04-Bio-A8 · December 2017
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format: National Exams, December 2017 — 04-Bio-A8 Biophysical Measurements. Three hours, open book, any non-communicating calculator. Seven questions of equal value (20 marks each); five constitute a complete paper and only the first five appearing in the answer book are marked. All seven are solved here, because this set is a study resource rather than an examination script. Every question is qualitative/descriptive — there is no numerical data to compute — so each answer follows flowing prose with instrumentation block diagrams where the question explicitly asks for one.
Reference texts (the books an open-book candidate should have on the desk for this subject):
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.
Diagnostic cardiac ultrasound uses short pulses of high-frequency (typically 2–5 MHz for adult cardiac imaging, balancing penetration to the heart against resolution) mechanical pressure waves. The wave travels through soft tissue at a nearly constant speed of about 1540 m/s, and whenever it encounters a boundary between tissues of different acoustic impedance $Z=\rho c$ (density × sound speed) — such as the interface between blood and a valve leaflet, or myocardium and pericardium — a fraction of the energy reflects back toward the transducer as an echo while the remainder is transmitted onward, refracted according to Snell's law. The amplitude of a reflection is set by the impedance mismatch at the boundary, and the wave is also progressively attenuated (absorbed and scattered) as it travels, roughly in proportion to depth and frequency, which is why gain must be compensated with depth (below).
The transducer is built from piezoelectric elements (commonly lead zirconate titanate, PZT) that convert an applied electrical pulse into a mechanical pressure pulse on transmit, and convert the mechanical pressure of a returning echo back into an electrical signal on receive — the same physical element performs both roles, switched in time. "Real-time imaging from a single fixed transducer position" is achieved not by physically moving the probe but by using a phased array of many small elements: by electronically delaying the excitation of each element in a programmed pattern, the transmitted wavefront is steered and focused to a chosen angle and depth without moving the transducer housing, and the same delay-and-sum principle is applied on receive to focus the array's sensitivity along that same line. Sweeping this electronic beam through a sector of angles, pulse by pulse, builds up a two-dimensional image from one fixed acoustic window — essential for cardiac imaging, where the intercostal space limits the transducer to a small fixed footprint on the chest wall.
The transmit beamformer/pulser generates the timed, delayed excitation pulses that steer and focus the outgoing beam to each successive scan angle. The same transducer array then receives the returning echoes, which pass to the receiver, time-gain-compensation (TGC), and receive beamformer block: TGC progressively increases amplifier gain with the time elapsed since the pulse was transmitted (i.e. with depth), compensating for tissue attenuation so that equally reflective structures appear with similar brightness regardless of depth, while the receive beamformer applies matched delays to each element's signal and sums them to reconstruct focused echo amplitude versus depth along the current scan line.
The beamformed radiofrequency signal is envelope-detected (rectified and low-pass filtered to extract the amplitude envelope, discarding the carrier phase) and logarithmically compressed to fit the very wide dynamic range of tissue echo strengths into the limited grey-scale range a display can show; this is the "envelope detect and signal processing" block. Because each scan line is acquired in polar coordinates (angle and range from the fixed transducer) while the display is a rectangular raster of pixels, a scan converter interpolates the polar-format echo data onto the Cartesian pixel grid, assembling successive scan lines into one complete 2D frame. Frames are refreshed at video rate (commonly 30–60 frames per second, driven by how many scan lines are needed per sector and the pulse repetition frequency permitted by the maximum imaging depth) and displayed in real time, so cardiac wall motion and valve opening/closing are seen as continuous, live motion from the single fixed acoustic window.
A parasternal long-axis transthoracic echocardiogram is acquired from one fixed intercostal window: the phased array electronically sweeps a roughly 90° sector through the left ventricle and mitral valve at 40+ frames per second, letting the sonographer watch valve leaflet motion and ventricular wall contraction live, entirely through electronic beam steering rather than physically sweeping the probe.
