Bone ages as a result of the metabolism occurring on its surfaces by BMU’s. Peak bone mass, structure and composition are initially deter-mined by genes [97, 98]. However, the composition and structure of bone adapts to prevailing loads as dictated by Wolff’s law [1, 2, 9, 47].
For example, periosteal bone formation is increased in areas where mechanical stresses are highest. This ultimately increases the sec-ond moment of areaI(the periosteal and endosteal walls are further displaced from the central axis of the bone [68]). During growth, a positive balance between the formation and the resorption of bone acts towards establishing the skeleton’s peak bone strength. With epiphyseal closure and the end of longitudinal growth, the balance shifts toward an equilibrium where the amount of bone formed
Table 2.1:Characteristic equations to describe mechanical parameters for elastic isotropic material [24, 85, 95, 96]
Parameter Equation
Young’s modulus (Pa) E=σ
e = µ(3λ+2µ) λ+µ
Bulk modulus (Pa) K= E
3(1−2ν) =λ+2 3µ
Poisson’s ratio (-) ν=−etransversal
eaxial = λ
2(λ+µ)
Maximum deflection of bending beam (m) δmax= ML
2
8EI
Stress (Pa) σ= F
S
Strain (-) e= ∆L
L0
First Lamé constant (Pa) λ= Eν
(1+ν)(1−2ν) Second Lamé constant (shear modulus) (Pa) µ= E
2(1+ν)
M= bending moment,L= length,I= second moment of area,F= force,S= surface area,∆L= change in the length andL0= original length.
and resorbed is equal. Throughout this phase, bone strength is main-tained by replacing old or damaged calcified matrix by new calcified matrix [68, 99]. Hence, bone tissue age is determined by its distance from active bone metabolic surfaces [100]. As the calcification of new osteons is slow, lasting even months, the process may result in varying degrees of mineralization (tissue mineral density) of osteons in any given bone cross-section [57, 101]. However, after skeletal mat-uration, tissue mineral density reaches a relatively stable value for older tissue (i.e., calcification does not continue indefinitely) [57,102].
This is apparent when comparing the mineralization or mechanical
Bone
properties between osteonal (degree of mineralization of bone, DMB:
1.06 g/cm3, elastic moduli: 21.8 GPa) and interstitial (DMB: 1.16 g/cm3, elastic moduli: 24.1 GPa) tissue [96, 103].
Im b a l a n c e i n b o n e m e t a b o l i s m
Four abnormalities have been identified to develop in bone model-ing and remodelmodel-ing due to agmodel-ing [66]. Firstly, there is the abrupt and rapid decline in periosteal apposition after completion of longi-tudinal growth. The second and third abnormalities are associated with BMU imbalance; ultimately less bone is deposited than is
be-ing resorbed, although the amounts of deposited and resorbed bone both decrease. In addition to increasing porosity, repetitive loading due to exercise and high impact, e.g., from a fall or some other phys-ical trauma, can induce cracks in the bone. These cracks that are initiated at the sub-micron level may eventually develop into visible cracks. The inability to replace the damaged bone as a result of the BMU imbalance can lead to its failure [9, 104]. The fourth abnormal-ity occurs in women, where increased remodeling, especially after menopause, accelerates bone loss and a deterioration in the quality of the bone structure.
Tr e b e c u l a r v s c o r t i c a l b o n e
Remodeling causes trabeculae to become thinner, leads to loss of trabecular connectivity, and ultimately to the complete loss of trabec-ulae. The loss of trabecular mass through a total loss of trabeculae compromises bone strength more than loss through trabecular thin-ning [66, 105]. The remodeling of cortical bone enlarges the canals and resorption cavities that eventually results in their coalescence.
After the age of 60, cortical bone loss is more prevalent than trabec-ular bone loss, because cortical bone comprises about 80% of the skeleton [45, 80]. This can be understood as an acceleration in corti-cal bone loss with increasing surface area, while trabecular bone loss decelerates due to decreasing surface area (Table 2.2). Consequently, increases in cortical porosity rather than trabecular bone porosity compromise bone strength with more than ∼80% of all fractures
occurring at cortical sites [80].
Table 2.2:Comparison between trabecular and cortical bone.
Trabecular bone Cortical bone Lamellae arrangement Irregular Concentric
“lamellar packets” around Haversians
Unit Rod or plate-like Osteon
trabeculae
BV/TV Low (10-50%) High (>70%)
Mass of skeleton 20% 80%
During aging Bone loss Bone loss
declines accelerates
BV/TV= bone volume fraction
Ag i n g a n d m e c h a n i c a l p r o p e r t i e s o f c a l c i f i e d m a t r i x Increase of longitudinal elastic coefficients of the calcified matrix has been associated with increasing age in men [37]. Increased elastic coefficients affect the bone such that it becomes more brittle and less tough with aging [106,107]. This may account for a greater part from changes in the organic phase of bone, since differences in degree of bone tissue mineralization contribute very little to the differences observed in tissue elastic properties [108–110]. These changes con-sist of several processes: variation in the co-alignment and orienta-tion of mineral crystals with the fiber axis of collagen [9, 104, 110];
changes in the relative amounts of enzymatic and non-enzymatic cross-links [104, 106], where an increase in the amounts of the latter make collagen more brittle [106,107]; and a decrease of water bound to the bone matrix plays a role in modifying the elastic properties of collagen [111].
