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ORIGINAL RESEARCH ARTICLE
published: 28 May 2014
doi: 10.3389/fnsys.2014.00097
Extraction and restoration of hippocampal spatial
memories with non-linear dynamical modeling
Dong Song1*, Madhuri Harway1, Vasilis Z. Marmarelis1, Robert E. Hampson2, Sam A. Deadwyler2
and Theodore W. Berger1
1Department of Biomedical Engineering, University of Southern California, Los Angeles, CA, USA
2Department of Physiology and Pharmacology, School of Medicine, Wake Forest University, Winston-Salem, NC, USA
Edited by:
Mikhail Lebedev, Duke University,
USA
Reviewed by:
Mikhail Lebedev, Duke University,
USA
Yoshio Sakurai, Kyoto University,
Japan
Yu Liu, The University of Tennessee
Health Science Center, USA
*Correspondence:
Dong Song, Department of
Biomedical Engineering, University
of Southern California, 403 Hedco
Neuroscience Building, Los
Angeles, CA 90089, USA
e-mail: dsong@usc.edu
To build a cognitive prosthesis that can replace the memory function of the hippocampus,
it is essential to model the input-output function of the damaged hippocampal region,
so the prosthetic device can stimulate the downstream hippocampal region, e.g., CA1,
with the output signal, e.g., CA1 spike trains, predicted from the ongoing input signal,
e.g., CA3 spike trains, and the identified input-output function, e.g., CA3-CA1 model. In
order for the downstream region to form appropriate long-term memories based on the
restored output signal, furthermore, the output signal should contain sufficient information
about the memories that the animal has formed. In this study, we verify this premise
by applying regression and classification modelings of the spatio-temporal patterns of
spike trains to the hippocampal CA3 and CA1 data recorded from rats performing a
memory-dependent delayed non-match-to-sample (DNMS) task. The regression model is
essentially the multiple-input, multiple-output (MIMO) non-linear dynamical model of spike
train transformation. It predicts the output spike trains based on the input spike trains and
thus restores the output signal. In addition, the classification model interprets the signal by
relating the spatio-temporal patterns to the memory events. We have found that: (1) both
hippocampal CA3 and CA1 spike trains contain sufficient information for predicting the
locations of the sample responses (i.e., left and right memories) during the DNMS task;
and more importantly (2) the CA1 spike trains predicted from the CA3 spike trains by the
MIMO model also are sufficient for predicting the locations on a single-trial basis. These
results show quantitatively that, with a moderate number of unitary recordings from the
hippocampus, the MIMO non-linear dynamical model is able to extract and restore spatial
memory information for the formation of long-term memories and thus can serve as the
computational basis of the hippocampal memory prosthesis.
Keywords: hippocampus, spatio-temporal pattern, spike, classification, regression, memory
INTRODUCTION
Cortical prosthesis is an emerging technology seeking to restore
cognitive functions lost in diseases or injuries (Berger et al., 2005,
2010, 2011, 2012). It is achieved by bi-directional, closed-loop
communications between the prosthetic device and the brain
regions. This is distinct from sensory or motor prostheses, where
one side of the communication is an external entity such as
the sensory input (Loeb, 1990; Humayun et al., 1999)orthe
motor output (Mauritz and Peckham, 1987; Taylor et al., 2002;
Nicolelis, 2003; Shenoy et al., 2003; Wolpaw and McFarland,
2004; Hochberg et al., 2006). Therefore, a cortical prosthesis
must deal exclusively with the internal brain signals, in which
sensory or motor information is embedded, by re-encoding the
upstream (input) brain signals into the downstream (output)
signals (Figure 1A).
For the past decade, we have been working on develop-
ing a hippocampal-cortical prosthesis for restoring the memory
functions. Hippocampus is a brain region responsible for the
creation of new long-term episodic memories (Milner, 1970;
Squire and Zola-Morgan, 1991; Eichenbaum, 1999). Damage
to the hippocampal areas can result in a permanent loss of
such cognitive functions. In a normal hippocampus, short-term
memories are encoded in the spatio-temporal patterns of spikes
(i.e., spike trains) as the input from the entorhinal cortex.
Memory information is then processed by the hippocampal feed-
forward tri-synaptic pathway, which consists of dentate gyrus,
CA3, and CA1 regions, and eventually transformed into the
output spike trains to the subiculum, that is appropriate for
the formation of long-term memories (Figure 1B). Although
the exact nature of such a transformation or the underlying
mechanisms is still largely unclear, it must be the neural sig-
nal (i.e., spike trains) flow from entorhinal cortex to dentate
gyrus, to CA3, to CA1, and to subiculum, that enables the
re-encoding of short-term memories into long-term memories.
Maintaining the normal signal flow with a prosthetic device that
bypasses a damaged or diseased hippocampal region provides a
feasible way of restoring the lost long-term memory functions
(Figure 1A).
For example, in our first-generation hippocampal memory
prosthesis applications, we (a) record input spike trains from the
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SYSTEMS NEUROSCIENC
E
Song et al. Extraction and restoration of memory with non-linear model
FIGURE 1 | Cortical prosthesis restores cognitive functions by
bypassing the damaged brain region to maintain the brain signal flow.
(A) Schematic diagram of a cortical prosthesis. (B) Intrinsic tri-synaptic
pathway of the hippocampus.
