METODOS DE ANALISIS.

Stereology is a collection of methods designed for quantifying the geometrical features of material objects and biological structures. Design-based methods are assumption-free and rigorously mathematically derived. The strength of design-based stereological methods is that, under a well-defined sampling design, they are unbiased regardless of the geometry of the object under study.

An estimator of GM volume is said to be unbiased when the average of all the possible estimates of GM volume that can be obtained is equal to the true value of GM volume. Unbiasedness itself however, cannot be proven from the data alone as it is an inherent feature of the methodological design (Dorph-Petersen and Lewis, 2010). The precision of an estimator measures the variability (variance) of the estimates, or how close/far the estimates are to one another and can be observed directly from the scatter of the final data. Increasing the sample size cannot eliminate or decrease an existing bias but it can increase the precision of the assessment, thus it could make the group mean more precisely inaccurate.

Design-based stereological methods have been widely applied to measure regional brain volumes on MR images in both healthy (García-Fiñana et al., 2003; Howard et al., 2003; Keller et al., 2007, 2009b; Mackay et al., 1998; Powell et al., 2010; Roberts et al., 2000; Sheline et al., 1996) and clinical populations (Dorph-Peterson and Lewis, 2010; García-Fiñana et al., 2006, 2009; Keller et al., 2002; MacKay et al., 2000; Salmenpera et al., 2005). Point-counting in combination with the Cavalieri method has been shown to have excellent inter- and intra-rater reliability (Cowell et al., 2007; Doherty et al., 2000; Howard et al., 2003; Mackay et al., 1998, 2000; Keller et al., 2002, 2007). Keller et al (2007) for instance, demonstrated reliability in the repeatability of measurements of the PO and PTR using stereological methods.

- 77 - The Cavalieri Method

The Cavalieri method is one sampling design-based stereological technique for obtaining an unbiased estimator of a reference volume. The Cavalieri method in conjunction with the well-established point counting technique is particularly useful in instances where the volume of a structure cannot be easily confined to a well-defined regular region such as that of cortical regions (Howard and Reed, 2005). The Cavalieri method can be used to obtain an unbiased estimator of the volume of a structure of arbitrary shape and size from high resolution 3D MR images. The Cavalieri method involves sectioning the structure of interest end-to-end with a series of parallel planes (or sections) with a uniform random position and a fixed distance apart, T (Figure 4.2).

Figure 4.2. The basis of the Cavalieri sections method of volume estimation in combination with point counting. A structure of interest is sectioned into a series of slices or sections. Each section is the same thickness or distance apart. Each section is overlain with a random grid of test points. Points falling within the structure of interest are counted.

When point counting is applied in combination with the Cavalieri method, each MR section is superimposed with a regular array of test points with uniform random position and points falling within the anatomical boundary of the subfield of interest are counted. The section area is estimated by counting the number of test points falling within the boundary of the ROI (see Equation (4.5)). The volume of the structure is estimated as the sum of the areas of the sections multiplied by the sampling distance (Gundersen and Jensen, 1987). The unbiased volume estimator (𝑉�) can be expressed as:

- 78 -

(4.4)

𝑉� = 𝑇 · ap· (𝑃1 + 𝑃2 + 𝑃3 + . . . +𝑃𝑛)

where 𝑇 is the distance between sections, 𝑃₁ + 𝑃₂ + 𝑃3 + . . . +𝑃_𝑛 represents point counts within image sections 1 to n, respectively, and ap represents the unit area per test point. The unbiased volume estimator as expressed in Equation (4.4) is based on two sampling stages, namely Cavalieri sampling and point counting. In order for the Cavalieri estimator to be unbiased, there should be no preferred starting position for slicing and sectioning should begin at a random position. The derivation of Equation (4.4) is based on the fact that an unbiased estimator of each section area, Âi can be

expressed as:

(4.5)

𝐴̂𝑖 = ap· 𝑃𝑖

where Pi is the number of points hitting the object on the ith section and a_pRis the unit area per test point. A benefit of the Cavalieri method in combination with point counting is that it is an efficient method for estimating the volume of a defined ROI, in comparison with traditional planimetry approaches. The efficiency is dependent upon the choice of sampling parameters i.e. the number of Cavalieri sections and the density of the point grid.

