A Neural Model of Delusions and 
Hallucinations in Schizophrenia 
Eytan Ruppin and James A. Reggia 
Department of Computer Science 
University of Maryland, College Park, MD 20742 
ruppin@cs.umd.edu reggia@cs.umd.edu 
David Horn 
School of Physics and Astronomy, 
Tel Aviv University, Tel Aviv 69978, Israel 
horn@vm.tau.ac.il 
Abstract 
We implement and study a computational model of Stevens' [1992] 
theory of the pathogenesis of schizophrenia. This theory hypoth- 
esizes that the onset of schizophrenia is associated with reactive 
synaptic regeneration occurring in brain regions receiving degener- 
ating temporal lobe projections. Concentrating on one such area, 
the frontal cortex, we model a frontal module as an associative 
memory neural network whose input synapses represent incoming 
temporal projections. We analyze how, in the face of weakened 
external input projections, compensatory strengthening of internal 
synaptic connections and increased noise levels can maintain mem- 
ory capacities (which are generally preserved in schizophrenia). 
However, These compensatory changes adversely lead to sponta- 
neous, biased retrieval of stored memories, which corresponds to 
the occurrence of schizophrenic delusions and hallucinations with- 
out any apparent external trigger, and for their tendency to con- 
centrate on just few central themes. Our results explain why these 
symptoms tend to wane as schizophrenia progresses, and why de- 
layed therapeutical intervention leads to a much slower response. 
150 Eytan Ruppin, James A. Reggia, David Horn 
1 Introduction 
There has been a growing interest in recent years in the use of neural models to inves- 
tigate various brain pathologies and their cognitive and behavioral effects. Recent 
published examples of such studies include models of cortical plasticity following 
stroke, Alzheimer's disease and schizophrenia, and cognitive and behavioral explo- 
rations of aphasia, acquired dyslexia and affective disorders (reviewed in [1, 2]). 
Continuing this line of study, we present a computational account linking specific 
pathological synaptic changes that are postulated to occur in schizophrenia, and 
the emergence of schizophrenic delusions and hallucinations. The latter symptoms 
denote persistent, unrealistic, psychotic thoughts (delusions) or percepts (halluci- 
nations) that may at times flood the patient in an overwhelming, stressful manner. 
The wealth of data gathered concerning the pathophysiology of schizophrenia sup- 
ports the involvement of both the frontal and the temporal lobes. On the one 
hand, there are atrophic changes in the hippocampus and parahippocampal areas 
including neuronal loss and gliosis. On the other hand, neurochemical and morpho- 
metric studies testify to an expansion of various receptor binding sites and increased 
dendritic branching in the frontal cortex of schizophrenics. Stevens has recently pre- 
sented a theory linking these temporal and frontal findings, claiming that the onset 
of schizophrenia is associated with reactive anomalous sprouting and synaptic re- 
organization taking place in the projection sites of degenerating temporal neurons, 
including (among various cortical and subcortical structures) the frontal lobes [3]. 
This paper presents a computational study of Stevens' theory. Within the frame- 
work of a memory model of hippocampal-frontal interaction, we show that the 
introduction of the 'microscopic' synaptic changes that underlie Stevens' hypothe- 
sis can help preserve memory function but results in specific 'pathological' changes 
in the 'macroscopic' behavior of the network. A small subset of the patterns stored 
in the network are now spontaneously retrieved at times, without being cued by any 
specific input pattern. This emergent behavior shares some of the important char- 
acteristics of schizophrenic delusions and hallucinations, which frequently appear in 
the absence of any apparent external trigger, and tend to concentrate on a limited 
set of recurrent themes [4]. Memory capacities are fairly preserved in schizophren- 
ics, until late stages of the disease [5]. In Section 2 we present our model. The 
analytical and numerical results obtained are described in Section 3, followed by 
our conclusions in Section 4. 
2 The Model 
As illustrated in Figure 1, we model a frontal module as an associative memory 
attractor neural network, receiving its input memory cues from decaying exter- 
nal input fibers (representing the degenerating temporal projections). The net- 
work's internal connections, which store the memorized patterns, undergo synaptic 
strengthening changes that model the reactive synaptic regeneration within the 
frontal module. The effect of other diffuse external projections is modeled as back- 
ground noise. A frontal module represents a macro-columnar unit that has been 
suggested as a basic functional building block of the neocortex [6]. The assumption 
that memory retrieval from the frontal cortex is invoked by the firing of incoming 
A Neural Model of Delusions and Hallucinations in Schizophrenia 151 
temporal projections is based on the notion that temporal structures have an im- 
portant role in establishing long-term memory in the neocortex and in the retrieval 
of facts and events (e.g., [7]). 
Other cortical 
(lnfluaw modll 
noise) 
Figure 1: A schematic illustration of the model. A frontal module is modeled 
as an attractor neural network whose neurons receive inputs via three kinds of 
connections: internal connections from other frontal neurons, external connections 
from temporal lobe neurons, and diffuse external connections from other cortical 
modules, modeled as noise. 