CA3 region, (b) process them with a multi-input, multi-output
(MIMO) non-linear dynamical model to predict the desired CA1
output spike trains, and (c) electrically stimulate the CA1 region
with the predicted CA1 output patterns. Previous results have
shown that, (a) the MIMO model can accurately predict the out-
put spike trains in real time based on the ongoing input spike
trains (Song et al., 2007, 2009a, 2013), and (b) the electrical
stimulation can restore or even enhance the memory functions
performed by the hippocampal CA3-CA1 system (Berger et al.,
2011, 2012; Hampson et al., 2012a,b).
However, despite the success of demonstrating such a pros-
thesis, how the external behavioral events (i.e., memory events)
are encoded in the two hippocampal regions and, more impor-
tantly, re-encoded by the prosthesis has not been clearly revealed,
precisely due to the internal nature of the cortical prosthesis. In
this study, we propose a new framework of modeling and rep-
resenting the re-encoding process performed by a brain region
at the memory representation level, as opposed to the signal
level in our previous studies. In addition to ask the question,
“What should the output signal be?” We further ask the ques-
tion, “What do the signals mean?” Specifically, we combine our
previously developed MIMO signal model (Song et al., 2007,
2009a, 2013), which predicts the output signal based on the input
signal, with an additional memory decoding model that relates
the input and/or output signals to the behaviors (memories) of
the animal (Figure 2). The MIMO signal model is essentially
a time-series regression model non-linear dynamically mapping
the multiple output (CA1) signals to the multiple input (CA3)
signals. On the other hand, the memory decoding model is a
multi-input, signal-output (MISO) classification model identify-
ing to which of a set of memory categories the spatio-temporal
patterns of the input and/or output signals belong. The for-
mer model quantifies the input-output signal transformation,
while the latter model decodes the memory by predicting the
behavior.
The paper is organized as the follows. In section Materials
and Methods, we formally formulate the modeling problem and
provide the mathematical expressions. In section Results, we
apply the methods to the modeling of the hippocampus during
amemory-dependenttaskinrodents.
MATERIALS AND METHODS
BEHAVIORAL TASK AND ELECTROPHYSIOLOGICAL PROCEDURES
All animal procedures are reviewed and approved by the
Institutional Animal Care and Use Committee of Wake Forest
University, in accordance with US Department of Agriculture,
International Association for the Assessment and Accreditation
of Laboratory Animal Care and National Institutes of Health
guidelines. Two male Long-Evans rats are trained to criterion on
a two-lever, spatial delayed-non-match-to-sample (DNMS) task
with random delay intervals (Deadwyler et al., 1996; Hampson
et al., 1999). Animals perform the task by pressing (sample
response) a single lever presented in one of the two positions in
the sample phase (left or right). This event is called the “sample
response.” The lever is then retracted and the delay phase initi-
ates; for the duration of the delay phase, the animal is required
to nose-poke into a lighted device on the opposite wall. When
the delay is ended, nose-poke light is extinguished, both levers are
extended, and the animal is required to press the lever opposite to
the sample lever. This event is called the “non-match response.” If
the correct lever is pressed, the animal is rewarded (Figure 3,top).
A session includes approximately 100 successful DNMS tasks that
each consists of two of the four behavioral events, i.e., right sam-
ple (RS) and left non-match (LN), or left sample (LS) and right
non-match (RN).
Spike trains are obtained with multi-site recordings from
different septo-temporal regions of the hippocampus of rats per-
forming the DNMS task (Figure 3,bottom).Foreachhemisphere
of the brain, a microwire multi-electrodes array (MEA) is surgi-
cally implanted into the hippocampus, with 8 electrodes in the
CA3 (input) region and 8 electrodes in the CA1 (output) region.
Spike trains are pre-screened based on mean firing rate and peri-
event histogram. Perievent (−2to+2s) spike trains of the four
behavioral events are extracted from each trial and then concate-
nated to form the datasets (Figure 3,bottom).Thespiketrain
data are discretized with a 2 ms bin size.
MIMO SIGNAL MODEL OF INPUT-OUTPUT SPIKE TRAIN
TRANSFORMATION
The MIMO signal model of input-output spike train transforma-
tion takes the form of the sparse generalized Laguerre-Volterra
model (SGLVM) we previously developed (Song et al., 2009a,b,
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Song et al. Extraction and restoration of memory with non-linear model
FIGURE 2 | MIMO signal model and MISO memory decoding
model. The MIMO signal model predicts the output spatio-temporal
patterns of spikes based on the ongoing input spatio-temporal patterns
of spikes. The MISO memory decoding model predicts the memory
(behavioral) events based on the input or output spatio-temporal
patterns of spikes.
