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An image processing and programming routine was developed using MATLAB (version 7.0; The MathWorks Inc., MA, USA) with the Image Processing Toolbox™ to reconstruct 3-D representations of the swimbladders from the MR image slices. The high image contrast between the gas-filled swimbladder and surrounding tissue enabled accurate assessment of the swimbladder boundaries. The MATLAB routine (see Figure 4.5) allowed the boundaries of the swimbladder to be defined on every slice of each scanning series by applying a threshold value to accept all the grey scale values corresponding to the darker pixels characteristic of the gas-filled bladder. Since the threshold value was set based on a subjective evaluation of the grey scale contrast between pixels associated with the swimbladder and surrounding tissue, the routine enabled the threshold to be altered from slice to slice if necessary. In that way, an acceptable threshold was defined that resulted in the swimbladder pixels forming a continuous shape. All pixels corresponding to grey scale values equal to or lower than the selected threshold appeared on a ‘selection window’ where they were manually selected (Figure 4.6). The swimbladder was then built up from its individual cross- sections on all individual image slices of the combined sequence. Since the pixel resolution and slice thickness was known, the swimbladder volume was calculated by adding all single voxels that made up the swimbladder. Similarly, the dorsal cross- sectional surface area of the swimbladder was defined as the area covered by pixels of all dorsal aspect swimbladder slices superimposed on each other. The swimbladder trace quality was improved by applying the ‘smooth3’ 3-D object smoothing function

with a Gaussian convolution kernel in the MATLAB routine. A 3-D object corresponding to the smoothed swimbladder was then created using the ‘patch’ function, and a mesh defining the surface was reconstructed based on the x, y, and z coordinates of the object boundaries.

Axial MRI

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Axial MRI

slice X

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(i = 1:n axial

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Figure 4.5 Flowchart illustrating the routine developed in MATLAB to extract swimbladder pixels from individual axial MRI slices and to eventually rebuild the swimbladder shape in 3-D.

Figure 4.6 Screen shots from the routine developed in MATLAB to extract the swimbladder shape in 3-D from individual axial MRI slices. (a, left panel): Example of an axial MRI slice of herring #2 at a pressure of 1 bar. At this stage, no pixels have yet been allocated to the swimbladder, producing only black pixels in the ‘selection window’ (a, right panel). (b): Histogram of pixel grey scale values (0 to 65,535) from the MRI slice with the set threshold indicated by the red triangle and dotted line. (c): threshold set too high. Pixels corresponding to values below the set threshold are superimposed in red colour on the MRI slice (c, left panel) and given as white pixels in the ‘selection window’ (c, right panel). (d): threshold set too low. (e): acceptable threshold value resulting in the swimbladder pixels forming a homogenous object in the ‘selection window’ (e, right panel) that can be manually selected (f).

4.2.4. Target strength modelling

The theoretical acoustic backscattering of the herring was modelled using the 3-D swimbladder shapes by applying the Kirchhoff ray-mode approximation (KRM) described previously as ‘model III’ in Chapter 2 (Clay and Horne 1994; see Section 2.2.5.6. for details of the model). The model essentially approximated the scattering objects as a series of 1 mm long elliptical cylinders. The backscattering cross-section of each object was then expressed as a function of size, frequency and fish orientation relative to the transducer by summing backscattering cross-sections of all individual cylinder components. The fish body was represented as a set of fluid-filled cylinders surrounding the gas-filled cylinder sections of the swimbladder. Total fish backscatter was eventually calculated as the coherent sum of backscattering-cross sections of both swimbladder and fish body according to Equation 2.4. Since the MRI scans focused on the swimbladders, true shapes of the fish body could not be traced and reconstructed from the scanning slices. Instead, fish body dimensions were traced from the silhouettes of lateral and dorsal aspect digital images of herring #43 and linearly scaled as a function of length for use with the other individual herring. Individual cylinder components of the fish body and swimbladder were generated based on the height and width of the respective scattering bodies along the axis directions from the snout to the tip of the caudal peduncle (Horne et al. 2000). The swimbladder was assumed to be gas-filled with a density of 1.3 kg m-3 (Brawn 1969), while the fish body component was assumed to be fluid-filled with a slightly higher density (1049 kg m-3, Section 3.2.1.1.; Fässler et al. 2008) than the surrounding sea water (1027 kg m-3, Section 2.2.5.6.). Speed of sound in sea water, fish body and swimbladder were 1500, 1570, and 340 m s-1, respectively.

Mean TS values were predicted for each individual herring specimen as a function of fish length and frequency by averaging 100,000 samples of modelled backscatter values applying tilt angle distributions with mean 0º (i.e. broadside dorsal aspect) and standard deviations used commonly for herring of 5º (Gorska and Ona 2003a; Fässler et al. 2008) and 10º (Ona et al.2001; Fässler et al.2007). All estimates were first averaged in the linear domain before being transformed logarithmically.

Standard length-dependent TS relationships were derived by fitting a linear regression to the modelled mean TS at 38 kHz to determine the value of the intercept. In order to compare results between the different herring used in this study to an extensive in situ TS data set collected by Ona (2003) for 32 cm herring, TS values for all specimens considered here were also scaled linearly to a common fish length of 32 cm. Consequently, length- and depth-dependent TS relationships were determined at 38 kHz from the model values of the size standardised herring specimens.

4.3. Results