Statistical analysis

All statistical analyses were conducted in Excel Office 2007 and PAST v2.15 (Hammer et al, 2001). For all microvolumeter measurements, the volumes were recorded 5 times and an average volume calculated. Differences between variables were tested for using a two-tailed unequal varience t-test, with p values>0.05 considered significant. The accuracy of the microvolumeter equipment was tested for by regression analysis, with average measured volumes plotted against calculated volumes.

Average volume measurements were taken over a series of time points. This data were then used to calculate the percentage of initial sample volume, for comparison between different sized samples (sample volume/intial sample volume x 100). Percentages of initial volumes were plotted against the incubation period to demonstrate the progressive shrinkage of samples.

The original volume of samples was plotted against the volume of the same samples at 14 days to test for a size related relationship of the extent of shrinkage. Least- square regression was used to establish slopes and euations of each iodine- concentration.

Least-squared multiple regressions were calculated in order to capture the

interdependency of shrinkage on the three principal variables of, initial sample size, I2KI concentration and incubation time. This allowed the creation of formulae to

103 Table 3.1 Summary of experimental conditions for shrinkage experiments. TA, tibialis anterior, TS, triceps surae, GM, gluteus medius, RF, rectus femoris

Tissue type Previous

treatment Solution Sample

Measurement (days post dissection) Skeletal Muscle Frozen, - 10°C for an excess of 6 months PBFS, I2KI 2%, 6%, 10%, 20% Muscles, TA, TS, GM, RF for each conc. 0, 1, 2, 7, 14, 21, 28 Skeletal Muscle none PBFS, Glutaraldehyde, 70% ethanol, I2KI 2%, 6%, 10%, 20% Muscles, TA, TS, GM, RF for each conc 0, 1, 2, 7, 14, 21, 28 Cardiac Muscle none PBFS, Glutaraldehyde, 70% ethanol, I2KI 2%, 6%, 10%, 20% A bisected heart, for each conc.

0, 1, 2, 7, 14, 21, 28 Cerebellum none PBFS, Glutaraldehyde, 70% ethanol, I2KI 2%, 6%, 10%, 20% A cerebellum sample at each conc. 0, 1, 2, 7, 14, 21, 28 3.3 Results

Repeated measurements in different volumeter reservoir solutions showed no significant difference (p>0.05, t-test of means) for either stained or unstained samples. This demonstrates that the hypotonic water reservoir has no significant effect on the measurements.

Findings for the standard volumes showed that the mean repeated microvolumeter readings were not significantly different from the microCT estimates of muscle

104 volume or the calculated steel bearing volumes (Fig.3.4). Regression analysis for the combined data gave a slope though the origin of 0.998 (R²=0.9997), and an average error of only +/- 0.00262ml (ranging from +0.005 to -0.007ml). This level of error (+/- 1.36% average, +/-0.21 to 2.8% range) is low relative to the changes of tissue volume under investigation (see below).

Figure 3.4 Regression analysis of measured ball-bearing volume against actual volume. The accuracy of the microvolumeter apparatus was tested by measuring the volume of ball-bearings of a known volume. The measured volumes of ball-bearings are plotted against their actual volumes.

Tissues immersed in the 3 different fixatives showed markedly different changes in volume. After immersion in PBFS all of the samples underwent an initial rapid increase in volume, and a subsequent, far more gradual decrease in volume. Immersion in 70% ethanol resulted in a gradual decrease in tissue volume. The tissue samples immersed in glutaraldehyde initially swelled and then began to shrink, but on average remained a little larger than their initial volume (Fig.3.5).

105 Figure 3.5Average tissue shrinkage caused by commonly used fixatives. A graph showing the average percentage of the initial volume of skeletal muscle, cardiac muscle and cerebellum samples immersed in 10% PBFS, 70% ethanol or 3% glutaraldehyde (GlutA) for a period of 28 days, (n=6 for each fixative).

Immersing specimens in I2KI solution (dissolved in PBFS), results in a rapid

decrease in volume in both freshly dissected and previously frozen specimens of skeletal muscle. There was no significant difference (p>0.05) between the volume of samples previously frozen and non-frozen (Fig.3.6). Subsequent analysis therefore used both frozen and un-frozen skeletal muscle data in order to maximise the data set.

106 Figure 3.6 The difference in tissue shrinkage caused by I2KI staining between previously frozen and unfrozen skeletal muscle. A graph showing the

proportional decrease in skeletal muscle volume over 14 days in 20% I2KI in both

previously frozen (solid light blue line, n=4) and un-frozen (dashed dark blue line, n=4) specimens. The average of the frozen and un-frozen specimens is displayed in black.

