The Role of Hippocampal Atrophy in Depression: A Neurocomputational Approach

Abstract

The role of hippocampal atrophy in the pathogenesis of major depression remains under investigation. Here, we show, within a neural network model, that the incorporation of atrophy reproduces the changes observed in cognitive impairment in depression and could also contribute to the maintenance of the depressed mood. Some other clinical observations, such as treatment resistance and frequent relapses of illness, could also be explained within the framework of the model. We also simulate the action of cognitive therapy and a combined treatment of cognitive therapy and antidepressant drugs. Our findings suggest that, in the presence of hippocampal atrophy, the incorporation of antidepressant drugs would be necessary for the reversal of symptomatology.

Appendix

1.1 Methods

1.1.1 Architecture of the Network

The architecture of the network is inspired by the concept of parallel processing of emotional and nonemotional aspects of information (see Fig. 1). Activation of 32 input nodes represents perceptual characteristics of a stimulus. Input nodes feed activation forward to 32 semantic nodes representing the semantic content of the stimulus and to 16 affective (or valence) nodes representing the affective content of the stimulus. The semantic and the affective nodes are roughly associated with the hippocampal and the amygdala systems, respectively. Feedback occurs between the semantic and the affective nodes. Semantic and affective nodes transmit their activations to 32 output semantic and 16 output valence nodes, respectively, where the decisional process of choosing a possible response takes place. In Siegle’s model, the output module is roughly associated with the frontal lobe.

1.1.2 Representation of Input, Semantic and Valence Patterns

For every stimulus, the input and semantic patterns were represented with the same vector. For these representations, 32-dimensional orthogonal Walsh vectors were used after normalization; n-dimensional Walsh vectors were obtained as columns of n-dimensional Hadamard matrices (n = 2^k; k ∈ N) of the form: H(2^k) = H(2) ⊗ H(2^k − 1), where H(2) = [1 1; 1 −1] and ⊗ is the Kronecker product. For valence representation, a near orthogonality between positivity and negativity was assumed. Valence patterns were constructed as linear combinations of two 16-dimensional Walsh vectors with the following linear coefficients: (cos10°, sin10°) for positivity, (cos80°, sin80°) for negativity, and (cos45°, sin 45°) for neutrality. Valence patterns were normalized.

1.1.3 Training of the Network

The network was trained on three positive, three negative, and three neutral stimuli. The training was implemented creating four weight matrices using the outer product rule [32]: the IS matrix (dimension 32 ×32, autoassociating a semantic pattern to the same input pattern), the IV matrix (dimension 16 ×32, associating a valence pattern to each in- put pattern), the VS matrix (dimension 32 ×16, associating a semantic pattern to a valence pattern), and the SV (dimension 16 ×32, associating a valence pattern with a semantic pattern).

Depression was induced overtraining the network on one negative stimulus from the training set, representing a relevant negative experience, and applying a forgetting rule to the old learning. During the overtraining, the feedback matrices (SV and VS) were adjusted according to the rule:

$$ {\rm {\bf M}}_t =\gamma {\rm {\bf M}}_{t-1} +\varepsilon \Delta ^{\text{overtraining}} $$

(1)

where γ (=0.89) is the forgetting coefficient, ε (=1.5) is the overtraining coefficient, and M _t is a feedback matrix (SV or VS) after t cycles of overtraining and Δ^overtraining is the outer product matrix for the overtrained stimulus. One overtraining cycle was applied to the matrix VS and seven overtraining cycles were applied to the matrix SV.

1.1.4 Network Activation

A unit in the network actualizes its activation as a function of its input and the activation already reached by the unit. We will represent this with s (v) as the activation of the semantic (valence) layer. During the presentation of the stimulus (lasting 10 iterations) bipolar and uniformly distributed noise with a magnitude of 0.005 also enters the net. Semantic and affective units activate according to the following rules:

$$ {\rm {\bf s}}_t =\left( {1-\tau } \right){\rm {\bf s}}_{t-1} +\tau \left( {{\rm {\bf IS}} \left( {{\rm {\bf input}}+{\rm {\bf noise}}} \right)} \right) $$

(2)

$$ {\rm {\bf v}}_t =\left( {1-\tau } \right){\rm {\bf v}}_{t-1} +\tau \left( {{\rm {\bf IV}} \left( {{\rm {\bf input}}+{\rm {\bf noise}}} \right)} \right) $$

(3)

where τ (=0.1) is the diffusion rate for inputs. After the stimulus presentation, only noise enters the network and feedback between semantic and valence nodes operates. Layers actualize activations according to the rules:

$$ {\rm {\bf s}}_t =\left( {1-\tau -\beta } \right){\rm {\bf s}}_{t-1} +\beta \left( {{\rm {\bf VS}} \left( {{\rm {\bf v}}_{t-1} } \right)} \right)+\tau\left( {{\rm {\bf IS}} \ {\rm {\bf noise}}} \right) $$