2013). In this approach, a MIMO model is a concatenation of
aseriesofMISOmodels(nottobeconfusedwiththeMISO
classification model), that each can be considered a spiking neu-
ron model (Song et al., 2006, 2007)(Figure 2). In this study,
each MISO model consists of (a) MISO second-order Volterra
kernels ktransforming the input spike trains xto the synaptic
potential u, (b) a Gaussian noise term εcapturing the stochastic
properties of spike generation, (c) a threshold θfor generat-
ing output spikes y, (e) an adder generating the pre-threshold
membrane potential w, and (d) a single-input, single-output first-
order Volterra kernel htransforming the preceding output spikes
to the spike-triggered feedback after-potential a. The model can
be mathematical expressed as:
w=u(k,x)+a(h,y)+ε(σ)(1)
y=0whenw<θ
1whenw≥θ(2)
u(t)=k0+
N
n=1
Mk
τ=0
k(n)
1(τ)xn(t−τ)
+
N
n=1
Mk
τ1=0
Mk
τ2=0
k(n)
2s(τ1,τ
2)xn(t−τ1)xn(t−τ2)(3)
a(t)=
Mh
τ=1
h(τ)y(t−τ)(4)
The zeroth-order kernel, k0,isthevalueofuwhen the input
is absent. First-order kernels k(n)
1describe the first-order linear
relation between the nth input xnand u, as functions of the
time intervals τbetween the present time and the past time.
Second-order self kernels k(n)
2sdescribe the second-order non-
linear interaction between pairs of spikes in the nth input xnas
they affect u.Nis the number of inputs. Mkand Mhdenote the
memory lengths of the feedforward process and feedback process,
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Song et al. Extraction and restoration of memory with non-linear model
FIGURE 3 | Input (CA3) and output (CA1) spatio-temporal patterns of spikes recorded with a multi-electrode array (MEA) during the sample phase of
the delayed-non-match-to-sample (DNMS) task.
respectively. They are chosen to be 2s in this study. Second-order
cross kernels and higher-order (e.g., third-order) kernels are not
included in this study.
To facilitate model estimation and avoid overfitting, the
Volterra kernels are expanded with Laguerre basis functions bas
in Song et al. (2009c,d):
u(t)=c0+
N
n=1
J
j=1
c(n)
1(j)v(n)
j(t)
+
N
n=1
J
j1=1
j1
j2=1
c(n)
2s(j1,j2)v(n)
j1(t)v(n)
j2(t)(5)
a(t)=
L
j=1
ch(j)v(h)
j(t)(6)
where v(n)
j(t)=Mk
τ=0bj(τ)xn(t−τ), v(h)
j(t)=Mh
τ=1bj(τ)
y(t−τ); c(n)
1,c(n)
2s,andchare the sought Laguerre expansion
coefficients of k(n)
1,k(n)
2s,andh,respectively(c0is equal to k0); Jis
the number of basis functions.
To achieve model sparsity, the coefficients are estimated with
a composite penalized likelihood estimation method, i.e., group
LASSO (Song et al., 2013). In maximum likelihood estimation
(MLE), model coefficients are estimated by minimizing the nega-
tive log likelihood function -l(c). In group LASSO, the composite
penalized criterion is written as
S(c)=−l(c)+λN
n=1
||c(n)
1(j)||1
2+
N
n=1
||c(n)
2s(j1,j2)||1
2
=−l(c)+λ⎛
⎜
⎝
N
n=1⎛
⎝
J
j=1
c(n)
1(j)2⎞
⎠
1
2
+
N
n=1⎛
⎝
J
j1=1
j1
j2=1
c(n)(j1,j2)2⎞
⎠
1
2⎞
⎟
⎠(7)
where λ≥0 is a tuning parameter that controls the relative
importance of the likelihood and the penalty term. When λ
takes on a larger value, the estimation yields sparser result of
the coefficients. λis optimized with a two-fold cross-validation
method.
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Song et al. Extraction and restoration of memory with non-linear model
MISO MEMORY DECODING MODEL OF SPATIO-TEMPORAL PATTERN
OF SPIKES
The MISO memory decoding model of spike spatio-temporal
patterns takes the form of the sparse generalized B-spline lin-
ear classification model (Song et al., 2013). In this approach, the
feature space is defined as a set of B-spline basis functions for
each neuron (input and/or output neurons depending on the
application). The classifier is essentially the logistic regression
(Figure 2).
B-splines are piecewise polynomials with smooth transitions
between the adjacent pieces at a set of interior knot points. A
polynomial spline of degree d≥0on[0,M]withm>0 interior
knot points and the knot sequence η0=0<η
1< ... < ηm<
ηm+1=Mis a function that is a polynomial of degree dbetween
each pair of adjacent knots, and has d-1 continuous derivatives
for d=1. B-spline basis functions of degree dcan be defined in a
recursive fashion as
Bj,d(τ)=τ−ηj
ηj+d−1−ηj
Bj,d−1(τ)+ηj+d−τ
ηj+d−ηj+1
Bj+1,d−1(τ)
(8)
where
Bj,0(τ)=1ifηj<τ <η
j+1
0otherwise (9)
For a given sequence of mknotsandafixeddegreed, the total
number of B-spline basis functions is J=m+d+1.
Spatio-temporal patterns of spikes are projected to the
B-spline feature space via inner product to yield the feature
vectors as
z(n)(j)=
M
τ=0
Bj(τ)xn(τ) (10)
where Mis the time widow for inner product. It is chosen to be
from −2to+2 s of the sample events (Figure 3,bottom).xnis the
nth neuron of the total Nneurons included in analysis. Different
from in the regression model, xcan be CA3 and/or CA1 neu-
rons depending on the context. z(n)(j) denotes the feature value
of the nth neuron using the jth B-spline function. Therefore, zis a
1-by-JN vector. Jis optimized in the range of 5–100 based on the
out-of-sample prediction accuracy. In most of the cases, J=20 is
found to be optimal.
