indii::fmri::hemodynamic::NeuralBalloonModel

NeuralBalloonModel Class Reference

Inherits BalloonModel.

Inheritance diagram for NeuralBalloonModel:

Inheritance graph
[legend]
List of all members.

Detailed Description

Balloon model driven by neural activity.

Author:
Lawrence Murray <lawrence@indii.org>
Version:
Rev
285
Date:
Date
2007-07-20 17:25:40 +0100 (Fri, 20 Jul 2007)
This class extends FlowBalloonModel to be driven by neural activity rather than blood flow, as proposed in Friston et al. (2000), and further described in Friston et al. (2003).

The model couples neural activity to blood flow via an additional vasodilatory signal $s$, which encapsulates a range of biological processes.

Details

The state variables $q$ and $v$ of FlowBalloonModel are extended to include $f \equiv f_{in}(t)$ and $s$, the vasodilatory signal. The system of differential equations then includes all four of these state variables:

\begin{eqnarray*} \frac{df}{dt} &=& s \\ \frac{ds}{dt} &=& \epsilon u(t) - \frac{s}{\tau_s} - \frac{(f-1)}{\tau_f} \\ \frac{dq}{dt} &=& \frac{1}{\tau_0}\left[ f\frac{E(t)}{E_0} - f_{out}(v)\frac{q(t)}{v(t)} \right] \\ \frac{dv}{dt} &=& \frac{1}{\tau_0}\left[ f - f_{out}(v) \right] \end{eqnarray*}

The effect of this is that the model becomes driven by the new function $u(t)$, representing neural activity, rather than the flow function $f_{in}(t)$.

Singularities are handled in the same fashion as FlowBalloonModel.

Usage

The model is used in the same way as FlowBalloonModel. Rather than creating your own function to replace FlowBalloonModel::F_IN and drive the system, however, create your own function to replace NeuralBalloonModel::U instead.

Definition at line 61 of file NeuralBalloonModel.hpp.

Public Types

enum  StateVariable { Q, V, F, S }
 State variables. More...
enum  BiophysicalParameter {
  V_0, E_0, TAU_0, ALPHA,
  EPSILON, TAU_S, TAU_F
}
 Parameter indices. More...
enum  BiophysicalFunction { F_IN, F_OUT, E, U }
 Function indices. More...

Public Member Functions

 NeuralBalloonModel ()
 Create new model with default biophysical parameters and functions as defined in NeuralBalloonModelDefaults and FlowBalloonModelDefaults.
virtual ~NeuralBalloonModel ()
 Destructor.
virtual indii::ml::aux::vector suggestInitialState ()
 Provide a suggested initial state.
virtual void calculateDerivatives (double t, const double y[], double dydt[])
 
See also:
indii::ml::ode::DifferentialModel

Member Enumeration Documentation

enum StateVariable

State variables.

Enumerator:
Q  $q = \frac{Q(t)}{Q_0}$; normalised dHb content of venous compartment at the current time.
V  $v = \frac{V(t)}{V_0}$; normalised volume of the venous compartment at the current time.
F  $\dot{f_{in}} = \frac{F_{in}(t)}{F_0}$; normalised flow into the venous compartment.
S  $s$; flow inducing signal.

Definition at line 66 of file NeuralBalloonModel.hpp.

enum BiophysicalParameter

Parameter indices.

The first part of this enum matches that of FlowBalloonModel for consistency.

Enumerator:
V_0  $V_0$; volume of the venous compartment at rest.
E_0  $E_0$; oxygen extraction rate of the venous compartment at rest.
TAU_0  $\tau_0 = \frac{V_0}{F_0}$; mean transit time through the venous compartment at rest.
ALPHA  $\alpha$; Grubb's exponent.
EPSILON  $\epsilon$; efficacy with which neural activity causes an increase in signal.
TAU_S  $\tau_s$; time constant for signal decay.

Note that $\tau_s$ in Friston et al. (2000) equals $\frac{1}{\kappa}$ in Friston et al. (2003).

TAU_F  $\tau_f$; time constant for autoregulatory feedback from blood flow.

Note that $\tau_f$ in Friston et al. (2000) equals $\frac{1}{\gamma}$ in Friston et al. (2003).

Definition at line 95 of file NeuralBalloonModel.hpp.

enum BiophysicalFunction

Function indices.

The first part of this enum matches that of FlowBalloonModel for consistency.

Enumerator:
F_IN  $f_{in}(t) = \frac{F_{in}(t)}{F_0}$; normalised flow into the venous compartment.
F_OUT  $f_{out}(t) = \frac{F_{out}(t)}{F_0}$; normalised flow out of the venous compartment.
E  $E(t)$; oxygen extraction rate of the venous compartment.
U  $u(t)$; neural activity.

Definition at line 144 of file NeuralBalloonModel.hpp.

Constructor & Destructor Documentation

NeuralBalloonModel (  ) 

Create new model with default biophysical parameters and functions as defined in NeuralBalloonModelDefaults and FlowBalloonModelDefaults.

Definition at line 16 of file NeuralBalloonModel.cpp.

~NeuralBalloonModel (  )  [virtual]

Destructor.

Definition at line 34 of file NeuralBalloonModel.cpp.

Member Function Documentation

aux::vector suggestInitialState (  )  [virtual]

Provide a suggested initial state.

This can be passed to the constructor of the ordinary differential equation solver being used on the model, such as indii::ml::ode::AdaptiveRungeKutta.

Returns:
Suggested initial state for the system.

Implements BalloonModel.

Definition at line 82 of file NeuralBalloonModel.cpp.

void calculateDerivatives ( double  t,
const double  y[],
double  dydt[] 
) [virtual]

See also:
indii::ml::ode::DifferentialModel

Definition at line 38 of file NeuralBalloonModel.cpp.

The documentation for this class was generated from the following files:
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