Table 2. Results from error propagation calculation for C1 and α. Column 1 shows the mean values of C1 and α calculated from the mean values of S1 (aTSC) and S2 (aISC) over 5 volunteers and for typical mean values of C2 (extracellular/CSF sodium concentration) and w (water fraction) in healthy brain tissue. Uncertainties (standard deviations - std) in the estimation of C1 and α were calculated for typical and extreme variations of C2 and w, and for std of S1 and S2 over 5 volunteers (considered as typical values). Columns 2 and 3 show the resulting std of C1 and α when the variations of all 4 parameters are taken into account, for typical and extreme std of C2 and w, respectively. Columns 4 to 9 show the effect of individual (typical and extreme) variations of S1, S2, C2 or w on the uncertainties of C1 and α. All std results for C1 and α are given in absolute value (and percentage).
Column | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |
---|---|---|---|---|---|---|---|---|---|---|
Variation type | Typical | Extreme | Typical | Typical | Typical | Extreme | Typical | Extreme | ||
Units | Mean | Std | Std | Std | Std | Std | Std | Std | Std | |
S1 | mM | 35 | 8 | 8 | 8 | |||||
S2 | mM | 8 | 3 | 3 | 3 | |||||
C2 | mM | 140 | 5 | 10 | 5 | 10 | ||||
w | 0.8 | 0.05 | 0.10 | 0.05 | 0.10 | |||||
C1 | mM | 13 | 4.8 (36%) | 5.1 (39%) | 1.2 (9%) | 4.5 (34%) | 0.15 (1%) | 0.3 (2%) | 1.1 (8%) | 2.2 (16%) |
α | 0.2 | 0.061 (32%) | 0.063 (32%) | 0.060 (30%) | 0.021 (11%) | 0.007 (4%) | 0.014 (7%) | 0 | 0 |