Since there are two possible behavioral outcomes, i.e., left
or right position, the model output can be represented as a
binary variable β. The classification model assumed by logistic
regression is
P(β=1|x)=⎡
⎣1+exp ⎧
⎨
⎩
−w0−
N
n=1
J
j=1
w(n)(j)z(n)(j)⎫
⎬
⎭⎤
⎦
−1
(11)
P(β=0|x)=1−P(β=1|x) (12)
where ware the sought model coefficients; 1 and 0 represent left
and right positions, respectively.
The linear classification rule is simply
β=⎧
⎪
⎨
⎪
⎩
1if
−w0−
N
n=1
J
j=1
w(n)(j)z(n)(j)<0
0otherwise
(13)
Compared with the MIMO regression model, the MISO classifi-
cation model may suffer even more serious overfitting problem
due to the high dimensional input (typically with hundreds of
features) and the relatively small number of data points (typically
100 trials in this study). Therefore, L1 regularization (Lasso) is
applied to achieve model sparsity and avoid overfitting as
S(c)=−l(c)+λ⎛
⎝
N
n=1
J
j=1
||w(n)(j)||1
2⎞
⎠(14)
Where −l(c)andλ=0 are the negative log likelihood function
and the tuning parameter of the classification model, respectively.
In this study, λis optimized with a four-fold cross-validation
method. By minimizing S, sparse weight matrix ware estimated
and further used to reconstruct the classification feature matrix F
with the B-spline basis functions as
F(n)(τ)=
J
j=1
Bj(τ)w(n)(j) (15)
Fcan be directly used in the logistic regression along with the
spatio-temporal pattern xas
P(β=1|x)=1+exp −w0−
N
n=1
M
t=1
F(n)(τ)x(n)(t)−1
(16)
RESULTS
HIPPOCAMPAL CA3 AND CA1 ACTIVITIES CONTAINS SUFFICIENT
INFORMATION FOR DECODING SPATIAL MEMORIES DURING THE
DNMS TASK
First, we apply the MISO memory decoding model to the CA3
spike trains recorded during the sample phase of the DNMS tasks.
For each sample event (left or right), we take the perievent spikes
2 s before and after the event with a 2 ms bin size. The spatio-
temporal patterns of spikes are then N-by-2000 matrices, where
Nis the number of neurons. A session typically consists of 80–100
trials with roughly half being left sample trials and half being
right sample trials. The spatio-temporal patterns are labeled with
1 for the left trials and 0 for the right trials. Figure 4 (case #1)
and Figure 5 (case #2) show the spatio-temporal patterns from
two animals with 26 and 43 CA3 neurons, respectively. For each
position, four representative patterns and the overall patterns are
shown. The overall patterns are obtained by smoothing the spike
trains with B-spline functions and then summing across all tri-
als for the specific position. It is evident that the two positions
show different spatio-temporal patterns and the differences exist
in specific time ranges of specific neurons (Figures 4,5). The task
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Song et al. Extraction and restoration of memory with non-linear model
FIGURE 4 | Spatio-temporal patterns of spikes in the hippocampal CA3 (input) region during left and right sample events of the DNMS (case #1).
of the MISO memory decoding model is to identify these sparsely
distributed differences from single trials of the spatio-temporal
pattern and then predict the positions of the animal. Results show
that the MISO memory decoding model can achieve a 100% out-
of-sample prediction accuracy using the CA3 spatio-temporal
patterns in both cases (Figure 8,toprow).
Using the same method, we build MISO memory decoding
models for the CA1 spike trains. Figure 6 (case #1) and Figure 7
(case #2) show the spatio-temporal patterns of CA1 during left
and right trials (row 1 and 3) from the same two animals. There
are 19 and 17 CA1 neurons recorded from these two animals,
respectively. Similar to CA3, CA1 also show different spatio-
temporal patterns during left and right trials. The prediction
accuracy is 100% in one case and 91.3% in the other (Figure 8,
middle row).
HIPPOCAMPAL CA1 ACTIVITIES CAN BE ACCURATELY PREDICTED BY
THE MIMO SIGNAL MODEL BASED ON THE HIPPOCAMPAL CA3
ACTIVITIES
In the second step, we build MIMO signal models for the trans-
formations from the CA3 spatio-temporal patterns to the CA1
spatio-temporal patterns. To build such a model, we concate-
nate CA3 perievent spike trains across all trials to form the input
data and the corresponding CA1 spike trains to form the output
data, and then apply our MIMO modeling method. The resulting
SGLVM non-linear dynamically predicts the CA1 spikes based on
the ongoing and past (within the memory window) CA3 spikes
(Song et al., 2007, 2009a; Song and Berger, 2010). Results show
that in both cases (Figures 6,7, row 2 and 4), the MIMO signal
model can accurately predict the CA1 spatio-temporal patterns
at both the single trial level (Figures 6,7, column 1–4) and the
overall level (Figures 6,7, column 5). Importantly, a single set of
the model coefficients are used for both the left and right trials.
In other words, the estimated MIMO signal models are memory-
invariant and can be used to predict the output signals without
explicitly knowing what the events are (Song et al., 2011).
