84
Y. Zhang
head. In previous chapters, we have addressed how EEG signals arise from the dipole
moments of synaptic communication. We have also addressed how EEG signals are
presented and detected. Calculating cortical source then requires us to mathematically
determine the relationship between our synaptic signals and the recorded potentials.
This will require us to give more attention to the biological environment of cortical activity, as well as the layers separating that source origin from the sensors on
the scalp. By understanding these, we open the pathway to perform accurate electrical source imaging. Once we have this understanding, we can continue forward
into the variety of methods that have been developed to observe brain activity and
how EEG source analysis can interact with other imaging modalities to enhance our
results. Finally, though the discussion below will focus on EEG-based source localization, it is important to acknowledge the process and principles described here are
not exclusive and can be expanded for use with other modalities as well, such as
electrocorticography (ECoG) [85] and electromyography (EMG) [50, 68, 86, 87].
5.1 From the Brain to the Scalp—The Forward Problem
When seeking to perform source analysis, the task can be broken down into two
major parts: (i) the Forward Problem, which models the transference of putative
source activity through the head to the scalp electrodes; and (ii) the Inverse Problem,
which uses the information provided by the forward problem to identify the most
likely locations and strengths of cortical activity. As mentioned above, we will begin
with the cortical sources within the context of their conductive environment. From
there, the discussion will build outward through the biological tissues to the scalp
detection. At that point, we will finally be able to invert our process to observe the
activity of unknown cortical sources.
5.1.1 Volume Source and the Poisson’s Equation
Let us first examine an active synapse, wherein a pre-synaptic axon is communicating with a post-synaptic dendrite. The small volume enclosing this synapse can be
assigned an overall current density J. The electrical model for the neuronal activity
can then be described using two current monopoles: (i) a current source at the axon
of a cell that injects positive ions into the extracellular space and (ii) a current sink at
the coinciding dendrite that removes positive ions from the extracellular space [38].
Over time, the net current entering and leaving this volume must be zero to ensure
that charge does not amass in the extracellular space, thus, ∇ · J 0.
This current density J comprises the primary current J p (also known as the
impressed current) [54] and the volume current J v (also known as the return current) [54]. The primary current is generated by the movement of ions across the
Y. Zhang
head. In previous chapters, we have addressed how EEG signals arise from the dipole
moments of synaptic communication. We have also addressed how EEG signals are
presented and detected. Calculating cortical source then requires us to mathematically
determine the relationship between our synaptic signals and the recorded potentials.
This will require us to give more attention to the biological environment of cortical activity, as well as the layers separating that source origin from the sensors on
the scalp. By understanding these, we open the pathway to perform accurate electrical source imaging. Once we have this understanding, we can continue forward
into the variety of methods that have been developed to observe brain activity and
how EEG source analysis can interact with other imaging modalities to enhance our
results. Finally, though the discussion below will focus on EEG-based source localization, it is important to acknowledge the process and principles described here are
not exclusive and can be expanded for use with other modalities as well, such as
electrocorticography (ECoG) [85] and electromyography (EMG) [50, 68, 86, 87].
5.1 From the Brain to the Scalp—The Forward Problem
When seeking to perform source analysis, the task can be broken down into two
major parts: (i) the Forward Problem, which models the transference of putative
source activity through the head to the scalp electrodes; and (ii) the Inverse Problem,
which uses the information provided by the forward problem to identify the most
likely locations and strengths of cortical activity. As mentioned above, we will begin
with the cortical sources within the context of their conductive environment. From
there, the discussion will build outward through the biological tissues to the scalp
detection. At that point, we will finally be able to invert our process to observe the
activity of unknown cortical sources.
5.1.1 Volume Source and the Poisson’s Equation
Let us first examine an active synapse, wherein a pre-synaptic axon is communicating with a post-synaptic dendrite. The small volume enclosing this synapse can be
assigned an overall current density J. The electrical model for the neuronal activity
can then be described using two current monopoles: (i) a current source at the axon
of a cell that injects positive ions into the extracellular space and (ii) a current sink at
the coinciding dendrite that removes positive ions from the extracellular space [38].
Over time, the net current entering and leaving this volume must be zero to ensure
that charge does not amass in the extracellular space, thus, ∇ · J 0.
This current density J comprises the primary current J p (also known as the
impressed current) [54] and the volume current J v (also known as the return current) [54]. The primary current is generated by the movement of ions across the