Andrew J. Bulpitt

A primer on learning in Bayesian networks for computational biology

Bayesian networks (BNs) provide a neat and compact representation for expressing joint probability distributions (JPDs) and for inference. They are becoming increasingly important in the biological sciences for the tasks of inferring cellular networks [1], modelling protein signalling pathways [2], systems biology, data integration [3], classification [4], and genetic data analysis [5]. The representation and use of probability theory makes BNs suitable for combining domain knowledge and data, expressing causal relationships, avoiding overfitting a model to training data, and learning from incomplete datasets. The probabilistic formalism provides a natural treatment for the stochastic nature of biological systems and measurements. This primer aims to introduce BNs to the computational biologist, focusing on the concepts behind methods for learning the parameters and structure of models, at a time when they are becoming the machine learning method of choice. There are many applications in biology where we wish to classify data; for example, gene function prediction. To solve such problems, a set of rules are required that can be used for prediction, but often such knowledge is unavailable, or in practice there turn out to be many exceptions to the rules or so many rules that this approach produces poor results. Machine learning approaches often produce better results, where a large number of examples (the training set) is used to adapt the parameters of a model that can then be used for performing predictions or classifications on data. There are many different types of models that may be required and many different approaches to training the models, each with its pros and cons. An excellent overview of the topic can be found in [6] and [7]. Neural networks, for example, are often able to learn a model from training data, but it is often difficult to extract information about the model, which with other methods can provide valuable insights into the data or problem being solved. A common problem in machine learning is overfitting, where the learned model is too complex and generalises poorly to unseen data. Increasing the size of the training dataset may reduce this; however, this assumes more training data is readily available, which is often not the case. In addition, often it is important to determine the uncertainty in the learned model parameters or even in the choice of model. This primer focuses on the use of BNs, which offer a solution to these issues. The use of Bayesian probability theory provides mechanisms for describing uncertainty and for adapting the number of parameters to the size of the data. Using a graphical representation provides a simple way to visualise the structure of a model. Inspection of models can provide valuable insights into the properties of the data and allow new models to be produced.

Learning spatio-temporal patterns for predicting object behaviour

Abstract Rule-based systems employed to model complex object behaviours, do not necessarily provide a realistic portrayal of true behaviour. To capture the real characteristics in a specific environment, a better model may be learnt from observation. This paper presents a novel approach to learning long-term spatio-temporal patterns of objects in image sequences, using a neural network paradigm to predict future behaviour. The results demonstrate the application of our approach to the problem of predicting animal behaviour in response to a predator.

Inference in Bayesian networks

Bayesian networks are increasingly important for integrating biological data and for inferring cellular networks and pathways. What are Bayesian networks and how are they used for inference?

3D reconstruction of multiple stained histology images.

Context: Three dimensional (3D) tissue reconstructions from the histology images with different stains allows the spatial alignment of structural and functional elements highlighted by different stains for quantitative study of many physiological and pathological phenomena. This has significant potential to improve the understanding of the growth patterns and the spatial arrangement of diseased cells, and enhance the study of biomechanical behavior of the tissue structures towards better treatments (e.g. tissue-engineering applications). Methods: This paper evaluates three strategies for 3D reconstruction from sets of two dimensional (2D) histological sections with different stains, by combining methods of 2D multi-stain registration and 3D volumetric reconstruction from same stain sections. Setting and Design: The different strategies have been evaluated on two liver specimens (80 sections in total) stained with Hematoxylin and Eosin (H and E), Sirius Red, and Cytokeratin (CK) 7. Results and Conclusion: A strategy of using multi-stain registration to align images of a second stain to a volume reconstructed by same-stain registration results in the lowest overall error, although an interlaced image registration approach may be more robust to poor section quality.

An efficient 3D deformable model with a self-optimising mesh

Deformable models are a powerful and popular tool for image segmentation, but in 3D imaging applications the high computational cost of fitting such models can be a problem. A further drawback is the need to select the initial size and position of a model in such a way that it is close to the desired solution. This task may require particular expertise on the part of the operator, and, furthermore, may be difficult to accomplish in three dimensions without the use of sophisticated visualisation techniques. This article describes a 3D deformable model that uses an adaptive mesh to increase computational efficiency and accuracy. The model employs a distance transform in order to overcome some of the problems caused by inaccurate initialisation. The performance of the model is illustrated by its application to the task of segmentation of 3D MR images of the human head and hand. A quantitative analysis of the performance is also provided using a synthetic test image.

