20-Bio-A6 Biomedical Signal Processing · Undated paper
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams May 2019 — 04-Bio-A6, 3 hours, closed book (one of two calculators permitted — any Casio or Sharp approved model). Six questions are printed; the first five as they appear in the answer book are marked, each of equal value; most require an essay-format answer. All six are answered here.
Reference texts: Guyton & Hall, Textbook of Medical Physiology (13th ed.); Junqueira & Mescher, Basic Histology: Text and Atlas (14th ed.); Robbins & Cotran, Pathologic Basis of Disease (9th ed., for the Q2 autopsy case).
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.
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.
Hydroxyapatite is a calcium phosphate mineral with the formula $\text{Ca}_{10}(\text{PO}_4)_6(\text{OH})_2$, i.e. a stoichiometric calcium:phosphate molar ratio of exactly $10/6 \approx 1.67$ (the corresponding calcium:phosphorus mass ratio is about 2.16, from the atomic masses 40.08 and 30.97). Bone hydroxyapatite is not perfectly stoichiometric: it is typically calcium-deficient and carbonate-substituted, so its measured molar Ca:P sits a little below the ideal value (roughly 1.5–1.67), and it also incorporates small amounts of carbonate, citrate, magnesium and other trace ions substituting into the crystal lattice.
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.
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.
