264
Biologically Inspired Robotics
incoming and outgoing signals of individual neurons during sensory
activation as well as a recently obtained microcircuitry characterization
for this structure. We find that system identification is a useful way to
find suitable mathematical models that capture the properties and transformation capabilities of the neuronal microcircuitry that constitutes the
cuneate nucleus. Future work will show whether specific aspects of the
mathematical properties can be ascribed to a specific microcircuitry
and/or neuronal property.
14.1 Introduction
In order to understand and describe how the brain organizes limb movement control, we aim to design a mathematical model of this control. The
study is based on a comprehensive neurophysiological characterization of
the cerebellar system for voluntary arm–hand control as described in Apps
and Garwicz (2005). This system may be viewed as a vast network of interconnected neurons that involves many parts of the brain, which all are interconnected through a specific area of the cerebellum (Bengtsson and Jörntell
2009; Jörntell and Ekerot 1999). A foundation for the model system is a previous, detailed characterization of all constituent neuron types and a systematic description of connectivity patterns both within the cerebellum and in
those brain regions outside the cerebellum, which are part of the network
devoted to this specific control as shown in previous publications from our
group (Bengtsson and Jörntell 2009; Ekerot and Jörntell 2001, 2003; Jörntell
and Ekerot 2002, 2006; Jörntell and Hansel 2006).
As for detailed electrophysiological neuron modeling, the Goldman–
Hodgkin–Katz voltage equation (or the Goldman equation) is the standard
model used in cell membrane physiology to determine the equilibrium
potential across a cell membrane, taking into account all of the relevant ion
species active through that membrane (Junge 1981).
Brain function may be viewed as a result of the transformation functions
of individual neurons and their precise interconnections. However, the network of neurons that constitute the brain is very well organized into discrete
subcomponents. Each subcomponent is connected to a limited set of other
subcomponents in specific, well-conserved connectivity patterns. Viewed in
this way, it is possible to make a control system-inspired interpretation of the
function of the brain in movement control (Fujita 1982; Ito 1972; Kawato and
Gomi 1992; Miall and Wolpert 1996; Schweighofer, Arbib, and Kawato 1998;
Schweighofer et al. 1998; Wolpert, Miall, and Kawato 1998) and we can interpret the neuronal system for arm–hand movement control as being organized
into a number of distinct functional units, in a similar fashion as a control
system. Each functional unit, or subcomponent of brain circuitry, hence has
a specific function, which can be expressed in mathematical terms. In the
Biologically Inspired Robotics
incoming and outgoing signals of individual neurons during sensory
activation as well as a recently obtained microcircuitry characterization
for this structure. We find that system identification is a useful way to
find suitable mathematical models that capture the properties and transformation capabilities of the neuronal microcircuitry that constitutes the
cuneate nucleus. Future work will show whether specific aspects of the
mathematical properties can be ascribed to a specific microcircuitry
and/or neuronal property.
14.1 Introduction
In order to understand and describe how the brain organizes limb movement control, we aim to design a mathematical model of this control. The
study is based on a comprehensive neurophysiological characterization of
the cerebellar system for voluntary arm–hand control as described in Apps
and Garwicz (2005). This system may be viewed as a vast network of interconnected neurons that involves many parts of the brain, which all are interconnected through a specific area of the cerebellum (Bengtsson and Jörntell
2009; Jörntell and Ekerot 1999). A foundation for the model system is a previous, detailed characterization of all constituent neuron types and a systematic description of connectivity patterns both within the cerebellum and in
those brain regions outside the cerebellum, which are part of the network
devoted to this specific control as shown in previous publications from our
group (Bengtsson and Jörntell 2009; Ekerot and Jörntell 2001, 2003; Jörntell
and Ekerot 2002, 2006; Jörntell and Hansel 2006).
As for detailed electrophysiological neuron modeling, the Goldman–
Hodgkin–Katz voltage equation (or the Goldman equation) is the standard
model used in cell membrane physiology to determine the equilibrium
potential across a cell membrane, taking into account all of the relevant ion
species active through that membrane (Junge 1981).
Brain function may be viewed as a result of the transformation functions
of individual neurons and their precise interconnections. However, the network of neurons that constitute the brain is very well organized into discrete
subcomponents. Each subcomponent is connected to a limited set of other
subcomponents in specific, well-conserved connectivity patterns. Viewed in
this way, it is possible to make a control system-inspired interpretation of the
function of the brain in movement control (Fujita 1982; Ito 1972; Kawato and
Gomi 1992; Miall and Wolpert 1996; Schweighofer, Arbib, and Kawato 1998;
Schweighofer et al. 1998; Wolpert, Miall, and Kawato 1998) and we can interpret the neuronal system for arm–hand movement control as being organized
into a number of distinct functional units, in a similar fashion as a control
system. Each functional unit, or subcomponent of brain circuitry, hence has
a specific function, which can be expressed in mathematical terms. In the