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Mathematical Modeling of Brain Circuitry
case of the brain, this function is carried out by a limited set of neuron types,
which typically can have relatively simple internal circuitry connectivity.
Conversely, a mathematical problem formulation of optimal control problem and related adaptive control with tentative solutions was published in
Johansson (1990a, 1990b).
In the present study, we aim to provide a mathematical description of the
function of one of these functional subunits, namely, the cuneate nucleus, which
carries out the first-order processing of movement-generated sensory feedback.
We illustrate the firing patterns of the primary afferents, main cuneate neurons,
and local inhibitory interneurons and how system identification methods can
be used to obtain a mathematical expression of the function carried out by the
cuneate nucleus. In ongoing work, we also simulate in detail how the underlying neuronal information processing is carried out, with the aim of providing
neuroscientific correlates for specific features in these mathematical expressions.
14.2 Problem Formulation
Because our approach rests on the understanding of the biological system,
that is, the brain, much work needed to be devoted the collection of the
biological data. The data collection should be from primary afferents; that
is, nerve fibers that mediate sensory input from peripheral receptors to the
central nervous system, from the main neurons of the cuneate, which project the processed sensory information to the cerebellum (Bengtsson and
Jörntell 2009). Ideally, we should record from the primary afferent and its
target cuneate neuron simultaneously, but this is technically very difficult.
An approximation is to record from primary afferents and cuneate neurons
driven by the same inputs. To compare the primary afferent data with the
data from the cuneate neurons, comparisons should only be made between
primary afferents and neurons that are activated by the same modality of
sensory information and from sensory input activated from the same topological area (on the skin or in the joints/muscles). If we can fulfill these
criteria, we can take advantage of previous findings suggesting that single primary afferents can have a dominant influence on the cuneate neuron (Ferrington, Rowe, and Tarvin 1987). The transformation taking place
between the primary afferent input and the cuneate neuron output for a
given stimulus can then be characterized through system identification.
In order to verify that the mathematical model obtained accurately represents the transformation between the primary afferent and the cuneate neuron in the more general case, data from both the primary afferent and cuneate
neuron should also be obtained from a very different type of stimulus. If the
mathematical model is correct, it should also be able to reproduce the input–
output transformation in this case.
Mathematical Modeling of Brain Circuitry
case of the brain, this function is carried out by a limited set of neuron types,
which typically can have relatively simple internal circuitry connectivity.
Conversely, a mathematical problem formulation of optimal control problem and related adaptive control with tentative solutions was published in
Johansson (1990a, 1990b).
In the present study, we aim to provide a mathematical description of the
function of one of these functional subunits, namely, the cuneate nucleus, which
carries out the first-order processing of movement-generated sensory feedback.
We illustrate the firing patterns of the primary afferents, main cuneate neurons,
and local inhibitory interneurons and how system identification methods can
be used to obtain a mathematical expression of the function carried out by the
cuneate nucleus. In ongoing work, we also simulate in detail how the underlying neuronal information processing is carried out, with the aim of providing
neuroscientific correlates for specific features in these mathematical expressions.
14.2 Problem Formulation
Because our approach rests on the understanding of the biological system,
that is, the brain, much work needed to be devoted the collection of the
biological data. The data collection should be from primary afferents; that
is, nerve fibers that mediate sensory input from peripheral receptors to the
central nervous system, from the main neurons of the cuneate, which project the processed sensory information to the cerebellum (Bengtsson and
Jörntell 2009). Ideally, we should record from the primary afferent and its
target cuneate neuron simultaneously, but this is technically very difficult.
An approximation is to record from primary afferents and cuneate neurons
driven by the same inputs. To compare the primary afferent data with the
data from the cuneate neurons, comparisons should only be made between
primary afferents and neurons that are activated by the same modality of
sensory information and from sensory input activated from the same topological area (on the skin or in the joints/muscles). If we can fulfill these
criteria, we can take advantage of previous findings suggesting that single primary afferents can have a dominant influence on the cuneate neuron (Ferrington, Rowe, and Tarvin 1987). The transformation taking place
between the primary afferent input and the cuneate neuron output for a
given stimulus can then be characterized through system identification.
In order to verify that the mathematical model obtained accurately represents the transformation between the primary afferent and the cuneate neuron in the more general case, data from both the primary afferent and cuneate
neuron should also be obtained from a very different type of stimulus. If the
mathematical model is correct, it should also be able to reproduce the input–
output transformation in this case.