HIPPOCAMPAL CA1 ACTIVITIES PREDICTED BY THE MIMO SIGNAL
MODEL CAN BE USED TO ACCURATELY DECODE THE SPATIAL MEMORY
Lastly, we build MISO memory decoding models for the CA1
spatio-temporal patterns predicted by the MIMO signal model,
as opposed to the actual CA1 spatio-temporal patterns. Results
show that the MISO memory decoding models can accurately
predict the spatial memory based on the predicted CA1 patterns
(Figure 8, bottom). The prediction accuracies are 91% and 87.5
for the two cases, respectively. Importantly, the MISO memory
decoding model coefficients remain the same for the actual CA1
patterns and the predicted CA1 patterns. This indicates that the
MIMO signal model has successfully transmitted the spatial infor-
mation from CA3 to CA1 in the same form as it is encoded in
the actual CA1 patterns. The MIMO signal model has not only
restored the signal,butalsore-encoded the memory representations.
SPATIAL INFORMATION IS SPARSELY DISTRIBUTED IN THE
HIPPOCAMPAL CA1 AND CA3 SPATIO-TEMPORAL PATTERNS OF
SPIKES
In order to gain more insights into how hippocampal CA3
and CA1 spike trains encode spatial information, we calculate
Equation (15) and plot the classification weight matrices. These
matrices have the same dimensions as their corresponding spatio-
temporal patterns. In order to perform classification, we can
simply calculate the dot products of the weight matrices and
Frontiers in Systems Neuroscience www.frontiersin.org May 2014 | Volume 8 | Article 97 |6
Song et al. Extraction and restoration of memory with non-linear model
FIGURE 5 | Hippocampal CA3 spatio-temporal patterns from a different animal (case #2).
the corresponding spatio-temporal patterns (strictly speaking, the
dot products of vectorized matrices), add the bias (i.e., w0), and
then use Equation (16) to predict the probability of the ani-
mal having left or right memories. Figure 9 show results of CA3
and CA1 from the two animals. The CA1 weight matrices are
for both the actual and MIMO predicted CA1 spatio-temporal
patterns. In both cases, non-zero values (warm and cold colors
represent positive and negative values, respectively) are sparsely
distributed in the weight matrices. These results indicate that
thespatialinformationexistsinaredundantfashioninmulti-
ple ranges of the perievent intervals of multiple neurons. The
MIMO signal model and the MISO memory decoding model
jointly describe the re-encoding of the memory representations
from CA3 to CA1.
DISCUSSIONS
Brain regions process and transmit information with spatio-
temporal patterns of spikes. In order to build a cortical prosthesis
to bypass a damaged brain region, it is necessary to restore
the output signals of the damaged region and send it to the
downstream region, so the information flow is maintained. We
have shown intensively that non-linear dynamical MIMO models
can predict accurately the output spatio-temporal patterns based
on the ongoing input spatio-temporal patterns, and electrical
stimulations of the output region following the predicted patterns
can effectively restore and even enhance the memory function
(Berger et al., 2011, 2012; Hampson et al., 2012a,b, 2013). The
unique contribution of this paper is to combine the MIMO
models with a new set of MISO memory decoding models so
that the input and output signals can be related to the memory
(behavioral)eventsandthusexplainwhyitispossibleforthe
downstream hippocampal region to correctly decode the MIMO
model generated signals.
In our previous publications on the MIMO signal model (Song
et al., 2006, 2007, 2009a,b, 2011, 2013; Song and Berger, 2010),
the model goodness-of-fit are validated with a Kolmogorov-
Smirnov (KS) test based on the time-rescaling theorem (Brown
et al., 2002; Haslinger et al., 2010). This KS test is a powerful tool
that allows the firing probability intensity function predicted by
the MIMO model to be directly validated with the actual output
spike train, and the model goodness-of-fit to be quantified sta-
tistically with confidence bounds. However, the KS test does not
necessarily indicate whether the model goodness-of-fit is suffi-
cient for decoding the behavior or restoring the cognitive function
since it is developed only for quantifying the accuracy of the pre-
dicted point-process output signal. The typically used 95 or 99%
confidence bounds will not guarantee a successful MIMO model
for building the prosthesis. For example, a perfectly predicted out-
put signal may contain no information about a specific memory
of interest; on the other hand, a less accurately predicted output
signal may still contain some or even sufficient information about
the memory. The MISO memory decoding model described here
directly quantifies the relations between output signals and mem-
ories, and provides a more functionally relevant measure to the
model performance that is complementary to the KS test.
In hippocampal prosthesis applications, MISO memory
decoding models are estimated with input-output data during
the sample phase (−2to2s).Thereasonisthat,intheDNMS
task, animals form the spatial memory (i.e., left or right level
position) during the sample phase, retain the memory during
the delay phase, and recall the memory during the non-match
phase. Previous results have shown that MIMO model-based
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Song et al. Extraction and restoration of memory with non-linear model
FIGURE 6 | Spatio-temporal patterns of spikes in the hippocampal
CA1 (output) region during left and right events of the DNMS. For
each position, the top row shows the actual CA1 spatio-temporal
patterns; the bottom row shows the CA1 spatio-temporal patterns
predicted by the MIMO model based on the ongoing CA3 spiking
activities (case #1).
electrical stimulation restores and enhances the spatial memory
during sample phases but not non-match phases (Berger et al.,
2011, 2012; Hampson et al., 2012a), despite that the MIMO sig-
nal model is able to predict accurately the output signal during
both sample and non-match phases (Song et al., 2011).