Prediction of Coefficient of Error

The technique used to calculate the volume of ROIs in this thesis, provides a mathematically unbiased volume estimator whose precision can be computed by applying an error-prediction formula (see e.g. Cruz-Orive, 1989; García-Fiñana and Cruz-Orive, 2004; Gundersen and Jensen, 1987; Kiêu et al., 1999) called the coefficient of error (CE). The CE is defined as the square root of its variance divided by its mean. The conventional formula used to estimate the variance of a volume estimator �𝑉�� when the observations (i.e., section area estimates) are independent is given in Equation (4.6).

(4.6)

- 79 -

where 𝑆𝐷�𝑉�� is the standard deviation of the volume estimator from one observation, and n is the total number of observations. This equation cannot be used when the observations are equally spaced since they cannot be regarded as independent. It is known that the variance of the Cavalieri volume estimator depends on the geometrical features of the structure under analysis (e.g., Cruz-Orive, 1999; García-Fiñana and Cruz-Orive, 2000; Gundersen et al., 1999; Kiêu et al., 1999; Matheron, 1965, 1971). Several expressions have been derived to take into account the connection of the precision of the Cavalieri estimator with the geometry of the structure. An estimator of the variance has been proposed in García-Fiñana and Cruz-Orive (2004, see also application in 2003) and this is the approach used in this thesis to calculate the CE.

The section areas of MRI slices are not independent and therefore the variance of the volume estimator in Equation (4.5) is affected by 2 different types of stereological error. The first is due to the variability among sections (Cavalieri sampling) and the second is due to the variability within sections (point counting). In terms of coefficient of error this can be expressed as:

(4.7)

𝐶𝐸2_{�𝑉��= CE}

𝑠𝑒𝑐2 �𝑉�� + CE𝑃𝐶2 �𝑉��

where CE𝑠𝑒𝑐2 �𝑉�� represents the contribution of the variability due to sectioning and CE𝑃𝐶2 �𝑉��� represents the variability due to point counting within sections. Equations for calculating the contribution of the variability due to sectioning and point counting are given elsewhere (see García-Fiñana and Cruz-Orive (2004) and García-Fiñana et al (2003).

In this thesis, EasyMeasure software (Roberts et al., 2000) was used to estimate regional brain volumes. A coefficient of error for each regional brain structure was automatically calculated within the software using the above formula. Stereological parameters were entered into the software manually.

- 80 - 4.4.2 Repeatability and Reproducibility

It is necessary to establish the repeatability and reproducibility of volumetric estimation techniques, prior to their application to a large-scale sample. The repeatability is the capacity of a same rater to obtain “similar” repeated measures of a given object (intra- rater) using an identical method, whereas reproducibility is the capacity of different raters (inter-rater) to obtain “similar” measures of a given object using an identical method. In this thesis, blind inter-rater and intra-rater studies were undertaken on PO, PTR and PFC subfields using the Cavalieri and point counting methods. Studies of inter-rater reliability were undertaken based on the analysis of a number of randomly selected T1-weighted MR images following a period of training for each region by a second observer. Specifically the following intra- and inter-rater studies were performed.

Intra- and inter-rater studies

Inter-rater study: The volume of PFC, PO and PTR subfields of 10 brains were

measured independently by two raters. Specifically, raters JP and SL measured PFC subfields and raters JP and CC measured PO and PTR subfields. Measurements were performed using the same demarcation, same Cavalieri sections and random grid positions. Raters SL and CC measured each ROI subfield once. Rater JP measured each ROI twice and the average of these measurements was taken when performing the inter- rater study. This study allows the estimation of the contribution to the variance of the volume estimator that is due to point counting and differences between observers.

Intra-rater study 1: The volume of PFC, PO and PTR subfields of 10 brains were measured by the same rater (JP) twice with several weeks between the first and second measurement sessions using different demarcations, different Cavalieri sections and random grid positions. This study was performed to investigate the variance of the volume estimator that is due to demarcation, Cavalieri sectioning, point counting and differences within observer.

Intra-rater study 2: Volumes of PFC, PO and PTR subfields were measured 10 times on one brain on 10 consecutive days by the same rater (JP). Measurements were performed using the same demarcation, same Cavalieri sections and same grid positions to investigate the variability of measurements within observer.

- 81 -

Intra-rater study 3: The volume of PFC, PO and PTR subfields were measured on 2 brains and each brain was measured 10 times by the same rater (JP). Measurements were performed using the same demarcations, Cavalieri sections and random grid positions to investigate the variability due to differences within observer and point counting.

