indii/fmri/hemodynamic/LogFlowBalloonModel.hpp

#ifndef INDII_FMRI_HEMODYNAMIC_LOGFLOWBALLOONMODEL_HPP
#define INDII_FMRI_HEMODYNAMIC_LOGFLOWBALLOONMODEL_HPP

#include "BalloonModel.hpp"
#include "indii/ml/aux/vector.hpp"

namespace indii {
  namespace fmri {
    namespace hemodynamic {

/**
 * Balloon %model driven by blood flow, and working in log space.
 *
 * @author Lawrence Murray <lawrence@indii.org>
 * @version $Rev: 285 $
 * @date $Date: 2007-07-20 17:25:40 +0100 (Fri, 20 Jul 2007) $
 *
 * This class modifies FlowBalloonModel so that \f$v\f$ and \f$q\f$
 * vary in log space as:
 *
 * @anchor LogFlowBalloonModel_diffsystem
 * \f{eqnarray*}
 *   \frac{d \ln q}{dt} &=& \frac{\dot{q}}{q} \\
 *   \frac{d \ln v}{dt} &=& \frac{\dot{v}}{v}
 * \f}
 *
 * References to \f$q\f$ and \f$v\f$ in biophysical functions are
 * substituted with the identities \f$q = e^{\ln q} \f$ and \f$v =
 * e^{\ln v}\f$.
 *
 * Working in log space ensures that \f$q\f$ and \f$v\f$ are always
 * positive. This is particularly important in a stochastic setting,
 * where noise may otherwise cause them to become negative, such as in
 * the case of the Wiener process or discretised Gaussian
 * noise. Introducing such noise into the log space instead ensures
 * positivity.
 *
 * @see FlowBalloonModel for more information on the usage of this
 * %model.
 */
class LogFlowBalloonModel : public BalloonModel {
public:
  /**
   * State variables.
   */
  enum StateVariable {
    /**
     * \f$\ln(q) = \ln\left(\frac{Q(t)}{Q_0}\right)\f$; natural
     * logarithm of the normalised dHb content at the current time.
     */
    LN_Q,

    /**
     * \f$\ln(v) = \ln\left(\frac{V(t)}{V_0}\right)\f$; natural
     * logarithm of the normalised volume at the current time.
     */
    LN_V
  };

  /**
   * Parameter indices. These match those of FlowBalloonModel for
   * consistency.
   */
  enum BiophysicalParameter {
    /**
     * \f$V_0\f$; volume of the venous compartment at rest.
     */
    V_0,
  
    /**
     * \f$E_0\f$; oxygen extraction rate of the venous compartment at
     * rest.
     */
    E_0,

    /**
     * \f$\tau_0 = \frac{V_0}{F_0}\f$; mean transit time through the
     * venous compartment at rest.
     */
    TAU_0,

    /**
     * \f$\alpha\f$; Grubb's exponent.
     */
    ALPHA
  };

  /**
   * Function indices. These match those of FlowBalloonModel for
   * consistency.
   */
  enum BiophysicalFunction {
    /**
     * \f$f_{in}(t) = \frac{F_{in}(t)}{F_0}\f$; normalised flow into
     * the venous compartment.
     */
    F_IN,

    /**
     * \f$f_{out}(t) = \frac{F_{out}(t)}{F_0}\f$; normalised flow out
     * of the venous compartment.
     */
    F_OUT,

    /**
     * \f$E(t)\f$; oxygen extraction rate of the venous compartment.
     */
    E
  };

  /**
   * Create new %model with default biophysical parameters and
   * functions as defined in LogFlowBalloonModelDefaults and
   * FlowBalloonModelDefaults.
   */
  LogFlowBalloonModel();

  /**
   * Destructor.
   */
  virtual ~LogFlowBalloonModel();

  virtual indii::ml::aux::vector suggestInitialState();

  /**
   * @see indii::ml::ode::DifferentialModel
   */
  virtual void calculateDerivatives(double t, const double y[], double dydt[]);

private:
  /**
   * Number of state variables.
   */
  static const unsigned int DIMENSIONS = 2;

  /**
   * Number of parameters.
   */
  static const unsigned int NUM_PARAMETERS = 4;

  /**
   * Number of functions.
   */
  static const unsigned int NUM_FUNCTIONS = 3;

};

    }
  }
}

#endif

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