Hippocampus is a mainly feedforward network consisting of
a large number of neurons. There are approximately 1 million,
330 thousand, and 420 thousand principal neurons in the rodent
dentate gyrus, CA3, and CA1 regions, respectively (Amaral et al.,
1990). However, despite the small number (tens to a hundred) of
recorded neurons allowed by the current MEA technology, our
hippocampal prosthesis has shown impressive success in both
rodents and non-human primates during the spatial memory
tasks. The main reason is that, at least during the DNMS task or
the delayed match-to-sample (DMS) task, spatial memories (e.g.,
locations of the levels) are encoded in a highly redundant and dis-
tributed fashion in a large portion of the hippocampal neurons.
Asshowninthisstudy,samplingasmallnumberofneuronsfrom
the whole population still allows accurate extraction of spatial
information.
The DNMS task is a highly restricted experimental paradigm
that involves only two positions. Under normal conditions, how-
ever, the animal needs to form much more complex memories
to maintain its normal life (Eichenbaum, 1999). A practical
Frontiers in Systems Neuroscience www.frontiersin.org May 2014 | Volume 8 | Article 97 |8
Song et al. Extraction and restoration of memory with non-linear model
FIGURE 7 | Hippocampal CA1 spatio-temporal patterns (actual and MIMO model predicted) from a different animal (case #2).
hippocampal prosthesis should be able to extract and restore a
large number of memories with the MIMO signal model and
MISO memory decoding model. This will likely require (1)
recording a larger number of hippocampal neurons to obtain
more information necessary for decoding the episodic memo-
ries, (2) stimulating with more electrodes for generating richer
output patterns to the downstream hippocampal region, and (3)
developing more powerful MIMO signal model and MISO mem-
ory decoding model to more accurately restore the output signal
and decode the memories. For example, the current MISO mem-
ory decoding model has binary (left or right) output; in order
to decode more memories, it needs to be extended to handle
multiple-category output. A natural solution is to use multino-
mial logistic regression (McCullagh and Nelder, 1989), instead of
the standard binary-output logistic regression used in this study.
Besides, other forms of discriminative models, e.g., support vec-
tor machine, or generative models, e.g., naive Bayes classifier, may
be considered for their specific advantages. In addition, to collect
input-output data for building multiple-memory models, new
experimental paradigms involving multiple forms of behavioral
events and sensory modalities need to be utilized (Hampson et al.,
2012b). Nonetheless, the study described in the paper for the first
time combines the regression model with the classification model
to illustrate how memory-related information is encoded and re-
encoded in the hippocampus, and has made a critical step toward
building a hippocampal memory prosthesis.
Interestingly, in both cases in this study, the MISO memory
decoding model shows higher prediction accuracy in the CA3
Frontiers in Systems Neuroscience www.frontiersin.org May 2014 | Volume 8 | Article 97 |9
Song et al. Extraction and restoration of memory with non-linear model
FIGURE 8 | Predicting spatial memory events based on inputs (CA3), outputs (CA1), or outputs predicted by the MIMO models (case #1 and #2). The
horizontal lines in the middle represent the decision boundaries (P=0.5).
FIGURE 9 | Sparse classification feature matrices of the MISO memory
decoding models (case #1 and #2). Black color represents zero-valued
weights.
than in the actual CA1, and higher accuracy in the actual CA1
than in the predicted CA1. The latter is unsurprising since the
predicted CA1 patterns are calculated with the MIMO signal
model using the actual CA1 patterns as target signals, although
the real-time calculation is driven by the ongoing CA3 patterns.
It is thus unlikely for the predicted CA1 patterns to contain more
memory-related information than the actual CA1 patterns. The
former observation can be caused by two factors. First, it is pos-
sible that CA3 neurons contain more spatial information than
CA1 neurons as suggested by previous studies (Lee et al., 2004).
Second, it could simply due to the fact that we have recorded more
CA3 units than CA1 units in the two cases included in this study.
A more systematic, comparative study of CA3 and CA1 patterns
needs to be performed to draw further conclusions.
In this study, the MISO memory decoding model takes the
form of a B-spline, logistic regression model. The B-spline basis
functions are utilized to reduce the model dimensionality and
introduce a continuous metric for the similarities between spike
trains. The optimal number of basis functions provides an esti-
mate to the relevant temporal resolution of the spike trains. The
logistic regression maps the spatio-temporal features to the prob-
ability of having a certain behavioral outcome. Despite the rather
general model structure and the high prediction accuracy, how-
ever, this study does not necessarily suggest that the downstream
hippocampal region decodes the CA1 spatio-temporal patterns in
the same way. Instead, the main biological implications of this
study are: first, the CA1 spatio-temporal patterns can be accu-
rately predicted from the CA3 spatio-temporal patterns using a
non-linear dynamical MIMO signal model; second, both CA3
and CA1 patterns contains sufficient information for decoding
the memory events; third, the MIMO-model predicted CA1 pat-
terns also contain sufficient information of the memory, and it
must be this fact that makes the successful implementation of the
hippocampal memory prostheses possible.
