Dalton’s Law (of partial pressures)

The total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of the individual gases.

Boyle’s Law

The pressure exerted by a gas is inversly proportional to the volume it occupies, assuming the amount of gas and the temperature is constant

Henry’s Law

where c=solubility of a gas at a fixed temp, k=Henry’s Law (equilibrium) constant p = partial pressure of the gas

Given a constant temperature, the amount of gas dissolved in a liquid, is proportional to the partial pressure of that gas

Graham’s Law

The rate of diffusion of a molecule is inversely proportional to the square root of its molecular weight

Fick’s Law of Diffusion

Diffusive flux goes from a high-concentration area to a low-concentration area proportional to both the concentration gradient and surface area and is inversely proportional to the thickness of the membrane.

JC / Sakurai 2016

2013B 12: 7 candidates passed (25.9%).

The universal gas laws form the basis of oxygen therapy and delivery, pressure and volumetric monitoring as well as a key to understanding the solubility of gases in blood. All the equations and relationship are straightforward so this question provided a good opportunity to score marks. Unfortunately many candidates were aware of the properties of the ideal gases but not the named laws. This led many candidates to omit major sections of the answer and thus scored no marks. Several candidates wasted time with complicated diagrams as well as equations and descriptions (scoring no additional marks). Many candidates were unable to identify Grahams Law (rate of diffusion inversely proportional to the square root of the molecular weight) but included it in an expanded Fick’s Equation.

DEFINITIONS

Viscosity (η)

Used to indicate a fluid’s internal resistance to flow. Also thought of as a measure of the friction of a fluid.
e.g. honey has a high viscosity than water and as such moves much slower if poured

Density (ρ)

relates the mass of a substance to its volume such that ρ = kg/m3
Although some gases may have similar viscosity, their densities may be different (eg. O2 and He)

Flow

measure of volume of fluid / gas moved per unit of time (e.g. ml/min).

FLOW

TYPES OF FLOW

Laminar

Turbulent

Transitional

Reynold’s Number

• The Reynolds Number is defined as the ratio of inertial forces to viscous forces in a flowing fluid.
• It is used in many fluid flow correlations and is used to describe the boundaries of fluid flow regimes (laminar, transitional and turbulent).
• Reynold’s number can predict the likelihood of turbulent flow occurring.

Flow	Reynold’s Number
Laminar	<2300
Transitional	2300-4000
Turbulent	>4000

• Density (ρ) is the major determinant of Re: ↑ρ (N2 v He) → ↑prob of turbulent flow
• Viscosity (η) has a much smaller contribution to the determination of Re: ↓η → ↑probability of turbulent flow

Laminar Flow

• Laminar flow is the flow that corresponds with low velocities and Reynolds numbers less than 2300.
• In this type of flow, the fluid flows in parallel layers, with no disruption between the layers.
  • At low enough velocities, the fluid will tend to flow without lateral mixing, while adjacent layers simply slide past one another
  • The movement of substance in the centre is twice the velocity of the movement of substance at the walls (there is no flow at the walls)
• For flow to be laminar, the tube in which it is travelling must have smooth, parallel sides with no branches in the system

• There is a linear relationship between pressure and flow
• Viscosity of the gas / fluid is directly proportionate to resistance:
  • ↑η → ↑R → ↓flow
  • Density has no effect on the flow of gas during laminar flow
• Altering the other variables will change R as seen

Turbulent Flow

• Turbulent flow is the most common form of flow in nature, and corresponds to the Reynolds numbers higher than a value of 4000
• chaotic and unpredictable, and is often seen with fluids at high velocities
• undergoes irregular fluctuations, or mixing, and continuously changes magnitude and direction
• Flow is disorganised with small eddies forming → creates a square wavefront

• Flow is inversely proportional to √ρ
• Pressure is proportionate to flow²
• Resistance proportional to density and not viscosity

Transitional Flow

• Transitional or Transient flow  is the phase of flow that occurs between laminar and turbulent flow, and corresponds to Reynolds numbers that land between 2300 and 4000.
• In this type of flow, there is a mixture of laminar and turbulent flows present.
• As Reynolds number increase from 2300 to ~4000, there are an increasing amount of disturbances appearing within the flow.
• Transition can occur in either direction, that is laminar–turbulent transitional or turbulent–laminar transitional flow.

