Question 5 of 6

Question 5

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

(a) Organic matrix and bone salts as a composite structure

Bone is a natural composite, structured the same way reinforced concrete is. The organic matrix is ≈90–95% type I collagen fibrils (with ground substance proteoglycans and osteocalcin/osteonectin), laid down by osteoblasts in an ordered, layered (lamellar) pattern; collagen, like steel rebar, resists tension well but buckles under compression. The inorganic bone salts (hydroxyapatite crystals) precipitate within and along the collagen fibrils, filling the matrix the way cured concrete fills around rebar; crystalline mineral resists compression well but is brittle in tension. Bound tightly together, the collagen network prevents brittle crack propagation through the mineral under tensile/bending loads, while the mineral prevents the collagen from buckling under compressive loads — so the composite as a whole tolerates both loading modes far better than either constituent alone, which is exactly why bone (unlike pure mineral, e.g. chalk) can bend slightly before fracturing.

(b) Composition of hydroxyapatite

Hydroxyapatite is a calcium phosphate mineral with the formula $\text{Ca}_{10}(\text{PO}_4)_6(\text{OH})_2$, i.e. a calcium:phosphate molar ratio of exactly $10/6 = 1.67$ for the stoichiometric mineral. Bone hydroxyapatite is not perfectly stoichiometric: it is calcium-deficient and carbonate-substituted, with a molar Ca:P typically in the range 1.5–1.67, and it also incorporates small amounts of citrate, magnesium, sodium and other trace ions substituting into the crystal lattice. (Guyton quotes the ratio on a mass basis, where it varies more widely — roughly 1.3 to 2.0 — with nutritional state; that figure is not the molar ratio and the two should not be interchanged.)

(c) Sequence of bone calcification

Mineralisation does not deposit hydroxyapatite directly. Osteoblasts first raise local calcium and phosphate concentrations (partly via alkaline phosphatase hydrolysing pyrophosphate inhibitors) until an amorphous, less-stable calcium phosphate salt — essentially calcium hydrogen phosphate (brushite-type, $\text{CaHPO}_4$) — precipitates within the collagen matrix at nucleation sites. Over the following days to weeks this amorphous precursor progressively takes up additional calcium and hydroxide ions and reorganises into the stable, needle-like crystalline hydroxyapatite lattice, growing along and within the collagen fibrils as it matures.

(d) Histological remodelling mechanisms, and their value

Bone is continually remodelled by coupled teams of cells operating as basic multicellular units (BMUs): osteoclasts (multinucleated cells derived from the monocyte/macrophage lineage) resorb a tunnel of old bone (a "cutting cone" through cortical bone, or a resorption pit on a trabecular surface), after which osteoblasts follow behind, laying down new lamellar bone matrix that subsequently mineralises — producing, in cortical bone, a new osteon (Haversian system) around a central canal. This activity is coordinated by mechanical strain (Wolff’s law — bone reshapes itself along its principal loading axes), by systemic hormones (parathyroid hormone, calcitonin, vitamin D/calcitriol) acting on the osteoblast–osteoclast balance, and by local paracrine signalling (RANKL/RANK/osteoprotegerin) that couples osteoblast activity to osteoclast recruitment. The value of continual remodelling is threefold: it repairs microscopic fatigue damage before it propagates into a stress fracture; it allows the skeleton's architecture to adapt to changing mechanical demand over a lifetime; and it keeps a large, readily mobilisable reservoir of calcium and phosphate in dynamic exchange with the blood, letting the skeleton participate in day-to-day plasma calcium homeostasis.