Frontiers in Systems Neuroscience www.frontiersin.org May 2014 | Volume 8 | Article 97 |10
Song et al. Extraction and restoration of memory with non-linear model
ACKNOWLEDGMENTS
This work was supported by the Defense Advanced Research
Projects Agency (DARPA) through the Restorative Encoding
Memory Integration Neural Device (REMIND) Program.
REFERENCES
Amaral, D. G., Ishizuka, N., and Claiborne, B. (1990). “Neurons, numbers and
the hippocampal network,” in Progress in Brian Research, Vol 83, eds J. Storm-
Mathisen, J. Zimmer, and O. P. Ottersen (Amsterdam: Elsevier), 1–11.
Berger, T. W., Ahuja, A., Courellis, S. H., Deadwyler, S. A., Erinjippurath, G.,
Gerhardt, G. A., et al. (2005). Restoring lost cognitive function. IEEE Eng. Med.
Biol. Mag. 24, 30–44. doi: 10.1109/MEMB.2005.1511498
Berger, T. W., Hampson, R. E., Song, D., Goonawardena, A., Marmarelis, V. Z.,
and Deadwyler, S. A. (2011). A cortical neural prosthesis for restoring and
enhancing memory. J. Neural Eng. 8, 046017. doi: 10.1088/1741-2560/8/4/
046017
Berger, T. W., Song, D., Chan, R. H. M., and Marmarelis, V. Z. (2010). The neu-
robiological basis of cognition: identification by multi-input, multioutput non-
linear dynamic modeling. Proc. IEEE 98, 356–374. doi: 10.1109/JPROC.2009.
2038804
Berger, T. W., Song, D., Chan, R. H. M., Marmarelis,V. Z., LaCoss, J., Wills, J., et al.
(2012). A hippocampal cognitive prosthesis: multi-input, multi-output nonlin-
ear modeling and VLSI implementation. IEEE Trans. Neural Syst. Rehabil. Eng.
20, 198–211. doi: 10.1109/TNSRE.2012.2189133
Brown, E. N., Barbieri, R., Ventura, V., Kass, R. E., and Frank, L. M. (2002). The
time-rescaling theorem and its application to neural spike train data analysis.
Neural Comput. 14, 325–346. doi: 10.1162/08997660252741149
Deadwyler, S. A., Bunn, T., and Hampson, R. E. (1996). Hippocampal ensem-
ble activity during spatial delayed-nonmatch-to-sample performance in rats.
J. Neurosci. 16, 354–372.
Eichenbaum, H. (1999). The hippocampus and mechanisms of declarative
memory. Behav. Brain Res. 103, 123–133. doi: 10.1016/S0166-4328(99)
00044-3
Hampson, R. E., Gerhardt, G. A., Marmarelis, V. Z., Song, D., Opris, I., Santos,
L., et al. (2012b). Facilitation and restoration of cognitive function in primate
prefrontal cortex by a neuroprosthesis that utilizes minicolumn-specific neural
firing. J. Neural Eng. 9, 056012. doi: 10.1088/1741-2560/9/5/056012
Hampson, R. E., Simeral, J. D., and Deadwyler, S. A. (1999). Distribution of spatial
and nonspatial information in dorsal hippocampus. Nature 402, 610–614. doi:
10.1038/45154
Hampson, R. E., Song, D., Chan, R. H. M., Sweatt, A. J., Fuqua, J., Gerhardt, G. A.,
et al. (2012a). A nonlinear model for cortical prosthetics: memory facilitation
by hippocampal ensemble stimulation. IEEE Trans. Neural Syst. Rehabil. Eng.
20, 184–197. doi: 10.1109/TNSRE.2012.2189163
Hampson, R. E., Song, D., Opris, I., Santos, L., Shin, D., Gerhardt, G. A., et al.
(2013). Facilitation of memory encoding in primate hippocampus by a neuro-
prosthesis that promotes task specific neural firing. J. Neural Eng. 10, 066013.
doi: 10.1088/1741-2560/10/6/066013
Haslinger, R., Pipa, G., and Brown, E. (2010). Discrete time rescaling theorem:
determining goodness of fit for discrete time statistical models of neural spiking.
Neural Comput. 22, 2477–2506. doi: 10.1162/NECO_a_00015
Hochberg, L. R., Serruya, M. D., Friehs, G. M., Mukand, J. A., Saleh, M., Caplan, A.
H., et al. (2006). Neuronal ensemble control of prosthetic devices by a human
with tetraplegia. Nature 442, 164–171. doi: 10.1038/nature04970
Humayun, M. S., de Juan, E., Weiland, J. D., Dagnelie, G., Katona, S., Greenberg,
R., et al. (1999). Pattern electrical stimulation of the human retina. Vision Res.
39, 2569–2576. doi: 10.1016/S0042-6989(99)00052-8
Lee, I., Yoganarasimha, D., Rao, G., and Knierim, J. J. (2004). Comparison of pop-
ulation coherence of place cells in hippocampal subfields CA1 and CA3. Nature
430, 456–459. doi: 10.1038/nature02739
Loeb, G. E. (1990). Cochlear Prosthetics. Annu. Rev. Neurosci. 13, 357–371. doi:
10.1146/annurev.ne.13.030190.002041
Mauritz, K. H., and Peckham, H. P. (1987). Restoration of grasping functions in
quadriplegic patients by Functional Electrical Stimulation (FES). Int. J. Rehabil.
