1 Introduction

Two key developments in medical imaging over the past thirty years have considerably increased the opportunity for measuring the size of structures (e.g. organs, compartments and lesions) in the living human body. Firstly, whereas previously medical images were obtained in the form of projections (i.e. conventional radiographs), images provided by ultrasound (Wild and Reid, 1952), X-ray Computed Tomography (CT) (Hounsfield, 1973) and MRI (Lauterbur, 1973)) are tomograms. They refer to 2D slices (i.e. ‘cuts’) through the body. Secondly, MR, CT, and now frequently also ultrasound, images are inherently digital and thus immediately available for processing and analysis by computer.

This thesis demonstrates that acquisition and analysis of medical images in accordance with the rules of modern design stereology (Cruz-Orive, 1997) enables precise unbiased estimates of geometric quantities such as volume and surface area to be obtained for only a moderate workload. This is achieved through the development of EASY MEASURE - an interactive software package that enables the convenient application of stereological methods for estimating parameters such as surface area, volume and length. A screenshot of EASY MEASURE, running on a standard PC, is shown in Figure 1.1. Many of the medical images used throughout this thesis were acquired using the MR scanner at the Magnetic Resonance and Image Analysis Research Centre (MARIARC), University of Liverpool, which is shown in Figure 1.2.

Figure 1.1: A screenshot of EASY MEASURE.

Unfortunately, many measurement techniques in use in both clinical practice and research studies are rooted in outdated and potentially biased methods developed to analyse projection images. By using stereological methods volume (Cruz-Orive, 1985; Gundersen and Jensen, 1987; Roberts et al, 1994), surface area (Gundersen, 1984; Baddeley et al, 1986; Henery and Mayhew, 1989; Puddephat et al, 1997) and curve length (Cruz-Orive and Howard, 1991; Roberts et al, 1991) are estimated free from any systematic error (i.e. bias) relating to the sampling strategy and without the need for any assumptions regarding the shape of the structure being investigated. If the measurement process is repeated the average of all the trials will be the true value of the quantity of interest. Although stereological methods are generally applied manually, they are extremely efficient. Time is not wasted gathering unnecessarily large amounts of data. Beginning from a random starting position, measurements are made at constant linear or angular intervals, and new statistical theory has been developed for predicting the precision of quantities obtained by sampling in this way (Matheron, 1965; Matheron, 1971; Gundersen and Jensen, 1987; Cruz-Orive, 1989; Cruz-Orive, 1993; Roberts et al, 1993, 1994; Souchet, 1995; Kieu, 1997; Kieu et al, 1997; Garcia Finana and Cruz-Orive, 1998; Cruz-Orive, 1999; Gundersen et al, 1999).

Figure 1.2: A patient entering the 1.5 Tesla SIGNA whole body MR imaging system (General Electric, Milwaukee) at MARIARC.

A variety of approaches have been used for measuring brain structures and lesions on MR images obtained in vivo (Duncan, 1996). For example, Bondareff et al (1990) measured the total volume of white matter plaques in the brain of patients with Alzheimer’s disease by weighing transects of them cut from hardcopy film with scissors. More commonly, computer-based planimetry and semi-automatic boundary tracing techniques have been employed on MR images to measure, for example, the volume of the hippocampus and amygdala in the pre-surgical assessment of patients with temporal lobe epilespy (Jack et al, 1992) and together with the volume of the frontal and temporal lobes to investigate cerebral abnormalities in schizophrenia (Shenton et al, 1992) and cerebral atrophy in Alzheimer’s disease (Killiany et al, 1993; Laakso et al, 1995). Increasingly, however, stereological methods are being used for analysis of MR images of the brain. For example, the Cavalieri method has been used in combination with point counting to estimate the volume of the sub-cortical nuclei (e.g. putamen and caudate nucleus) (McDonald et al, 1991; Lisanby et al, 1993; Husain et al, 1991; MacFall et al, 1994), pituitary (Axelson, 1992), hippocampus (Sheline et al, 1996a) and amygdala (Sheline, 1998). The Cavalieri method has also been applied in conjunction with Computed Tomography (CT) (Pakkenberg et al, 1989) and MRI (Keshaven et al, 1995; Vogels et al, 1995) to estimate the volume of the lateral cerebral ventricles. Planimetric techniques are tedious to employ for repeatedly outlining boundaries of the gyri and sulci on MR images. However, the Cavalieri method has been used in combination with point counting to estimate the volume of the cerebellum (Escalona et al, 1991), frontal lobes (Sheline et al, 1996b) and cerebral hemispheres (Subsol et al, 1997).

Measurements have been reported of the fractal dimension (Bullmore et al, 1994) and radius of gyrification (Bullmore et al, 1995) of the boundary between cerebral cortex and underlying white matter on coronal MR images, leading to the suggestion that this interface is significantly more ‘rounded’ in schizophreniics, and more ‘jagged’ in patients with manic depression, compared to controls. In contrast, stereology provides several methods for estimating the surface area of this boundary but requires isotropic sampling. In the case of the brain it is interesting to investigate whether the surface areas of the cerebral hemispheres, and individual lobes and gyri, have a different functional significance than the volumes of the same structures and regions. The cerebral cortex is highly convoluted, so that approximately two thirds of its surface is hidden within gyri, and measurement of its total surface area is not trivial. In particular, the stereological methods require isotropic sampling of the brain in 3-dimensions.

