Anatomical connectivity changes in bipolar disorder and schizophrenia investigated using whole-brain tract-based spatial statistics and machine learning approaches

Abstract

Schizophrenia and bipolar disorder have similar clinical features. Their differential diagnosis is crucial because each has different prognostic and therapeutic characteristics. Earlier studies have used numerous methods, including magnetic resonance investigation, in an effort to differentiate these two disorders. Research has consistently shown that there is reduced white matter density in the fronto-temporal and fronto-thalamic pathways in both patients with bipolar disorder and schizophrenia; however, the sensitivity of the methods used is limited. Tract-based spatial statistics is a method of whole-brain analysis that relies on voxel-based comparison, and uses nonlinear image transformation and permutation tests with correction for multiple comparisons. The primary aim of the present study was to investigate anatomical connectivity changes in patients with bipolar disorder and schizophrenia using tract-based spatial statistics, to classify the patients according to white matter integrity patterns using machine learning, and to identify features that represent the key differences between the disorders. Whole-brain images of 41 bipolar disorder patients, 39 schizophrenia patients, and 23 controls were acquired using a 1.5 T magnetic resonance investigation scanner. As compared to the controls, the schizophrenia and bipolar disorder patients had reduced fractional anisotropy in similar white matter tracts. In addition, the imaging method employed differentiated the schizophrenia and bipolar disorder patients with 81.25% accuracy. Although the bipolar disorder and schizophrenia patients exhibited similar anatomical connectivity changes, as compared to the controls, the connectivity reductions in the right hemisphere in the bipolar disorder patients differentiated them from the schizophrenia patients. The present findings improve our understanding of the etiology and pathogenesis of bipolar disorder and schizophrenia, and can potentially be used as a biomarker for the diagnosis and treatment of both disorders.

Appendices

Appendix 1: Artificial neural network—supervised learning

An artificial neural network (ANN) could be described as a machine learning approach that mimics a biological nervous system, and is a powerful modeling tool for approximating nonlinear relationships and finding patterns within a dataset. An ANN is a structure used for processing information and approximating functions based on a number of inputs. With adaptive ability to be used as an arbitrary function approximation mechanism, ANNs “learn” from the observed data. Following the training process, an ANN model predicts response for any given input. That is, an ANN can be used to infer a function based on the collected input/output data. The main features of an ANN are learning adaptation, generalization, massive parallelism, robustness, and abstraction. The structure of a basic ANN can be theoretically modeled, as depicted in Fig. 4, where X{x_i, i = 1, 2, …, n} is the input matrix to the neuron and Y denotes the output of the model.

Fig. 4

Basic structure of an ANN

Inputs are connected to each neuron via a mathematical process. Each input is multiplied by a weight (w_i) associated with each neuron, and a constant bias (b) is added to that scalar value. The process is repeated for each input for all neurons, and finally, their sum goes through a transfer function (f) that is expressed as given in Eq. 1 [8].

$$Y = f\left( {\mathop \sum \limits_{i = 1}^{n} w_{i} x_{i} + b} \right)$$

(1)

There is a wide variety of transfer functions and selection of the proper transfer function is crucial. As there is a nonlinear relationship between the input and output, nonlinear transfer functions are widely adopted for medical image processing. With selection of proper activation functions and connection of neurons, various neural networks can be constructed and trained to generate specified outputs. ANN learning paradigms for medical image processing generally include supervised learning and unsupervised learning. For supervised learning, a network is trained with preset input and output data. During the training process, a set of inputs is used to generate associated output values until the ANN output converges to the reference target with a predefined error value that is ideally zero. Accordingly, the aim of the training process is to minimize the network’s overall output error for all training cases by iteratively adjusting the neuron connection weights and bias values using a specific training algorithm.