Bone
Os t e o p o r o s i s
Osteoporosis is essentially a skeletal disease where compromised bone strength is followed by an increased fracture risk (particularly of the hip, spine or forearm as a result of minimal trauma, e.g., in conjunction with routine daily activity). Conceptually, bone strength can be thought of as the product of BMD, bone material properties, thickness and porosity of both cortical and trabecular bone [13, 18].
However, an areal BMD value (grams per square centimeter) of 2.5 or more standard deviations at the femoral neck and/or total hip below the young female adult mean value (T-score) as measured with a dual X-ray absorbtiometry (DXA) device indicates
osteoporo-sis. The reference range is based on femoral neck measurements of Caucasian women aged 20 to 29 years (the Third National Health and Nutrition Examination Survey, NHANES III, database). The reference values also apply to men aged 50 or more because the age-adjusted risks of hip fracture for a given BMD value are similar for both sexes [11]. For women prior to menopause and men below the age of 50, BMD is compared to the corresponding value in an age, gender and ethnicity matched healthy reference population. In practice, for men under 50 years of age, a BMD measurement on its
own is not sufficient to diagnose osteoporosis [112].
There are many different causes of osteoporosis; the disease can be hereditary, mechanical (extended periods of unloading), hor-monal, and nutritional. These factors can act independently or syner-gistically to compromise bone strength [113]. In Finland alone, 400 000 people are estimated to have osteoporosis and approximately 30 000-40 000 fractures per year are attributed to the deterioration of bone [114]. The prevention of osteoporosis mainly focuses on sufficient mechanical stimuli, a balanced diet, preventing falls, and stopping smoking. Drug therapy is commonly directed to individ-uals with the highest risk of fracture [114]. Individindivid-uals referred to drug therapy and those already under treatment are recommended to be monitored with DXA [19]. DXA scans conducted every 1-2 years serve as a means to verify the response to treatment in clinical practice. Due to the two-dimensional (2D) nature of the
measure-ment, areal BMD may overestimate the fracture risk for individuals with a smaller body size (lower areal BMD) than on average.
Ad-ditionally, variations in bone marrow composition and structures overlying central sites such as the spine (e.g., aortic calcification) and hip can affect the determined BMD value [19, 66].
Wh e n D X A i s n o t ava i l a b l e
When BMD-measurements are not available, the presence of one or more low-impact fragility fractures is considered as a sign of osteo-porosis. This can also be the case even if an individual does not have an osteoporotic BMD value [21, 115]. This discrepancy has led to the development of fracture prediction tools that take into account clin-ical risk factors (fracture history, smoking, alcohol, glucocorticoids, and rheumatoid arthritis) with age, weight, height, ethnicity and sex to estimate an individual’s 10-year probability of fracture (e.g., WHO’s FRAX tool) [11,29,116]. Additionally, in Finland according to
the recommendations of the International Society for Clinical Densit-ometry (ISCD), individuals may be referred to pharmacological ther-apy on the basis of peripheral ultrasound measurements [117, 118].
Co m p l e m e n t a r y d i a g n o s t i c s
Much effort has been invested in providing quantitative measures of status of bone in addition to that provided by BMD. Potentially, they could also be adopted to monitor outcomes of pharmaceuti-cal trials. There are some widely used radiologic modalities, i.e., quantitative computed tomography (QCT) [119], high-resolution pe-ripheral quantitative computed tomography (HR-pQCT) [120], mag-netic resonance imaging (MRI) [121] and quantitative ultrasound (QUS) [25, 32, 118]. This thesis is mainly concerned with recent ad-vances in QUS. Therefore, in the following section, the principles of ultrasound physics will be discussed, and some current approaches to assess bone with ultrasound will be introduced.
3 Ultrasound assessment of bone
Bone mass, shape and qualities (i.e., geometry, microstructure and mechanical properties) are factors that account for the strength of the whole bone; of these, bone qualities are the most difficult to assess. One modality proposed for the evaluation of bone qualities is non-ionizing quantitative ultrasound (QUS) since it is cost-effective [26]. Currently established QUS parameters, such as speed of sound and attenuation, have displayed statistically significant correlations with BMD and fracture risk, in both trabecular and cortical bone [26–28]. Additionally, QUS has been used with variable success to explore bone elastic properties [36, 91, 122], microstructure [36, 123–
127], matrix constituents (i.e., organic and mineral phases) [128–131]
and microdamage accumulation [132, 133].
Ultrasound measurements on cortical bone have been applied since the mid twentieth-century [134, 135]. However, only after the introduction of the first clinical QUS parameters in 1984 [25], was ul-trasound proposed for screening and diagnosing osteoporosis [136].