The majority of the studies which have used MRI to measure the surface area of the cerebral hemispheres have been concerned with the investigation of language development and function. Following the early clinical observation of patients with aphasia by Broca (1861), there is now considerable evidence to suggest that in almost all right-handed subjects and the majority of left-handers the left cerebral hemisphere is preferentially involved in language function. Galaburda et al (1978) suggested that asymmetry favouring an increased surface area of the planum temporale in the left temporal lobe is a structural correlate of left hemisphere dominance for language, and there are several reports of the measurement of planum temporale surface area using MRI (see, for example, Kulynych et al, 1994; DeLisi et al, 1994; Barta et al, 1995). Measurements of the planum temporale have also been obtained to investigate whether the impairment in language function in dyslexia correlates with departures from so called ‘normal planum temporale asymmetry’ (Kusch et al, 1963; Rumsey et al, 1997), and in schizophrenia (Kulynych et al, 1994; DeLisi et al, 1994) which is hypothesised by Crow (1997) to represent a failure of left cerebral hemisphere dominance for language.

The surface area of the whole cerebral hemispheres on MR images has been measured by S. M. Sisodiya and colleagues who report that in normal subjects significant relationships exist between the surface area of the boundary between cortical grey matter and sub-cortical matter (i.e. white matter plus central grey matter), the volume of hemispheric grey matter, the volume of hemispheric sub-cortical matter and the cross-sectional area of the corpus callosum (Sisodiya et al, 1996), and that these are disrupted in patients with epilepsy related to cerebral dysgenesis (Sisodiya and Free, 1997). Volumes and surface areas were estimated using image analysis techniques. Segmentations of cortical grey matter and sub-cortical matter, produced through a process of semiautomatic region of interest growing, allowed volumes to be estimated while surface areas were estimated using contour tracing techniques. Sisodiya et al suggest that the relationship of brain surface area with the cross-sectional area of the corpus callosum observed in healthy subjects indicates that a fixed proportion of cortical neurons extend inter-hemispheric axons, while its relationship with cortical grey matter volume suggests that growth of the neocortex is primarily tangential, with repetition of a basic structural unit (Sisodiya et al, 1996). Furthermore, following studies of cortical surface area in monozygotic twins and unrelated pairs of subjects, Tramo et al (1995) suggest that the total area and folding of the cortical surface is under genetic control and that this may be greater for the language-dominant left cerebral cortex. There is, however, no evidence of abnormal cerebral surface area in patients with schizophrenia to enable distinction from their co-twin or from controls, which it is claimed indicates that schizophrenia may be dependent on environmental factors and not only on genetic predisposition (Noga et al, 1996).

In the above mentioned studies a wide range of strategies have been employed for obtaining the reported surface area measurements. However, in common with studies using CT (Lancaster et al, 1992), confocal scanning (Guilak, 1994) and physical sectioning (Fahle and Palm, 1983; see also, Weil, 1928) based on geometric modelling, none have used the isotropic sampling required for unbiased estimation of surface area. Moran (1944) measured the surface area of a convex body using line probes oriented in the directions of the vertices of regular solids (Moran, 1944), and this was a precursor to the development of the proper stereological methods (Elias and Schwartz, 1966; Gundersen, 1984; Baddeley et al, 1986; Sandau, 1987; Michel and Cruz-Orive, 1988; Mattfeldt et al, 1990; Cruz-Orive and Howard, 1995; Cruz-Orive,1997), which have been used by, for example, Haug (1987), Henery and Mayhew (1989), Mayhew (1989), Howard and Sandau (1992), Pache et al (1993) and Kubinova and Janacek (1998). It is these proper stereological methods that underpin EASY MEASURE.

One of the first examples of stereology implemented on a computer is the system described by Moss et al (1989), for measuring volume-weighted mean particle volume using the point-sampled intercept method (Gundersen and Jensen, 1983, 1985). A ‘BBC Master’ microcomputer with 32K RAM was used and the software was written in BASIC and 6502 assembler. More recently, Jolleys (1995) has produced a software package called Digital Stereology, which is capable of implementing a number of stereological estimators. In this thesis, the construction and application of EASY MEASURE is described.

Chapter 2 contains a detailed list of objectives that were agreed upon at the outset of this project, as well as a list of materials that were used to accomplish those objectives. The medical images found in this thesis were acquired by MRI and so an introduction to the basic principles of MRI is given in Chapter 3. This is followed by Chapter 4, which describes from first principles single object stereology (Cruz-Orive, 1997). New results concerning the precision of an unbiased estimator for determining 2D object boundary length are presented at the end of Chapter 4. Chapter 5 describes algorithms that allow single object stereology to be implemented on a computer. This is followed, in Chapter 6, by a guided tour of the EASY MEASURE user interface.

Chapters 7 and 8 show the application of EASY MEASURE to various problems. In Chapter 7, validations of EASY MEASURE's probe plotting routines and the transition counting rule (for automatically counting intersections between test probe and object boundary on binary images) are provided through the exhaustive investigation of several well-defined, two-dimensional mathematical objects. In Chapter 8, EASY MEASURE is applied to the problems of estimating vertebral column length (Section 8.1), pear surface area and volume (Section 8.2) and mean thickness of the cerebral cortex (Section 8.3). Finally, Chapter 9 ends with discussions and conclusions.