,000 microstrain,
the resulting fatigue damage increases over 500 times.
modeling: the biologic processes that produce function-
ally purposeful sizes, shapes and organization to all
skeletal organs (Jee, 1989)*. Mostly independent resorption and formation modeling drifts do it in bones.
Normally it fits bones to their voluntary mechanical
usage to keep that usage from breaking them. That is
done by making a bone strong enough to keep its typical
peak strains from exceeding bone’s modeling threshold.
modeling threshold: the genetically-determined Minimum Effective Strain range (or equivalent Stimulus;
MESm in Fig. 3) for mechanically controlled bone modeling. Where strains exceed it modeling turns on; where
strains stay below it modeling turns off. It seems to center
near 1,000 microstrain in most young adults, which corresponds to a stress of about 20 megapascals (Table 4).
muscle strength: the maximum momentary contractile force exerted by a muscle can be expressed in Newtons or kiloponds (the attraction of earth’s gravity for a
mass of one kilogram) (Dickinson et al., 2000; Murray et
al., 1980)*. Or muscle strength can be measured as the
peak torque in Newton-meters produced by muscle
forces across joints like the hip, elbow, knee, and fingers. That differs from endurance, which concerns how
long and often submaximal muscle forces can be exerted, as in marathon running*. It differs from mechanical work or energy, which can be expressed in Newtonmeters, Joules, or kilowatt-hours*. It differs from
muscle power, which concerns how rapidly mechanical
work is done and is usually expressed in Newtonmeters/sec, Joules/sec, or watts (one Joule/sec ⫽ one
watt)*. Since bones seem to adapt their strength and
stiffness to the typical peak momentary loads they
carry, accounting for these distinctions can minimize
errors in interpreting and discussing mechanical usage
effects on bone strength and “mass.”
osteopenia: here, less whole-bone strength than usual
for most healthy people of the same age, height, weight,
sex, and race. Also less bone strength than before in the
same person. It need not represent a disease nor stem
from an intrinsic bone disorder. Affected bones would
break more easily. In clinical work, probably the commonest cause of an osteopenia is chronic muscle weakness. But it is currently and usually expressed in terms
of reduced bone “mass” as evaluated by DEXA.
osteoporosis: defining this was debated for decades (Nor-
WOLFF’S LAW AND THE UTAH PARADIGM
din, 1987; Urist, 1960). The currently accepted 1994 WHO
“standard” for diagnosing an “osteoporosis” consisted of a
bone mineral “density” or content over 2.5 standard deviations below the applicable norm (Kanis, 1994). Some
suggested an “osteopenia” consists of a reduction in bone
“mass” between 1.0 and 2.4 standard deviations below the
applicable norm. That idea does not depend on the osteopenia’s pathogenesis, yet effective treatment should depend on it. Reviews published after 1985 show many authors find the “Type I, Type II” terms confusing (Riggs et
al., 1998). The pathogenetically-based terms in Part III of
this text would supplement older ones. In this text, without quotes the term signifies any osteopenia in which
voluntary activities (not trauma) cause spontaneous fractures. When in quotes, it would have the above absorptiometric meaning,
remodeling: turnover of bone in small packets by BMUs
(Jee, 1989)*. Pre-1964 literature did not distinguish it
from modeling and lumped them together as “remodeling.”
While drifts and BMUs seem to create and use the same
kinds of osteoblasts and osteoclasts to do their work, in
different parts of the same bone at the same time the
‘blasts and ’clasts in drifts and BMUs can even respond
oppositely to the same stimulus (Chen et al., 1995; Yeh et
al., 1995). Since locally increased remodeling increases
local bone formation, scintigrams (“bone scans”) usually
show increased local uptake of the bone-seeking radioactive tracer, usually technetium.
remodeling space: increased BMU creations also increase the number of temporary holes in a bone and
excavations on its surfaces. That causes a temporary
bone loss called the remodeling space. It is temporary
because when BMU creations return to normal, the
existing holes refill with bone (because of the ARF sequence in BMUs) (Parfitt, 1980). Since increased bone
formation accompanies increased remodeling and an
increased remodeling space, that can help bone scans
(scintograms) with radioactive bone-seeking agents to
locate skeletal pathology when ordinary X-rays appear
normal (Jergensen et al., 1990).
