TestAS · Life Sciences
Physics in living systems: pressure and flow, electricity in nerves, radiation and heat.
testas.de lists this topic for the Life Sciences module. In the test it comes as testlets: a short text, table or formula, then 4 to 8 questions you answer from it.
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Full exam-length testlets from the Kollego course, generated the same way as our mocks. Answer from the material, then open each answer to check.
Pressure and flow in the circulation
Pressure is force per area. Its SI unit is the pascal (Pa), equal to one newton per square metre, but blood pressure is still measured in millimetres of mercury: 1 mmHg is about 133 Pa. Atmospheric pressure at sea level is about 101 kPa, or 760 mmHg. Blood pressure values are given relative to the atmosphere, so a mean arterial pressure of 93 mmHg means 93 mmHg above atmospheric pressure.
p = F ÷ A hydrostatic pressure: p = ρ × g × h
In a column of liquid, pressure increases with depth because of the weight of the liquid above: the hydrostatic pressure equals the density times gravitational acceleration times height. Blood has a density of about 1,060 kg/m³, so a column of blood 1 m high exerts about 10.4 kPa, or roughly 78 mmHg. In a standing person, the arterial pressure in the feet is therefore much higher than at the level of the heart, and in the head it is lower. This is why blood pressure is measured at the level of the heart, and why divers feel the pressure of water, which increases by about one atmosphere for every 10 m of depth.
Flow is the volume passing a point per unit of time. In a tube without branches, the same volume must pass every cross-section, so the flow velocity is inversely proportional to the cross-sectional area (the continuity equation): where a vessel narrows to half its area, blood flows twice as fast. In the circulation as a whole, the total cross-section of all capillaries together is far larger than that of the aorta, so blood flows very slowly in the capillaries, which leaves time for exchange with the tissues.
flow = area × velocity Hagen-Poiseuille: flow ∝ r⁴ × Δp ÷ (η × l)
Flow through a vessel is driven by the pressure difference between its ends and opposed by resistance. According to the Hagen-Poiseuille law, which holds for steady flow in rigid tubes, the flow at a given pressure difference is proportional to the fourth power of the radius and inversely proportional to the viscosity of the fluid and the length of the tube. Small changes in radius therefore have large effects: this is how arterioles control blood flow to organs, and why narrowing of arteries by deposits can reduce blood supply so strongly.
1. A blood pressure of 120 mmHg corresponds to about how many kilopascals?
C: 16.0 kPa
The text: 1 mmHg ≈ 133 Pa. 120 × 133 Pa ≈ 16,000 Pa = 16 kPa.
2. A diver is at a depth of 20 m. What is the total pressure acting on the diver?
C: About 3 atmospheres
The text: water pressure rises by about one atmosphere per 10 m. 20 m adds 2 atmospheres, plus 1 atmosphere of air above: 1 + 2 = 3 atmospheres.
3. The feet of a standing person are about 1.2 m below the heart. By roughly how much is arterial pressure in the feet higher than at heart level?
B: About 90 mmHg
The text: 1 m of blood exerts about 78 mmHg. 1.2 m × 78 mmHg ≈ 94 mmHg, so about 90 mmHg higher in the feet.
4. An artery narrows locally to one third of its cross-sectional area. How does the flow velocity change there?
A: It triples
The text: velocity is inversely proportional to cross-sectional area (area × velocity is constant). One third of the area means three times the velocity.
5. An arteriole's radius falls by half while the pressure difference stays the same. What happens to the flow?
C: It falls to one sixteenth
Hagen-Poiseuille: flow ∝ r⁴ at the same pressure difference. Half the radius gives (1/2)⁴ = 1/16 of the flow.
6. Why does blood flow slowly in the capillaries?
D: Their total cross-sectional area is very large
The text: the total cross-section of all capillaries together is far larger than the aorta's. With velocity inversely proportional to area, a large total area means slow flow.
X-ray imaging and radiation dose
X-rays are electromagnetic waves with very short wavelengths and high photon energies. When they pass through the body, some are absorbed or scattered, and the rest reach a detector behind the patient. Tissues that absorb strongly, such as bone, which contains calcium, appear light on the image, while tissues that absorb little, such as the air-filled lungs, appear dark. The contrast of an X-ray image is therefore a picture of how strongly different tissues attenuate the beam.
Attenuation follows an exponential law. Each layer of material of a certain thickness removes the same fraction of the photons that reach it. The thickness that halves the intensity is called the half-value layer. It depends on the material and on the photon energy: dense materials with high atomic numbers attenuate much more strongly, which is why lead aprons protect staff, and higher-energy photons penetrate further. After n half-value layers, the intensity has fallen to (½)ⁿ of its initial value.
I = I₀ × (½)^(x ÷ HVL) effective dose in sieverts (Sv); 1 mSv = 0.001 Sv
Absorbed X-rays deposit energy in tissue and can damage DNA. The absorbed dose, measured in gray (Gy), is the energy absorbed per kilogram of tissue. To compare the health risk of different exposures, the effective dose, measured in sieverts (Sv), takes into account the type of radiation and the sensitivity of the irradiated organs. Typical effective doses are about 0.02 mSv for a chest X-ray, about 7 mSv for a CT scan of the abdomen, and about 2 to 3 mSv per year from natural background radiation in Germany, mainly from radon gas, cosmic rays and radioactive substances in food and rock.
Radiation protection follows three basic principles. Justification means that an examination should be performed only if its expected benefit outweighs the risk. Optimisation, often summarised as ALARA (as low as reasonably achievable), means using the lowest dose that gives an adequate image. Protection of staff relies on distance, shielding and time: the intensity from a small source falls with the square of the distance, lead absorbs X-rays, and a shorter exposure means a smaller dose. Doubling the distance from the source reduces the dose rate to a quarter.
| Material | Half-value layer |
|---|---|
| Soft tissue | 4 cm |
| Bone | 1.5 cm |
| Lead | 0.25 mm |
1. What fraction of the beam passes through 12 cm of soft tissue?
A: 1/8
Table: soft tissue half-value layer 4 cm. 12 cm ÷ 4 cm = 3 half-value layers, (½)³ = 1/8.
2. What fraction passes through a lead apron 0.5 mm thick?
C: 1/4
Table: lead half-value layer 0.25 mm. 0.5 mm ÷ 0.25 mm = 2 half-value layers, (½)² = 1/4.
3. Why does bone appear light on an X-ray image?
B: It absorbs X-rays more strongly than soft tissue
The text: bone, which contains calcium, absorbs strongly, so fewer X-rays reach the detector behind it, and strongly absorbing tissues appear light.
4. About how many chest X-rays correspond to the effective dose of one abdominal CT scan?
C: About 350
The text: chest X-ray about 0.02 mSv, abdominal CT about 7 mSv. 7 ÷ 0.02 = 350 chest X-rays.
5. A technician stands 2 m from a source and moves to 4 m. How does the dose rate change?
C: It falls to a quarter
The text: intensity falls with the square of the distance. 4 m is twice 2 m, so the dose rate falls by 2² = 4, to a quarter.
6. What does the principle of justification require?
D: The expected benefit must outweigh the risk
The text: justification means an examination is done only if its expected benefit outweighs the risk.
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