Statistical Analysis of inter- and intra-rater studies

Agreement between two measurements of a ROI can be quantified using the differences between measurements obtained on two different occasions on the same ROI by the same rater and different raters. Some lack of agreement between different measurements is inevitable (Bland and Altman, 1999). The 95% limits of agreement, estimated by the mean difference ± 1.96 standard deviation of the differences, provide an interval within which 95% of differences between measurements by the two raters (or based on two different occasions by the same rater) are expected to lie. The mean difference between raters (or occasions for the intra-rater studies) and the standard deviation of the differences between measurements is calculated. The 95% limits of agreement were estimated for the sum of the four PFC subfields within the left hemisphere (i.e. DM, DL, OM, and OL subfields) and then the right hemisphere for each rater. Similarly the 95% limits of agreement were estimated for the sum of the four PO and PTR regions (Broca’s area) in the left hemisphere (i.e. grey/white matter PO and PTR) and then the right hemisphere.

Results of inter- and intra-rater studies

Results for the inter- and intra-rater studies are shown in Table 4.4. Table 4.4 shows that for the inter-rater study the mean value of the right PFC is slightly larger than the mean value of the left PFC (i.e. 94.8 vs. 91.17cm3 respectively). In intra-rater study 1 the right PFC is also larger than the left PFC (i.e. 90.85 vs. 89.45cm3 respectively). This could be explained by the “Yakovlevian torque” which is a clockwise twist in brain morphology resulting in larger right hemisphere frontal lobe than left hemisphere frontal lobe (Kertesz et al., 1986; LeMay and Kido, 1978). Mean values for the left and right Broca’s area for the inter-rater study are 16.14 and 13.33cm3, and for intra-rater study are 16.43 and 13.62cm3 respectively which are very similar.

- 82 -

Inter-rater study: The 95% limits of agreement included zero indicating that one rater did not systematically overestimate or underestimate the volume when compared to the other rater. The CE is less than 6% in all cases, which shows good inter-rater reliability.

Intra-rater study 1: Table 4.4 shows that the mean difference and the standard deviation of the difference in measurements within observer was small (i.e. less than 1cm3) for all regions. Also, the 95% limits of agreement included zero indicating that rater JP did not systematically overestimate or underestimate volume for ROIs on different occasions. The CE is less than 8% for all the subfields. The CE is expected to be higher for this intra-rater study than for the other two intra-rater studies as this takes into account the error that appears in the measurement due to Cavalieri sectioning, point counting and within observer variability.

Intra-rater study 2: Results indicate an average CEow (within observer) of less than 3% for each ROI. A CE of less than 5% is considered necessary. This study indicates that only a small percentage of the error comes from variability within observer. This is particularly important as rater JP performed all volume estimates in this thesis.

Intra-rater study 3: The CE for all subregions in this intra-rater study is less than 4% and this value takes into account both the contribution to point counting and within observer variability.

- 83 -

Table 4.4. Results for the 95% limits of agreement for volume estimates for inter- and intra-rater studies. The lower and upper 95% limits of agreement define the range within which 95% differences between measurements by the two raters (or based on two occasions by the same rater) lie. Values are given in cm3. LH=left hemisphere, RH=right hemisphere. Mean average Mean difference Standard deviation of the difference Limits of agreement CE (%) Lower 95% Upper 95% Inter-rater study: LH PFC 91.17 3.42 2.13 -0.76 7.60 2.7% RH PFC 94.80 7.88 9.91 -11.53 27.30 5.9% LH Broca 16.14 -0.61 0.64 -1.88 0.65 2.8% RH Broca 13.33 -0.05 2.00 -3.96 3.87 4.0% Intra-rater study 1: LH PFC 89.45 -0.73 1.46 -3.60 2.13 1.1% RH PFC 90.85 -0.59 1.87 -4.27 3.08 1.3% LH Broca 16.43 0.51 0.90 -1.26 2.27 2.4% RH Broca 13.62 0.69 1.71 -2.66 4.05 7.7% Intra-rater study 2: LH PFC RH PFC LH Broca RH Broca CEow(%) 2.8% 1.7% 1.7% 1.7% Intra-rater study 3: LH PFC RH PFC LH Broca RH Broca CEPC(%) 1.2% 0.9% 1.8% 3.1%

- 84 - Biological Variability

Biological variability of a geometrical parameter of a biological structure, such as brain volume, refers to the true variability in volume across individuals’ studied, assuming volume has been obtained without measurement error. Inter-individual variability includes the contributions from both the biological variation among a given sample, and the variability due to sampling error on the obtained estimates (i.e. volume). This sampling error is contained in the CE. The coefficient of variation (CV) represents the ratio of the standard deviation to the mean and can be represented as a percentage when multiplied by 100 (CV = SD/mean x 100). In this case the CV represents the degree of variation in volume for each structure among individuals. The contribution of biological variability to the overall variance can be determined by calculating the predicted CE from the obtained estimates (which comes from the variance due to Cavalieri sectioning, demarcation, point counting and differences within and between observers) and subtracting this from the total CV. This can be expressed using Equation (4.8).