Spiral CT of abdominal aortic aneurysms: comparison of segmentation with an automatic 3D deformable model and interactive segmentation

A self-optimizing 3D deformable model has been developed which is able to segment branching anatomy. Its performance is compared with that of interactive segmentation in spiral CT of abdominal aortic aneurysms. SCT data from six individuals were selected retrospectively, representing a range of vascular geometry and tortuosity. As a reference, segmentation was performed twice by one observer using interactive 2D region growing. The self-optimizing 3D deformable model was applied twice, each with different initializations of the model in the aortic lumen. Dimensional and volume measurements were made, and boundary positions compared. The model was found to give qualitatively good representation, but was not able to follow vessels distal to the iliac bifurcation. The results agreed very well with the 2D interactive technique where structures ran orthogonal to the slice plane, with structures localized to 0.5 mm. The percentage difference in volume estimation between the model and the reference was 3% (the same as the agreement between the two reference segmentations). The mean closest distance between model and reference boundaries was 1.2 +/- 0.5 mm. Most discrepancies occurred at the bifurcations, and we conclude that the 3D deformable model requires further development for accurate representation of branching vascular structures in disease, but the accuracy of the model segmentation is sufficient for visualization or training.

Predicting the effect of missense mutations on protein function: analysis with Bayesian networks

BackgroundA number of methods that use both protein structural and evolutionary information are available to predict the functional consequences of missense mutations. However, many of these methods break down if either one of the two types of data are missing. Furthermore, there is a lack of rigorous assessment of how important the different factors are to prediction.ResultsHere we use Bayesian networks to predict whether or not a missense mutation will affect the function of the protein. Bayesian networks provide a concise representation for inferring models from data, and are known to generalise well to new data. More importantly, they can handle the noisy, incomplete and uncertain nature of biological data. Our Bayesian network achieved comparable performance with previous machine learning methods. The predictive performance of learned model structures was no better than a naïve Bayes classifier. However, analysis of the posterior distribution of model structures allows biologically meaningful interpretation of relationships between the input variables.ConclusionThe ability of the Bayesian network to make predictions when only structural or evolutionary data was observed allowed us to conclude that structural information is a significantly better predictor of the functional consequences of a missense mutation than evolutionary information, for the dataset used. Analysis of the posterior distribution of model structures revealed that the top three strongest connections with the class node all involved structural nodes. With this in mind, we derived a simplified Bayesian network that used just these three structural descriptors, with comparable performance to that of an all node network.

AI-based algorithms for protein surface comparisons

Many current methods for protein analysis depend on the detection of similarity in either the primary sequence, or the overall tertiary structure (the Calpha atoms of the protein backbone). These common sequences or structures may imply similar functional characteristics or active properties. Active sites and ligand binding sites usually occur on or near the surface of the protein; so similarly shaped surface regions could imply similar functions. We investigate various methods for describing the shape properties of protein surfaces and for comparing them. Our current work uses algorithms from computer vision to describe the protein surfaces, and methods from graph theory to compare the surface regions. Early results indicate that we can successfully match a family of related ligand binding sites, and find their similarly shaped surface regions. This method of surface analysis could be extended to help identify unknown surface regions for possible ligand binding or active sites.

Combining 3D Deformable Models and Level Set Methods for the Segmentation of Abdominal Aortic Aneurysms

In this paper we present a system that combines the benefits of 3D deformable models and level set methods for medical volume segmentation. Our 3D deformable model is a very computationally efficient method for segmenting medical volumes, however it is not currently able to segment features, such as renal arteries, that are small relative to the imaging slice thickness used. Level Set methods are an alternative approach to deformable models that re-pose the volume segmentation problem as the calculation of the steady state of an initial value Partial Differential Equation (PDE) system on a regular rectilinear or cubic mesh. The segmentation obtained is parameterised by the zero value level set of this mesh (analogous to an iso-surface). These methods are very computationally expensive, but have the advantage of being able to segment relatively small features such as renal arteries. The problem domain explored in this paper is the segmentation of arterial structures. The results of these segmentations are to be used in the assessment of patient suitability for minimally invasive (keyhole) surgical procedures in patients with abnormal aortic aneurysms. An abdominal aortic aneurysm (AAA) is a dilation of the abdominal aorta. AAAs usually increase in size with time, and if left untreated eventually rupture causing catastrophic haemorrhage. An AAA may be treated by conventional surgical methods, but increasingly minimally invasive techniques, where a stent graft is placed in the lumen, are being used. Patient suitability is assessed using CT data and a calibrated projection angiogram - only about 10% of patients are suitable for the keyhole repair. Once a candidate has been assessed as suitable, measurements are made from the same images to determine the key dimensions of the required stent. Our overall aim is to automate both of these stages of image analysis, ensuring that the full 3D nature of the CT is used. In this paper we describe a segmentation aproach that combines the benefits of a 3D deformable model

Histopathology in 3D: From three-dimensional reconstruction to multi-stain and multi-modal analysis

Light microscopy applied to the domain of histopathology has traditionally been a two-dimensional imaging modality. Several authors, including the authors of this work, have extended the use of digital microscopy to three dimensions by stacking digital images of serial sections using image-based registration. In this paper, we give an overview of our approach, and of extensions to the approach to register multi-modal data sets such as sets of interleaved histopathology sections with different stains, and sets of histopathology images to radiology volumes with very different appearance. Our approach involves transforming dissimilar images into a multi-channel representation derived from co-occurrence statistics between roughly aligned images.