remodeling threshold: the genetically-determined
Minimum Effective Strain range (or equivalent Stimulus; MESr in Fig. 3) that helps to control the switching
of BMU-based remodeling between its conservation and
disuse modes. When strains exceed it, completed BMUs
begin to make and resorb equal amounts of bone to
provide conservation-mode remodeling. When strains
stay below it, completed BMUs next to marrow make
less bone than they resorb to provide the disuse-mode
remodeling that mainly affects trabecular and endocortical bone. This threshold may center near 50 –100 microstrain, which would correspond to a tension or compression stress of ⬇ 1–2 megapascals. One might also
define the threshold as the region just to the left of the
“adapted window” in Figure 3, which could put the
corresponding threshold strain range in the 400 – 600
microstrain region.
resorption: different meanings of this term in the literature cause some confusion. Some authors use it to
mean net bone loss, and in that sense discuss “antiresorption agents.” While often called antiresorption
agents, estrogen and bisphosphonates really depress
BMU creations (Fleisch, 1995; Jee, 1995). At first, that
decreases global resorption, but due to the ARF sequence in the BMU, an equal decrease in global bone
419
formation usually and eventually follows, so these are
really “antiremodeling agents.” This text uses resorption to mean bone resorption by osteoclasts. It refers to
net losses of bone as such and separately.
strain: the deformation or change in dimensions and/or
shape caused by a load on any structure or structural
material*. It includes stretching, shortening, twisting,
and/or bending. Loads always cause strains, even if very
small ones, and three kinds occur: compression, tension,
and shear. Biomechanicians can express strain in microstrain units (millionths of a 100% strain), where
1,000 microstrain in compression would shorten a bone
by 0.1% of its original length, 10,000 microstrain would
shorten it by 1% of that length, and 100,000 microstrain
would shorten it by 10% of that length (and break it).
Strain emerges as an important signalling mechanism
in controlling a skeleton’s structural adaptations to its
mechanical usage.
strength: the load or strain that, when applied once,
usually fractures a bone (also the “ultimate strength”;
Fx in Fig. 3)*. Normal lamellar bone’s fracture strength
expressed as a strain is a range centered near 25,000
microstrain (somewhat lower in adults and higher in
rapidly growing mammals). That corresponds to a
change from 100% of its original length to 97.5% of that
length under compression, or to 102.5% of it under tension (Table 4).
strength-safety factor: when defined as how much
stronger a bone is than needed to carry the typical
largest voluntary loads on it, this factor would equal the
ultimate strength divided by the modeling threshold
when both are expressed as stresses. From Table 4 and
in young adults, that would equal 120 mpa ⫼ 20 mpa ⫽
6. Since the modeling threshold determines the largest
allowed bone strain or stress, when that threshold lies
below the ultimate strength it creates the safety factor.
Bones cannot foresee and adapt their strength to future
injuries, so they must adapt to past and present voluntary physical activities instead, whether the activities
are subnormal, normal, or supranormal.
“supranormal” exercise: here, high-force muscular
activities that cause the largest momentary voluntary
loads on bones. Examples include weight lifting and highacceleration sports like soccer and US-style football.
typical peak strains: visualize a histogram that plots
the sizes of a bone’s strains (or loads) on the vertical axis,
and on the horizontal axis the number of times dynamic
strains of a given size occurred during, say, a week. The
strains large enough to turn modeling on would be the
largest ones in that histogram, but would comprise fewer
than 0.01% of all strain events in that week. For example,
each systolic pulse in the marrow cavity is a loading event
on a hollow bone like the femur. In a week it would carry
over 725,000 corresponding strains, of which only ⬇ 50
from peak muscle forces might be large enough to reach or
exceed bone’s modeling threshold. The bone would adapt
its strength and “mass” to those ⬇ 50 events and pay little
attention to all others. While some controversy affected
this feature, the different bone strengths of long distance
runners and weight lifters strongly suggest it is true. It
would also be an obligatory effect of a modeling threshold’s
existence, which led me to infer that threshold’s existence
before in vivo strain studies verified its existence (Frost,
1964).
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