1.1 Training process

BP neural network is a typical multilayer feed-forward network trained according to backpropagation algorithm. BP neural network uses parallel distributed processing approach to handle both qualitative and quantitative knowledge. It has strong robustness, fault tolerance, and adaptability and can fully approximate any complex nonlinear relationship. Because of these advantages, BP neural network is more appropriate for processing EEG data which are possible noisy, unstable, and nonlinear. In this study, for modeling process, feed-forward neural network trained by a backpropagation algorithm is used. The network is based on the supervised procedure, i.e., the network constructs a model based on examples of data with known outputs. The architecture of the network is a layered feed-forward neural network, in which the nonlinear elements (neurons) are arranged in successive layers, and the information flows from input layer to output layer, through the hidden layer(s). Sigmoid transfer function used in each neuron because of its nonlinear behavior. In order to minimize the error between the model output and a reference value, MSE (mean square error) is used as the cost function, given in Eq. 2. The cost function is minimized by GA.

$$J\left( w \right) = \frac{1}{N}\mathop \sum \limits_{k = 1}^{N} \left( {y_{k} - z_{k} } \right)^{2}$$

(2)

The sigmoid function was used in the present study as the activation function, and TrainBR (Bayesian regularization backpropagation) was used as the training algorithm. TrainBR is a function that updates the weight and bias values according to the Levenberg–Marquardt optimization method, and minimizes a combination of squared errors and weights in order to determine the correct combinations, so that the generated model can generalize well. For the validation process, fourfold cross-validation with shuffled sampling was employed. The ANN structure was set as a multilayer perceptron (MLP)—a powerful function approximator for prediction and classification using a supervised learning algorithm. The architecture of an MLP neural network is constructed with two layers. A basic two-layer ANN contains an input layer connected to input variables and an output layer that generates the corresponding output. Although an MLP is a satisfactory approximator for linear problems, hidden layers for analyzing nonlinearity and complexity problems are added.

Appendix 2: Genetic neural network

A genetic algorithm (GA) is a very powerful meta-heuristic and evolutionary algorithm that has been used with other evolutionary algorithms for multiple problems across disciplines. Despite the advent of newly adapted meta-heuristic methods, GA remains a popular choice for solving many challenging optimization problems for exact methods that are computationally too expensive. Moreover, due to its intrinsic structure, which is similar to the use of a set (a population) of solutions to be optimized in parallel, GA is considered a natural method for solving problems with multi-objective characteristics.

GA is a stochastic approach inspired by actual genetic processes and follows the “survival of the fittest” mechanism. GA is widely used for optimizing large, complex, and multi-dimensional problems, and generating optimal solutions. The optimization process begins with a set of possible solutions obtained from the whole search space consisting of all features. Each solution is encoded by a set of string expressions (referred to as chromosomes). The set of chromosomes are considered the population. Via the optimization process shown in Fig. 5, the performance of each string is associated with an objective function that evaluates the fitness of a string for the next generation. As such, the objective function is referred to as the fitness function. Considering the fitness values of the strings, the fittest strings are selected and genetic operators, such as crossover and mutation, are applied to generate subsequent generations. This process of selection, crossover, and mutation is iteratively repeated until a maximum number of generations are performed. Therefore, with an adaptive structure GA is able to converge to the best solution (chromosome) that is either the global or the almost global optimal solution. The design process of GA is based primarily on four parameters (population size, crossover rate, mutation rate, and elitist selection), whereas the objective function is defined according the problem. Here, the objective function is taken into consideration apart from the aforementioned four features and only modification to the objective function is sufficient for changing the GA for new problems [43,44,45,46].

Fig. 5

Flowchart of an ANN-GA architecture

2.1 Fitness function of the wrapper approach

A fitness function is used to put forth the degree of goodness of selected subset. For a classification problem, if two subsets with different number of features present quite similar performance, the subset with less number of features comes into prominence. Therefore, the evaluation of fitness function regards two concerns: the classification accuracy and the number of features in the subset. In order to satisfy these concerns, the fitness function is designed in terms of both accuracy and number of features as:

$$f\left( {x_{j} } \right) = m*J\left( {X_{j} } \right) + n*\left( {1/\left| {X_{j} } \right|} \right)$$

(3)

where X_j is the subset constituted by jth chromosome, J(X_j) is the classification accuracy using X_j, |X_j| is the number of features of X_j, and m ∈ [0, 1] and n ∈ [0, 1] are the two coefficients used assign relative importance to classification accuracy and number of the selected subset parameters.