The attractor network we use is a biologically-motivated variant of Hopfield's ANN 
model, proposed by Tsodyks & Feigel'man [8]. Each neuron i is described by a 
binary variable $i = {1,0) denoting an active (firing) or passive (quiescent) state, 
respectively. M = cN distributed memory patterns " are stored in the network. 
The elements of each memory pattern are chosen to be i (0) with probability p 
(1-p) respectively, with p << 1. All N neurons in the network have a fixed uniform 
threshold 0. 
In its initial, undamaged state, the weights of the internal synaptic connections are 
M 
co Z(, i _ P)("J - P)' (1) 
Wij= 
/=1 
where co = 1. The post-synaptic potential (input field) hi of neuron i is the sum of 
internal contributions from other neurons and external projections Fi e 
hi(t) = Z wijsj(t - 1)+ 
(2) 
The updating rule for neuron i at time t is given by 
1, with prob. G(hi(t)- O) 
Si(t) = O, otherwise 
152 Eytan Ruppin, James A. Reggia, David Horn 
where G is the sigmoid function G(x) = 1/(1 +exp(-x/T)), and T denotes the noise 
level. The activation level of the stored memories is measured by their overlaps 
with the current state of the network, defined by 
N 
i E(_p)Si(t) ' 
rn"(t) = p(1 - p)N i=1 
(4) 
Stimulus-dependent retrieval is modeled by orienting the field F* with one of the 
memorized patterns (the cued pattern, say ix), such that 
Fi e -- e.x i , (e  0) . (5) 
Following the presentation of an external input cue, the network state evolves until 
it converges to a stable state. The network parameters are tuned such that in its 
initial, undamaged state it correctly retrieves the cued patterns (e0 = 0.035, co = 1, 
T = 0.005). 
We also examine the network's behavior in the absence of any specific stimulus. The 
network may either continue to wander around in a state of random low baseline 
activity, or it may converge onto a stored memory state. We refer to the latter 
process as spontaneous retrieval. 
Our investigation of Stevens' work proceeds in two stages. First we examine and an- 
alyze the behavior of the network when it undergoes uniform synaptic changes that 
represent the pathological changes occurring in accordance with Stevens' theory. 
These include the weakening of external input projections (e ) and the increase in 
the internal projections (c ]') and noise levels (T ]'). In the second stage, we add 
the assumption that the internal synaptic compensatory changes have an additional 
Hebbian activity-dependent component, and examine the effect of the rule 
W,j(t) = W,j(t - l) + (, - p)(j - p) , (6) 
where  is 1 (0) only if neuron k has been consecutively firing (quiescent) for the 
last r iterations, and ? is a constant. 
3 Results 
We now show some simulation and analytic results, examining the effects of the 'mi- 
croscopic' pathological changes, taking place in accordance with Stevens' theory, on 
the 'macroscopic' behavior of the network. The analytical results presented have 
been derived by calculating the magnitude of randomly formed initial 'biases', and 
comparing their effect on the network's dynamics versus the effect of externally pre- 
sented input cues. This comparison is performed by formulating a corresponding 
overlap master equation, whose fixed point dynamics are investigated via phase- 
plane analysis, as described in [9]. First, we study whether the reactive synaptic 
changes (occurring in both internal and external, diffuse synapses) are really com- 
pensatory, i.e., to what extent can they help maintaining memory capacities in the 
face of degenerating external input synapses. As illustrated in Figure 2, we find that 
increased noise levels can (up to some degree) preserve memory retrieval in the face 
of decreased external input strength. Increased synaptic strengthening preserves 
A Neural Model of Delusions and Hallucinations in Schizophrenia 153 
(b) 
1.0 
0.8 
0.6 
0,4 
0.2 
t 
0.010 
T 
--  m 0.035 ., 
 0,025 
....   0.015 
-----   0.005 
1,0 
0.8 
0.6 
0.4 
0.2 
0,0 , 0.0 
0.000 0.020 0.( 
 = 
.......  - 10.025 
.....  = f0.015 
----- e- !0.014 
(3.-- --0 e = i 0.013 \ 
O'--- e  = 10.012 
----- e= ;0.005 
i .e. ' ',,, 
; / , ',,, ,, 
; o, ',, 
x ...... O.OLO 0.02o 
T 
Figure 2: Stimulus-dependent retrieval performance, measured by the average final 
overlap m, as a function of the noise level T. Each curve displays this relation at 
a different magnitude of external input projections e. (a) Simulation results. (b) 
Analytic approximation. 
memory retrieval in a similar manner, and the combined effect of these synaptic 
compensatory measures is synergistic. 
Second, although the compensatory synaptic changes help maintain memory re- 
trieval capacities, they necessarily have adverse effects, leading eventually to the 
emergence of spontaneous activation of non-cued memory patterns; the network 
converges to some of its memory patterns in a pathological, autonomous manner, 
in the absence of any external input stimuli. This emergence of pathological spon- 
taneous retrieval, when either the noise level or the internal synaptic strength (or 
both) are increased beyond some point, is demonstrated in Figure 3. 