Res. 10, 57–61. doi: 10.1097/00004356-198712005-00010
McCullagh, P., and Nelder, J. A. (1989). Generalized Linear Models.BocaRaton,FL:
Chapman & Hall/CRC. doi: 10.1007/978-1-4899-3242-6
Milner, B. (1970). “Memory and the medial temporal regions of the brain,” in
Biology of Memory edsK.H.PribramandD.E.Broadbent(NewYork,NY:
Academic Press), 29–50.
Nicolelis, M. A. L. (2003). Brain-machine interfaces to restore motor function and
probe neural circuits. Nat. Rev. Neurosci. 4, 417–422. doi: 10.1038/nrn1105
Shenoy, K. V., Meeker, D., Cao, S. Y., Kureshi, S. A., Pesaran, B., Buneo, C. A.,
et al. (2003). Neural prosthetic control signals from plan activity. Neuroreport
14, 591–596. doi: 10.1097/00001756-200303240-00013
Song, D., and Berger, T. W. (2010). “Identification of nonlinear dynamics in
neural population activity,” in Statistical Signal Processing for Neuroscience
and Neurotechnology ed K. G. Oweiss (Amsterdam: Elsevier), 103–128. doi:
10.1016/B978-0-12-375027-3.00004-1
Song,D.,Chan,R.H.,Marmarelis,V.Z.,Hampson,R.E.,Deadwyler,S.A.,
and Berger, T. W. (2007). Nonlinear dynamic modeling of spike train trans-
formations for hippocampal-cortical prostheses. IEEE Trans. Biomed. Eng. 54,
1053–1066. doi: 10.1109/TBME.2007.891948
Song,D.,Chan,R.H.M.,Marmarelis,V.Z.,Hampson,R.E.,Deadwyler,S.A.,
and Berger, T. W. (2006). Physiologically plausible stochastic nonlinear kernel
models of spike train to spike train transformation. Conf. Proc. IEEE Eng. Med.
Biol. Soc. 1, 6129–6132. doi: 10.1109/IEMBS.2006.259253
Song,D.,Chan,R.H.M.,Marmarelis,V.Z.,Hampson,R.E.,Deadwyler,
S. A., and Berger, T. W. (2009a). Nonlinear modeling of neural popula-
tion dynamics for hippocampal prostheses. Neural Netw. 22, 1340–1351. doi:
10.1016/j.neunet.2009.05.004
Song,D.,Chan,R.H.M.,Marmarelis,V.Z.,Hampson,R.E.,Deadwyler,S.A.,
and Berger, T. W. (2009b). Sparse generalized Laguerre-Volterra model of neural
population dynamics. Conf. Proc. IEEE Eng. Med. Biol. Soc. 2009, 4555–4558.
doi: 10.1109/IEMBS.2009.5332719
Song,D.,Chan,R.H.M.,Marmarelis,V.Z.,Hampson,R.E.,Deadwyler,
S. A., and Berger, T. W. (2011). Estimation and statistical validation of
event-invariant nonlinear dynamic models of hippocampal CA3-CA1 popu-
lation activities. Conf.Proc.IEEEEng.Med.Biol.Soc.2011, 3330–3333. doi:
10.1109/IEMBS.2011.6090903
Song, D., Marmarelis, V. Z., and Berger, T. W. (2009d). Parametric and non-
parametric modeling of short-term synaptic plasticity. Part II: experimental
study. J. Comput. Neurosci. 26, 21–37. doi: 10.1007/s10827-008-0098-2
Song, D., Wang, H., Tu, C. Y., Marmarelis, V. Z., Hampson, R. E., Deadwyler, S.
A., et al. (2013). Identification of sparse neural functional connectivity using
penalized likelihood estimation and basis functions. J. Comput. Neurosci. 35,
335–357. doi: 10.1007/s10827-013-0455-7
Song, D., Wang, Z., Marmarelis, V. Z., and Berger, T. W. (2009c). Parametric and
non-parametric modeling of short-term synaptic plasticity. Part I: computa-
tional study. J. Comput. Neurosci. 26, 1–19. doi: 10.1007/s10827-008-0097-3
Squire, L. R., and Zola-Morgan, S. (1991). The medial temporal lobe memory
system. Science 253, 1380–1386. doi: 10.1126/science.1896849
Taylor, D. M., Tillery, S. I. H., and Schwartz, A. B. (2002). Direct cortical con-
trol of 3D neuroprosthetic devices. Science 296, 1829–1832. doi: 10.1126/sci-
ence.1070291
Wolpaw, J. R., and McFarland, D. J. (2004). Control of a two-dimensional move-
ment signal by a noninvasive brain-computer interface in humans. Proc. Natl.
Acad.Sci.U.S.A.101, 17849–17854. doi: 10.1073/pnas.0403504101
Conflict of Interest Statement: The authors declare that the research was con-
ducted in the absence of any commercial or financial relationships that could be
construed as a potential conflict of interest.
Received: 26 February 2014; accepted: 06 May 2014; published online: 28 May 2014.
Citation: Song D, Harway M, Marmarelis VZ, Hampson RE, Deadwyler SA and
Berger TW (2014) Extraction and restoration of hippocampal spatial memories
with non-linear dynamical modeling. Front. Syst. Neurosci. 8:97. doi: 10.3389/fnsys.
2014.00097
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