Sources: cfdsupport.com, cvphysiology.com

JC 2019

2018A 13: 46% of candidates passed this question.

Whilst most candidates defined density correctly, there was a lot of uncertainty regarding viscosity. Most candidates recognised that flow may be laminar, turbulent or transitional. Most accurately recounted Reynolds number and applied this correctly. Additionally, the Poiseuille equation was correctly stated by most candidates and correctly related to laminar flow. Few candidates recalled the equation describing turbulent flow

Ultrasonography

• Piezoelectric and converse piezoelectric effect
  • Change of polarization of molecules in a quartz crystal in response to
    mechanical stress
  •  Application of electrical field creates mechanical deformation in a crystal
• Piezoelectric transducers in US
  • Electrical current converted into precise sound waves (1~20mHz)
  • Sound waves penetrate tissues
    • Lower frequency = better penetration, however lower resolution
    • Sound energy attenuated due to
      • Reflection – Directly back to transducer
      • Scattering – Some reflected sound waves travel in other directions and do not reach transducer
      • Refraction (Change in direction) – Snell’s law – amplitude of
        reflected sound wave is a function of the tissue acoustic mismatch and angle of incidence
      • Absorption – Tissue absorption of sound energy contributes most to attenuation
  • Interface of tissues of different densities reflect sound waves back to
    transducer
  • Sound waves returning to piezoelectric crystal converted to electrical current
• Central Processor
  • Electrical current generated by piezoelectric crystal signalled to CPU
  • CPU calculates the distance between transducer and object according to
    • Speed of sound (1540m/sec)
    • Delay in echo return
  • Information relayed to display for visualization
  • Gain
    • Sensitivity of CPU to signals received from transducer
    • Time-Gain Compensation – selective sensitivity of CPU to different interval of sound delay

Doppler effect

• Change in apparent frequency of sound for an observer moving relative to its source
• Use in ultrasound
  • Sound waves reflected off objects moving toward or away from transducer
    (usually blood)
    • If object moving toward transducer, frequency appears increased – displayed as red (however this is not standardized across machines)
    • If object moving away from transducer, frequency appears decreased –
      displayed as blue
  • Can be used to measure velocity of flow, as well as direction
    
    

Sakurai 2016

2022A 17: 23% of candidates passed this question.
This question was taken from core syllabus that requires level one (L1) understanding. Physical principles of ultrasound can be illustrated by outlining how ultrasound waves are generated from piezoelectric crystals, how they travel through the tissues, how they interact with different tissue planes and how the reflected waves return to the transducer and create images. Properties of ultrasound transducers include different geometric configurations of transducer probes and frequency-wavelength bandwidth properties of the crystals used in diagnostic ultrasound. Understanding of physical concepts of image resolution including its various aspects (e.g., spatial, temporal, contrast resolution) is required to address the next portion of the question. “Doppler effect” can be illustrated by a definition and equation along with some practical implications. This question was not answered well by majority of the candidates. Lack of knowledge and limited understanding resulted in poor average mark.

2010A 14: 7 (70%) of candidates passed this question.

2007B 04: 4 (57%) candidates passed this question.

It was expected candidates would outline the underlying principles of ultrasound imaging (reflection, scattering, refraction, and attenuation) and discuss that the basic image is the result of reflection of the transmitted ultrasound wave. Most candidates appreciated that the amplitude of the reflected echo is a function of the acoustic mismatch of the tissues and the angle of incidence and many candidates provided details mathematical descriptions concerning these principles.

While high levels of technical details were not required the answer should include a mention of the use a piezoelectric transducer and that an ultrasound beam has 3 dimensions — Axial, Elevation and Lateral. Some comment of the modes of Display (A= Amplitude, M Time Motion, 21), etc) was expected.

Extra credit was given for answers that included details regarding limits of depth of penetration (longer wavelength penetrate deeper, but loose image quality with longer wavelengths) and the varying properties of human tissue regarding refraction and attenuation (little refraction (path deviation) in human tissue and air attenuates).

Specific comment on the Doppler Effect was required. It was expected candidates would described that it refers to the change in frequency of a sound wave reflected by a moving target and that the reflected frequency differs if moving toward or away. Correctly stating that the reflected Frequency is Higher Towards and Lower Away scored additional marks. Comments concerning obtaining the best Doppler images with lower frequencies (opposite to ultrasound) and colour Doppler attracted additional marks.