20-Bio-A6 Biomedical Signal Processing, December 2014, Q3

Question 3

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) Functional anatomy of the kidney

Each kidney is organised into an outer cortex and inner medulla, the medulla arranged as 8–18 renal pyramids whose papillae drain into minor, then major, calyces and the renal pelvis, which narrows into the ureter. The functional unit is the nephron (≈1–1.3 million per kidney): a glomerulus (a tuft of fenestrated capillaries) invaginated into Bowman’s capsule, filtering plasma into the tubule — proximal convoluted tubule → loop of Henle (descending thin limb, ascending thin/thick limb) → distal convoluted tubule → collecting duct. Blood enters each glomerulus via an afferent arteriole and leaves via an efferent arteriole (the only capillary bed in the body fed and drained by arterioles, letting the kidney control glomerular pressure independently of downstream pressure); the efferent arteriole then supplies a second capillary bed, the peritubular capillaries (and, for juxtamedullary nephrons, the vasa recta running alongside the loop of Henle) that reabsorb tubular fluid. Where the thick ascending limb passes back between its own afferent and efferent arterioles, specialised macula densa cells and juxtaglomerular (granular) cells of the afferent arteriole form the juxtaglomerular apparatus, the sensor/effector unit for tubuloglomerular feedback and renin release.

(b) Proportion of filtrate reabsorbed

Of the ≈180 L/day of glomerular filtrate produced (GFR ≈ 125 mL/min in a healthy adult), only ≈1–1.5 L/day is excreted as urine, so on average about 99% of the filtrate is reabsorbed by the tubules and only roughly 1% is excreted — the bulk (≈65%) reabsorbed isosmotically in the proximal tubule, with the loop of Henle, distal tubule and collecting duct fine-tuning the remainder under hormonal control.

(c) Glomerular filtration rate from inulin clearance

Given. Plasma inulin concentration $P_{in}=0.05\ \text{g}/100\ \text{mL}$; urinary inulin excretion rate $U_{in}V = 0.02\ \text{g/min}$.

Find. GFR, using inulin clearance (inulin is freely filtered and neither reabsorbed, secreted, nor metabolised by the tubule, so its clearance equals GFR exactly).

Approach. $\text{GFR}=C_{in}=\dfrac{U_{in}V}{P_{in}}$, with both quantities expressed per unit volume of plasma.

Convert the plasma concentration to g/mL. $P_{in}=0.05\ \text{g}/100\ \text{mL}=0.0005\ \text{g/mL}$.
Apply the clearance formula. $$\text{GFR}=\frac{U_{in}V}{P_{in}}=\frac{0.02\ \text{g/min}}{0.0005\ \text{g/mL}}=\boxed{40\ \text{mL/min}}$$

Question 3(c) result
Quantity	Value
Glomerular filtration rate (from the given inulin data)	40 mL/min

Check — context: 40 mL/min is well below the textbook average adult GFR of ≈ 125 mL/min; the paper's own numbers are used as given (a smaller illustrative excretion rate relative to the stated plasma concentration), and the method — not the absolute magnitude — is what the question is testing.

(d) Importance of the renin–angiotensin system

A fall in blood pressure (or renal perfusion, or NaCl delivery to the macula densa) triggers renin release from the juxtaglomerular apparatus. Renin cleaves circulating angiotensinogen to angiotensin I, which angiotensin-converting enzyme (mainly in the pulmonary circulation) converts to angiotensin II, a potent vasoconstrictor that also stimulates aldosterone release from the adrenal cortex. The system serves two goals at once: angiotensin II constricts the systemic arterioles generally (raising blood pressure) but preferentially constricts the efferent glomerular arteriole, which raises glomerular capillary hydrostatic pressure and defends GFR even as renal blood flow falls — so filtration (and hence waste excretion, since urea/creatinine are filtered, not actively secreted in bulk) continues. Aldosterone acts downstream on the distal tubule and collecting duct to increase Na$^+$ (and secondarily water) reabsorption, directly conserving extracellular volume and electrolytes. Angiotensin II also stimulates thirst and ADH release, further favouring water retention. The net effect is a coordinated response that restores circulating volume and pressure by conserving water and salt, while the efferent-arteriolar mechanism specifically protects filtration so that nitrogenous and other wastes are not retained in the process.

Topic: Renal functional anatomy, glomerular filtration and clearance, and the renin–angiotensin–aldosterone axis.

Key relations: clearance/GFR $=U_xV/P_x$ for a freely-filtered, non-reabsorbed, non-secreted marker (inulin, or creatinine as its clinical proxy); RAAS cascade angiotensinogen → angiotensin I → (ACE) → angiotensin II → aldosterone.

Why this works: inulin's clearance equals GFR only because none of it is added to or removed from the tubular fluid after filtration, so the amount excreted per minute must equal the amount filtered per minute; the RAAS works because efferent-arteriolar constriction raises glomerular pressure independently of the fall in renal blood flow that triggered the response, decoupling "conserve volume" from "keep filtering."

Common pitfall: using the wrong volume basis when applying the clearance formula (mixing g/100 mL with g/mL), and, for RAAS, describing angiotensin II as only a vasoconstrictor while missing that its efferent-selective action is precisely what preserves GFR during volume depletion.

Source: Guyton & Hall, Textbook of Medical Physiology, chapters on renal functional anatomy, glomerular filtration and clearance, and the renin–angiotensin system in the long-term regulation of arterial pressure and extracellular fluid.

Question 3 of 6

Question 3

(a) Functional anatomy of the kidney

(b) Proportion of filtrate reabsorbed

(c) Glomerular filtration rate from inulin clearance

(d) Importance of the renin–angiotensin system