(4)

$$ {\rm {\bf v}}_t =\left( {1-\tau -\beta } \right){\rm {\bf v}}_{t-1} +\beta \left( {{\rm {\bf SV}} \left( {{\rm {\bf s}}_{t-1} } \right)} \right)+\tau \left( {{\rm {\bf IV}} \ {\rm {\bf noise}}} \right) $$

(5)

where β (=0.002) is the diffusion rate for feedback between semantic and valence layers. When the feedback is operating, semantic and valence layers normalize activations on every iteration.

1.1.5 Stimulus Identification at the Output Module

As in Siegle’s model, once a stimulus is presented to the network, evidence is progressively accumulated for each possible response until one of them reaches a threshold (Fig. 7). Following this idea, devices called counters, which accumulate evidence for every possible response of the network, were defined. Specifically, a counter was defined for each of the nine semantic and for each of the three valence stored patterns. At the beginning of a trial, counters are set to zero. In every iteration, counters change their value according to how well the output semantic or output valence node activation fits the semantic or valence patterns, respectively. The fit between the activation of output nodes and the stored patterns is evaluated as the cosine of the angle between the vectors. The amount that every counter i adds on each iteration is calculated according to the rule:

$$ \mu _i =\alpha \left( {\cos _i -\max \left( {\cos _{j\ne i} } \right)} \right) $$

(6)

where α (=0.1) is the rate of evidence accumulation. If the semantic (valence) task is running, a reaction time is computed when one of the semantic (valence) counters reaches the threshold. The threshold values for the lexical and valence tasks were 4 and 1.5, respectively.

Fig. 7

Computation of reaction times for the valence task when a positive stimulus enters the network. During the valence task, the network could identify a stimulus as positive, negative, or neutral. For each of these possible responses, counters are defined (C ₊: counter for positive valence; C ₋: negative valence; C _n : neutral valence). At the beginning of the trial, all counters are set to zero. In every iteration, each counter changes its value according to how well the output affective activation fits the valence pattern that the counter represents, evaluated as the cosine between the vectors (see Eq. 6 in the Appendix). When one of the counters reaches a threshold, the trial ends, and the number of iterations elapsed until that moment is computed as the reaction time of the network. In the figure, a positive stimulus enters the network and the counter that represents positivity is the first one in reaching the threshold (confusion may occur when a counter corresponding to a valence different from the stimulus reaches the threshold). For the lexical task, reaction times are computed in an analogous way, but in this case, nine counters are used

1.1.6 Implementation of HA in the Network

HA was simulated by randomly destroying synapses in memories attributed to the hippocampal system. Specifically, synaptic weights in matrices IS and VS were randomly selected and set to a zero value. According to data from anatomical studies, percentages of HA going from 5% to 20% were explored.

1.1.7 Effect of a Cognitive Therapy in the Network

The effect of a cognitive therapy was simulated by reinstructing the connection matrices with the whole set of stimuli and applying a forgetting rule to the old learning to withdraw previous overtraining on negative stimulus. During the relearning, the weight matrices were adjusted according to the rule:

$$ {\rm {\bf M}}_t =\gamma {\rm {\bf M}}_{t-1} +0.1 {\rm {\bf M}}^{normal} $$

(7)

where γ (=0.89) is the forgetting coefficient, M _t is one of the weight matrices of the network, and M ^normal is the sum of the outer products for the whole set of stimuli. When the cognitive therapy is applied on the network with HA, the atrophied connections do not adjust their weights according to the rule (Eq. 7), staying with a zero value weight.

1.1.8 Effect of a Combined Treatment of Antidepressants and Cognitive Therapy

Antidepressant drugs might oppose or even reverse HA. In the model, the effect of antidepressants was simulated, reattributing basal synaptic weights to the previous atrophied connections (that were set to a value of zero), hence allowing them to adjust their weights with the cognitive therapy relearning mechanism. Basal synaptic weights were calculated as the average of the weights of the corresponding matrix (IS or VS) in the normal state, plus a random number normally distributed with mean zero and variance 1 ×10^− 4.

1.1.9 Statistical Analysis

Randomness was introduced in the model through the noise that enters the network, and also by the implementation of HA. The reaction times presented in the graphics are averages over 1,000 random realizations. For each curve in the graphs of the figures, a new independent set of 1,000 realizations was randomly chosen. A z test was used for comparing means. A z value of 2.33 was used to establish the rejection region. All results were significant with p < 0.001.