## Principles of Measurement: Applications to Pressure, Volume, and Flow

### Abstract

1 Preliminary Considerations
3 Instrument Response
4 Signal Processing
5 Interpretation of Measurements
5.1 Indirect Measurements (Inference)
5.2 Models
6 Noise
6.1 Intrinsic Noise
6.2 Extrinsic Noise
7 Calibration
7.1 Static Calibrations
7.2 Dynamic Calibrations
7.3 Additional Procedures for Specific Variables
8 Probes
9 Linear Versus Nonlinear Systems
10 Conclusion
 Figure 1. Schematic diagram of the entire measurement process. Figure 2. Electrical analogue of the phenomenon of loading. The biological system has a source impedance ZS, whereas the measuring device has an input impedance that is functionally a load ZL. A: pressure or voltage loading. The measured value E1 systematically deviates from the desired value E0 by virtue of a nonzero ZS and a finite ZL. B: flow or current loading. The measured value I1 systematically deviates from the desired value I0 by virtue of a finite ZS and a nonzero ZL. Figure 3. Magnitude (A) and phase (B) of the second‐order transfer function T(ω) = [1 + 2iζω/ω0 – (ω/ω0)2]−1 as a function of normalized frequency, as a family in the damping coefficient ζ; ω is the angular frequency 2πf. Dotted line shows the response of a first‐order transfer function T(ω) = (1 + iωτ)−1, where τ is the time constant of the system. Abscissa for the second‐order transfer function is ω/ω0, whereas that for the first‐order is ωτ.Adapted from Shearer et al. 29 Figure 4. Effect of connectors on the amplitude and phase response of a Validyne MP‐45 transducer with 2‐cmH2O sensitivity. Unlabeled lines: minimum attachments; Luer: male‐male Luer slip fitting; Stub: needle stub adapter; a, b, c: 15‐cm, 30‐cm, and 45‐cm PE‐200 air‐filled catheters, respectively.From Jackson and Vinegar 17 Figure 5. Electrical analogue of a flow plethysmograph. Cg, box gas compliance; R, flow resistance of a pneumotachograph; Pbox, box pressure; , flow rate. Note that ground for resistor is atmospheric pressure, and ground for capacitor is zero pressure. These 2 points nevertheless represent a common virtual ground for the signals of interest. Figure 6. Modification of a hypothetical straight‐line flow‐volume curve. A: effect of first‐order transducer system with various time constants (T); τ is the lung time constant for exponential flow decay. B: effect of second‐order transducer system that is slightly underdamped, showing the characteristic “bounce” that accompanies rapid flow onset. Note that flow is shown in units of vital capacities per lung time constant (VC/τ). RV, residual volume; TLC, total lung capacity; ω0, natural frequency; ζ, damping coefficient.From Sinnett et al. 31 Figure 7. Magnitude‐frequency plot showing partial compensation of chamber characteristics (C) by judicious choice of transducer characteristics (T). Overall response of the system (S) is remarkably flat.From Sinnett et al. 31 Figure 8. Diagram of a dual‐chamber system for volume and flow calibration. Sinusoidally driven loudspeaker separates the reference chamber (volume, V1; pressure, P1) from the testing chamber (volume, V2; pressure, P2).Adapted from Jackson and Vinegar 17
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