All three tissue types showed a concentration dependent shrinkage after immersion in I2KI solution (Fig.3.7) which was more extensive than that brought about by

immersion in PBFS alone. A higher I2KI concentration resulted in a greater level of

shrinkage. The cerebellar samples showed least shrinkage, and the skeletal and cardiac samples showed similar levels of shrinkage (Fig. 3.8). The muscle samples undergo an initial rapid phase of specimen shrinkage over the first 2 days of

staining, with the rate beginning to reach a plateau at around 7 days. The higher I2KI

concentrations brought about a more rapid and extensive shrinkage than the lower concentrations.

107 Table 3.2The average percentage volume of skeletal muscle volume

remaining after 14 days immersion in PBFS or I2KI. Standard deviation values

are in brackets.

Fixative Average/ Percentage of original volume after 14 days (±SD) PBFS Glutaraldehyde 70% Ethanol 81 (±15.35) 105 (±8.18) 78 (±7.24) 2% I2KI 74 (±7.08) 6% I2KI 58 (±11.40) 10% I2KI 53 (±9.52) 20% I2KI 33 (±9.34)

108 Figure 3.7 Bisected mouse hearts stained in different iodine concentrations, in a similar orientation on day 4 of immersion in: a) 10% PBFS, b) 2% I2KI, c) 6% I2KI,

d) 10% I2KI, e) 20% I2KI. On day 0 all 5 samples were measured as being between

0.07-0.09ml. Image obtained by photography, and to scale, scale bar 5mm.

There is a linear relationship between the original volume of the tissue sample and the volume after 14 days of immersion (Fig. 3.10) with the gradients dependent upon the concentration of I2KI used. Figure 3.10 illustrates that there was no

correlation between the original tissue volume and the percentage remaining of the original volume after 14 days of immersion in each solution. Therefore smaller samples did not show more extensive shrinkage than larger samples. Some concentrations in figure 3.10b appear to show weak correlations between original muscle size and the degree of shrinkage experienced (see 2% I2KI) but none were

found to be statistically significant. For all microvolumeter data see Appendix 1.

Figure 3.8 Graph of tissue volume across a 28 day incubation period. Graphs show the percentage of the initial tissue volume after immersion in differing

concentrations of I2KI solution, or PBFS over a 28 day incubation period for: a)

110 Figure 3.9Graphs demonstrating the influence of initial sample volume on the extent of shrinkage. a) Plot of skeletal muscle volume after 14 days incubation, against initial tissue volume. Least square regression slopes and equations are shown. b) Comparison of initial skeletal muscle sample volume versus the

percentage of sample volume remaining after 14 days incubation. Both previously frozen and unfrozen material was used to maximise the data set. Spearman rank correlation coefficients were 0.48 ns for PBFS, 0.55 ns at 2%, 0.35 ns at 6%, 0.41ns at 10%, 0.19 at 20%.

111 Least-squared multiple regressions were calculated in order to capture the

interdependency of shrinkage on the three principal variables of, initial sample size, I2KI concentration and incubation time. The R2 values (coefficient of determination)

are given in Table 3.3, and demonstrate that in all three tissues the percentage reduction in volume is most closely related to I2KI concentration. Only in cardiac

samples was there a secondary relationship, with initial sample size, however the range of sample sizes had very little influence beyond 14 days as the shrinkage plateaus between 3 and 7 days (Fig. 3.8). The multiple regressions can be used to create a formula to predict the percentage volume of the original sample following staining:

Skeletal muscle E.vol. = 90.66 (o.vol) - 2.18 (conc.) - 0.66(t) + 75.39;

Cardiac muscle E.vol. = 463.77 (o.vol) - 2.06 (conc.) - 0.97 (t) + 49.32;

Cerebellar E.vol. = -102.51 (o.vol) - 1.70 (conc.) - 0.79 (t) + 92.28

(o.vol = original volume in ml, conc. = I2KI concentration in %, and t = incubation

time in days, E.vol.= end volume, as a percentage of original volume).

Table 3.3 Multiple regression statistics for shrinkage experiments. R2 values indicate the strength of the relationship between each variable and the overall percentage shrinkage of the tissue. Individual R2 values for each determinant are given in [ ]. N reflects the number of samples, each of which is recorded for each variable. Tissue type N Multiple R2 Original Volume (ml) [R2] I2KI Concentration (%)[R2] Incubation (days) [R2] Intercept Skeletal 128 0.77 90.66 [0.06] -2.18 [0.70] -0.66 [0.04] 75.39 Cardiac 16 0.91 463.77 [0.73] -2.06 [0.83] -0.97 [0.07] 49.32 Cerebellar 16 0.83 --102.51 [0.02] -1.70 [0.71] -0.79 [0.10] 92.28

112 Table 3.4 Linear regression statistics for shrinkage experiments. Spearman's rank correlation coefficient and p-value statistics indicating the relationship between the overall percentage shrinkage of the tissue and each of the variables

independent of the other variables investigated. R-rank gives the strength of

correlation between the variables (±1 reflects a strong correlation, 0 reflects a weak correlation). P-values indicate the significance of this correlation (p < 0.05 is

significant).

Regression

series R rank p-value RMA slope (a)

95%