38 
Fishery Bulletin 109(1 ) 
Table 1 
List of all possible bioelectrical equations that could be correlated with specific fisheries parameters (TBW=total body water, 
TBP=total body protein, FFM=fat-free mass, TBA=total body ash, DW=dry weight, and TBF=total body fat) or overall condition 
of the fish. Fisheries parameters listed here and their correlated equations are the ones presented by the authors in this article. 
Resistance (R) and reactance (A c ) are measured in biological tissue and the values are then inserted into each equation. In some 
equations, the distance between electrodes ( L d ) is needed. 
Obtained 
Name 
Equation 
symbol 
Electrical 
equation 
Volume 
symbol 
Electrical 
volume equation 
Fisheries 
parameter 
Measured 
Resistance in series 
R 
R 
Ksv 
Lf!R 
TBW, TBP, FFM 
Measured 
Reactance in series 
X c 
X c 
W'x c 
— 
Derived 
Resistance in parallel 
R P 
R+(X C 2 /R) 
R pv 
WiR P 
TBA 
Derived 
Reactance in parallel 
x c 
X C +(R 2 /X C ) 
x cv 
W'x c 
DW, TBF 
Derived 
Capacitance (farad) 
° P f 
(1-10- 12 )/(314000-Z f ) 
Cpfv 
W!C pf 
— 
Derived 
Impedance series 
Z s 
V(R 2 +X C 2 ) 
Z sv 
L d 2 'Z s 
— 
Derived 
Impedance parallel 
z p 
(X C -R)N(X 2 +R 2 ) 
z pv 
W-z P 
— 
Derived 
Phase angle 
phase angle 
Arctan KXJR) 
— 
Condition 
were anesthetized in a tricane methanesulfonate (MS- 
222) solution of 1 g/9 L water. 
Sensitivity analysis 
To evaluate how sensitive models were to errors, six 
significant and nonsignificant errors along with six 
errors in distance between electrodes were incorporated 
into predictive models of total body water, dry weight, 
and phase angle (Table 1). Equations used in models 
were derivatives of R, X c , and combinations of these two 
values which can be representative of biological tissue. 
Significant and nonsignificant differences (e.g., errors) 
from the previous experiments were converted into a 
percent difference from controls and used in the sen- 
sitivity analysis. The brook trout data set used in this 
analysis were from Cox and Hartman (2005) and the 
trout ranged in size from 10 to 227 g. For the predictive 
models used to determine total body water, dry weight, 
and total body fat estimates, equations including R in 
series (for total body fat), X c in parallel (for dry weight 
and total body fat), and the electrical equation phase 
angle (for condition) (Table 1) were used. The significant 
R errors (in percentages) ranged from -58% (conductive 
board) to 10% (decreased needle depth) (Table 2). The 
significant X c errors (in percentages) ranged from -45% 
(high temperature) to 47% (decreased needle depth) 
(Table 2). All length errors ranged from 0% to 5%. To 
consider how nonsignificant errors affect parameter 
estimates, a range of the nonsignificant R and X c errors 
was inserted into each equation. The range of nonsig- 
nificant R errors (in percentages) that was inserted was 
-3% (full-stomach) to 3% (time=3 h). The nonsignificant 
X c errors (in percentages) ranged from 1% (Al) to 9% 
(full-stomach) (Table 2). 
For total body water, a single 6x6 matrix consisting 
of 36 combinations was formed from the six R and 
length errors. For dry weight estimates, two matri- 
ces were formed, one for R in parallel (used in the 
predictive model which had both R and X c terms in 
it), and a second for the actual predictive model that 
estimated dry mass (Table 1). The data were plotted 
in three-dimensional matrix plots, with the x and 
y axes describing the range of values for either the 
length between detectors, R, X c , or R in parallel, and 
with the z axis depicting the difference (in percent- 
age) between predicted estimates with and without 
errors. In phase angle models, length between detec- 
tors is not a variable, and therefore R and X c values 
were the only variables modeled. During analysis with 
significant errors added, phase angle values seemed to 
offset one another. To clarify this relationship, range 
of error values of -10% to 10% were added to both the 
R and X c values. Three-dimensional matrices were 
plotted with the x and y axes representing R and X c 
values and with the errors and the z axis depicting 
the difference between phase angle estimates with 
and without errors. 
Results 
Anatomical location of the electrode needle 
The insertion of electrode needles in different loca- 
tions within the fish resulted in different R and X c 
mean values (Fig. 1A). Specifically, mean R and X c 
values at locations C and D were significantly differ- 
ent from A for both R (LME t 16 25 >8, PcO.001), and 
X c (LME t 16 25>3, PcO.001). The difference in mean 
R values between location A (mean=306.62 £2) and 
location C was -84.82 £2 (-28%), and D was -146.44 
Q (-47%). The difference in X c means between loca- 
tion A (mean=75.44 £2) and location C was -26.64 £2 
(-35%), and between location A and D the difference 
was -13.80 £2 (-18%). There was not enough evidence 
to indicate that locations Al and B were significantly 
different from A for either R (LME t 16 25 <2, P>0.12) 