Nevertheless, widespread clinical exploitation of QUS methods is still lacking due to the low agreement between peripheral QUS pa-rameters and BMD at the proximal femur [26, 28, 32]. On the other hand, recent progress in pulse-echo ultrasound technology has re-vealed diagnosticin vivoinformation relevant for severe fracture sites, such as the proximal femur [31]. Therefore, even though not yet fully clarified, QUS possesses substantial potential, e.g., in evaluation of fracture risk, osteoporosis screening and monitoring the effects of drug therapies for osteoporosis (Axial Transmission: [137–141], Through Transmission: [142], Pulse-Echo: [31–34]).
3.1 BASIC PHYSICS OF ULTRASOUND
A vibrational wave propagating in matter (gas, fluid, solid or plasma) at a frequency > 20 kHz, i.e., above the upper audible limit of an av-erage healthy young human, is known as ultrasound (US). In solids, US waves can propagate in four principle modes, i.e., longitudinal waves, shear waves, surface (Rayleigh) waves and plate waves in thin materials. Longitudinal waves are most commonly used in assessing biological tissues [24, 143–145]. Longitudinal waves can propagate in all kinds of media, and result from particle motion in parallel to the direction of wave propagation (forming compressional waves).
When the particle motion is small (linear propagation), wave prop-agation speed (i.e., speed of sound, SOS) is independent of the am-plitude of the particle motion and is influenced by the density as well as the geometric and elastic properties of the medium. Typical relationships characterizing the linear propagation of ultrasound in an elastic solid are presented in Table 3.1.
In summary, an examination of the equation concerning particle displacement reveals that a wave radiated by a source reproduces the motion of that source. For a plane wave in a non-attenuating medium, the product of a medium’s density and SOS is commonly known as the medium’s characteristic acoustic impedance (or spe-cific acoustic impedance). It describes the resistance an ultrasound wave encounters as it passes through the medium. Moreover, it
de-termines the acoustic transmission and reflection at the boundary of two materials with different characteristic acoustic impedances and contributes to the attenuation of sound in a medium. Attenuation results from the combined effects of wave spreading (decreasing of wave amplitude with distance), scattering (i.e., deviation of sound energy from the initial propagation direction) and absorption (the conversion of sound energy to other forms of energy, e.g., heat) and depends on the sound frequency and characteristics of the medium.
Attenuation in a homogeneous medium is typically observed as the (exponential) decrease of the initial amplitude of the wave.
In addition to the effect of impedance mismatch, reflection at
Ultrasound assessment of bone
Table 3.1: Basic equations describing the interaction of planar ultrasonic waves with media [24, 143, 144, 146]
Parameter Equation
Particle displacement [m] u=u0sin(ωt−φ) Angular frequency of particle [rad/s] ω=2πf
Wavelength [m] λw= cp
f =cpT
Acoustic impedance [rayl] Z=ρcl
Longitudinal speed of sound in isotropic elas-tic solid [m/s]
cl=
r E(1−ν)
ρ(1+ν)(1−2ν)
Sound wave pressure for plain waves [Pa] p=ρclcu
Snell’s law [-] sinθc 1
1 =sinθc 2
2 = sinθc 3
3
Reflection coefficient [-] RC= ZZ2cosθ1−Z1cosθ2
2cosθ1+Z1cosθ2
Transmission coefficient [-] TC= 4Z1Z2cos2θ1
(Z2cosθ1+Z1cosθ2)
Attenuation law [-] p(d) =p0e−αdandI(d) =I0e−2αd
u0 = maximum displacement amplitude,t= time, φ= phase angle, f = fre-quency,cp= phase velocity,T= period,E= Young’s modulus,ν= Poisson’s ratio,ρ= mass density,cu= particle velocity,d= distance,α= attenuation coef-ficient,p0andI0are the initial pressure and intensity atd= 0, respectively.θ1
andθ2are the angles of the incidence and refraction, respectively. Subscripts 1, 2, and 3 refer to the first and second medium and shear wave, andlto the
longitudinal speed of sound.
the boundary of two materials occurs only if the object’s boundary is thicker and the dimensions of its surface are much smaller than the wavelength of the incident wave. The angle and fraction of the reflected wave pressure amplitude can be derived from the princi-ples of Snell’s law, continuity of particle velocity and local pressures
across the boundary. Acoustic scattering occurs as a result of the interaction between the primary wave and the rough surface of a het-erogeneous object with different density and/or elastic properties than those of the surrounding medium. Scattering is most likely to take place when the dimensions of the surface of the object (scatterer) are similar to or smaller than the wavelength of the incident wave.
When the wavelength is much greater than the dimensions of the scatterer, it is known as Rayleigh scattering. In Rayleigh scattering, sound is uniformly scattered in all directions and the incident wave undergoes a minor deflection at the edges of the object. When the wavelength and dimensions of the scatterer are comparable, the
scat-tering is more complex and may be estimated by Faran scatscat-tering models as is the case for trabecular bone [123, 147].