(4.8)

𝐶𝑉𝐵2 = 𝐶𝑉𝑇2− 𝐶𝐸2

In this equation 𝐶𝑉_𝐵2 represents the coefficient of variation attributable to biological variation, 𝐶𝐸2 is the mean coefficient of error calculated as the mean of the coefficient of errors of the volume estimator for the different levels of sampling involved, and

𝐶𝑉𝑇2represents the total coefficient of variation based on the sample. The results of the average CE for each region in each inter- and intra-rater study performed on sample data are given in Table 4.4.

Equation (4.8) does not however, take into account biasedness in the volume estimates. Bias is systematic error in the measurement and there is no way of being able to measure this from the data. In this thesis all volume estimates were obtained by rater JP. Assuming there is any bias this is expected to be consistent across all measurements obtained and therefore will not affect the findings reported which show significant differences between left- and right-handers (e.g. Broca volume the results of which are shown in Chapter 5).

- 85 - 4.4.3 Anatomical Regions of interest Image pre-processing

Prior to demarcation the newly acquired MR datasets were first imported into BrainVoyager software (www.Brainvoyager.com, Brain Innovation, Maastricht, The Netherlands) for pre-processing. Pre-processing required re-orienting images to a standardised sagittal plane, orthogonal to the bi-commissural plane, following the approach used by others (Cowell et al., 2007; Howard et al., 2003; Keller et al., 2007; Powell et al., 2010).

Re-alignment of the structural images was carried out using the 3D volumes tool in the Analysis menu of BrainVoyager software, which allows the operator to view images in sagittal, coronal and axial planes (see Figure 4.3). On a sagittal section closest to midline, a line was drawn (AC-PC line) connecting the anterior commissure (AC) and posterior commissure (PC) so that both structures could be viewed in the same axial slice. This can be seen in Figure 4.3D.

The bi-commissural plane (containing the AC-PC line) was taken on the axial slice to correct for anterior-to-posterior tilt (Figure 4.3A and D). Side-to-side tilt (i.e. left-to- right tilt) was corrected for by aligning the superior-most aspect of the orbital cavities at their maximum cross-sectional area in the coronal plane (Figure 4.3B and E). The orbital cavities are extrabrain landmarks, however, since the frontal lobe is larger in the right hemisphere, a system was chosen that would be reproducible across raters and would not add systematic error (bias).

To correct for deviations from sagittal midline, a plane taken through the longitudinal fissure of the corrected transaxial plane resulted in the standardised sagittal plane (Figure 4.3C and 4.3F). This corrects for a twist in head positioning. The standardised sagittal image was then rotated so that the bi-commissural axis (i.e. the superior view of the AC-PC corrected image) was positioned at zero degrees. This correction in positioning ensured that vertical and horizontal lines used in the parcellation process would transect similar anatomical landmarks across all participants. These pre- processed, AC-PC corrected images were then used for PFC subfield and Broca area subfield demarcations.

- 86 -

Figure 4.3. Sagittal, coronal and axial planes from a T1-weighted MR image prior to standardised sagittal orientation (A-C). A plane is taken through the AC-PC line to correct for anterior-to-posterior tilt (D). A plane was taken at the superior most point of the orbital cavities where the cavities were at their maximum to correct for side-to-side tilt (E). A sagittal plane was taken along the longitudinal fissure from a more superior view (F) to that shown in C to correct for the twist in head positioning.

Prefrontal cortex measurements

The protocol employed to estimate volumes of anatomically defined subfields of the PFC is based on the previously established methodology developed by Howard et al (2003). The protocol divides the right and left PFC into dorsolateral (DL), dorsomedial (DM), orbitolateral (OL) and orbitomedial (OM) regions, yielding 8 subfields which can be seen in Figure 4.4. Volume estimates for the 8 PFC subfields are given in Table 4.6, separated by sex and handedness groups.

Parcellation of the 3D dataset was made according to macroanatomical landmarks. These landmarks were either fixed boundaries (such as the division between medial and

- 87 -

lateral regions and the division between dorsal and orbital regions represented by the blue and green lines in Figure 4.4, respectively) or were visualised by the rater from one