indii/fmri/hemodynamic/FlowBalloonModelDefaults.hpp

#ifndef INDII_FMRI_HEMODYNAMIC_FLOWBALLOONMODELDEFAULTS_HPP
#define INDII_FMRI_HEMODYNAMIC_FLOWBALLOONMODELDEFAULTS_HPP

#include "indii/ml/ode/FunctionStatic.hpp"

namespace indii {
  namespace fmri {
    namespace hemodynamic {

/**
 * Default biophysical parameter and function settings for
 * FlowBalloonModel. These defaults are based on values given in @ref
 * Buxton1998 "Buxton et al. (1998)" and @ref Friston2003
 * "Friston et al. (2003)".
 *
 * @author Lawrence Murray <lawrence@indii.org>
 * @version $Rev: 285 $
 * @date $Date: 2007-07-20 17:25:40 +0100 (Fri, 20 Jul 2007) $
 */
class FlowBalloonModelDefaults {
public:
  /**
   * \f$V_0\f$; volume of the venous compartment at rest.
   */
  static const double V_0;

  /**
   * \f$E_0\f$; oxygen extraction rate of the venous compartment at
   * rest.
   */
  static const double E_0;

  /**
   * \f$\tau_0\f$; mean transit time through the
   * venous compartment at rest.
   */
  static const double TAU_0;

  /**
   * \f$\alpha\f$; Grubb's exponent.
   */
  static const double ALPHA;

  /**
   * \f$f_{in}(t) = 1\f$; normalised flow into the venous compartment.
   */
  static indii::ml::ode::f_t F_IN;

  /**
   * \f$f_{out}(t) = v^{1/\alpha}\f$; normalised flow out of the
   * venous compartment.
    */
  static indii::ml::ode::f_t F_OUT;

  /**
   * \f$E(t) \approx 1 - (1 - E_0)^{1/f_{in}(t)}\f$; oxygen extraction
   * rate of the venous compartment.
   */
  static indii::ml::ode::f_t E;

  /**
   * \f[
   * \frac{dq}{dt} = \left\{
   *   \begin{array}{lcc}
   *     \frac{1}{\tau_0}\left[f_{in}(t)\frac{E(t)}{E_0} -
   *       f_{out}(v)\frac{q}{v}\right] & v \neq 0 & f_{in}(t) \neq 0 \\
   *     -\frac{qf_{out}(v)}{\tau_0v} & v \neq 0 & f_{in}(t) = 0 \\
   *     \frac{f_{in}(t)}{\tau_0} & v = 0 & f_{in}(t) \neq 0 \\
   *     0 & v = 0 & f_{in}(t) = 0 \\
   *   \end{array}\right\}
   * \f]; differential equation. Singularities are handled by taking
   * the limit of the function in a manner consistent with @ref
   * Riera2004 "Riera et al. (2004)".
   */
  static indii::ml::ode::f_t DQDT;

  /**
   * \f$\frac{dv}{dt} = \frac{1}{\tau_0}\left[
   *     f_{in}(t) - f_{out}(v)
   *     \right]
   * \f$; differential equation.
   */
  static indii::ml::ode::f_t DVDT;

};

    }
  }
}

#endif

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