Third, when the compensatory regeneration of internal synapses has an additional 
Hebbian component (representing a period of increased activity-dependent plastic- 
ity due to the regenerative synaptic changes), a biased spontaneous retrieval dis- 
tribution is obtained. That is, as time evolves (measured in time units of 'trials'), 
the distribution of patterns spontaneously retrieved by the network in a patholog- 
ical manner tends to concentrate only on one or two of all the memory patterns 
stored in the network, as is shown in Figure 4a. This highly peaked distribution is 
maintained for a few hundred additional trials until memory retrieval sharply col- 
lapses to zero as a global mixed-state attractor is formed. Such a mixed attractor 
state does not have very high overlap with any memorized pattern, and thus does 
not represent any well-defined cognitive or perceptual item. It is an end state of 
the Hebbian, activity-dependent evolution of the network. Yet, even after activity- 
dependent changes ensue, if spontaneous activity does not emerge the distribution 
of retrieved memories remains homogeneous (see Figure 4b). Eventually, a global 
154 Eytan Ruppin, James A. Reggia, David Horn 
(b) 
,.0 ' / ,/:  .0 
0 8 t t 
0.6 [  
0.6 
0.4 / ! ,' -- smte 't / 
0.0 0.0 ""' [ 
0.5 0.010 0.01 5 0. 2.0 2.5 3.0 3.5 4.0 
T c 
Figure 3: (a) Spontaneous retrieval, measured as the highest final overlap m 
achieved with any of the stored memory patterns, displayed as a function of the 
noise level T. c = 1. (b) Spontaneous retrieval as a function of internal synaptic 
compensation factor c. T = 0.009. 
mixed-state attractor is formed, and the network looses its retrieval capacities, but 
during this process no memory pattern gets to dominate the retrieval output. Our 
results remain qualitatively similar even when bounds are placed on the absolute 
magnitude of the synaptic weights. 
4 Conclusions 
Our results suggest that the formation of biased spontaneous retrieval requires the 
concomitant occurrence of both degenerative changes in the external input fibers, 
and regenerative Hebbian changes in the intra-modular synaptic connections. They 
add support to the plausibility of Stevens' theory by showing that it may be real- 
ized within a neural model, and account for a few characteristics of schizophrenic 
symptoms: 
The emergence of spontaneous, non-homogeneous retrieval is a self-limiting 
phenomenon (as eventually a cognitively meaningless global attractor is 
formed) - this parallels the clinical finding that as schizophrenia progresses 
both delusions and hallucinations tend to wane, while negative symptoms 
are enhanced [10]. 
Once converged to, the network has a much larger tendency to remain in a 
biased memory state than in a non biased one - this is in accordance with 
the persistent characteristic of schizophrenic florid symptoms. 
As more spontaneous retrieval trials occur the frequency of spontaneous 
retrieval increases - indeed, while early treatment in young psychotic adults 
A Neural Model of Delusions and Hallucinations in Schizophrenia 155 
(a) 
(b) 
0.8 
0.6 
0.2 
0.0 
0.0 
After 200 trials 
G - - (: After 500 trials 
  After 800 trials 
10.0 20.0 30.0 40.0 
Memories 
0.00  After 200 trials 
. (. After 400 trials 
0.020  ! t  
40.0 
Mnories 
Figure 4: (a) The distribution of memory patterns spontaneously retrieved. The x- 
axis enumerates the memories stored, and the y-axis denotes the retrieval frequency 
of each memory. 3' = 0.0025. (b) The distribution of stimulus-dependent retrieval 
of memories. 3' = 0.0025. 
leads to early response within days, late, delayed intervention leads to a 
much slower response during one or more months [11]. 
The current model generates some testable predictions: 
On the neuroanatomical level, the model can be tested quantitatively by 
searching for a positive correlation between a recent history of florid psy- 
chotic symptoms and postmortem neuropathological findings of synaptic 
compensation. (For example, this kind of correlation, between indices of 
synaptic area and cognitive functioning was found in Alzheimer patients 
[12]). 
On the physiological level, the increased compensatory noise should mani- 
fest itself in increased spontaneous neural activity. While this prediction is 
obviously difficult to examine directly, EEG studies in schizophrenics show 
significant increase in slow-wave delta activity which may reflect increased 
spontaneous activity [13]. 
On the clinical level, due to the formation of a large and deep basin of 
attraction around the memory pattern which is at the focus of spontaneous 
retrieval, the proposed model predicts that its retrieval (and the elucida- 
tion of the corresponding delusions or hallucinations) may be frequently 
triggered by various environmental cues. A recent study points in this 
direction [14]. 
156 Eytan Ruppin, James A. Reggia, David Horn 
Acknowledgement s 
This research has been supported by a Rothschild Fellowship to Dr. Ruppin. 
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