ChamberSphere.h

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// SPDX-FileCopyrightText: Copyright (c) Stanford University, The Regents of the
// University of California, and others. SPDX-License-Identifier: BSD-3-Clause
/**
 * @file ChamberSphere.h
 * @brief model::ChamberSphere source file
 */
#ifndef SVZERODSOLVER_MODEL_ChamberSphere_HPP_
#define SVZERODSOLVER_MODEL_ChamberSphere_HPP_
 
#include <math.h>
 
#include <map>
#include <memory>
#include <string>
 
#include "ActivationFunction.h"
#include "ActiveStress.h"
#include "Block.h"
#include "SparseSystem.h"
#include "SphereMaterial.h"
 
/**
 * @brief Spherical heart chamber model
 *
 * Models the mechanical behavior of a spherical heart chamber with active
 * contraction. For reference, see \cite caruel13 Equations (13a-b) for
 * continuum mechanics (without length-dependent contraction valves, vessels)
 * and \cite pfaller2019importance Equations (12-16) for the simplified active
 * contraction model.
 *
 * ### Helper Functions
 *
 * Cauchy-Green deformation tensor and time derivative:
 * \f[
 * C = \left(1 + \frac{r}{r_0} \right)^2
 * \f]
 * \f[
 * \dot{C} = 2 \left(1 + \frac{r}{r_0} \right) \frac{\dot{r}}{r_0}
 * \f]
 *
 * ### Governing equations
 *
 * 1. Balance of linear momentum:
 * \f[
 * \rho d_0 \dot{v} + \frac{d_0}{r_0} \left(1 + \frac{r}{r_0} \right) S -
 P_\text{out} C = 0
 * \f]
 *
 * 2. Spherical stress:
 * \f[
 * -S + \tau + S_\text{el}(r, r_0) + \eta \dot{C}
 * (1 + 2 C^{-6}) = 0
 * \f]
 * where \f$S_\text{el}\f$ is the elastic stress term supplied by the
 * chamber's \ref SphereMaterial.
 *
 * 3. Volume change:
 * \f[
 * 4 \pi r_0^2 Cv - \dot{V} = 0
 * \f]
 *
 * 4. Active stress:
 * \f[
 * \tau = \tau(t, r, r_0, \dots)
 * \f]
 * the specific form of which (and any accompanying internal state and
 * equations) is supplied by a separate \ref ActiveStress object (e.g.
 * `strain_independent`, `strain_dependent`) selected in the JSON
 * configuration. The active stress model is driven by the chamber's
 * \ref ActivationFunction (e.g. `two_hill`, `half_cosine`, `piecewise_cosine`,
 * `piecewise_rate`), also selected in the JSON configuration.
 *
 * 5. Acceleration:
 * \f[
 * \dot{r} - v = 0
 * \f]
 *
 * 6. Conservation of mass:
 * \f[
 * Q_\text{in} - Q_\text{out} - \dot{V} = 0
 * \f]
 *
 * 7. Pressure equality:
 * \f[
 * P_\text{in} - P_\text{out} = 0
 * \f]
 *
 * ### Parameters
 *
 * Parameter sequence for constructing this block:
 *
 * * `rho` - Density \f$\rho\f$
 * * `thick0` - Wall thickness \f$d_0\f$
 * * `radius0` - Reference radius \f$r_0\f$
 * * `eta` - Viscosity parameter \f$\eta\f$
 *
 * An `activation_function` object is also required alongside
 * `zero_d_element_values` to select and parameterize the activation function
 * \f$f(t)\f$ (see \ref ActivationFunction, e.g. `two_hill`, `half_cosine`,
 * `piecewise_cosine`, `wrapping_cosine`, `fourier`, `double_tanh`,
 * `piecewise_rate`).
 *
 * Furthermore, a `material` object is required to select and parameterize
 * the material model for the elastic stress term \f$S_\text{el}(r, r_0)\f$
 * (see \ref SphereMaterial, e.g. `exponential`, `mooney_rivlin`).
 *
 * Finally, an `active_stress` object is required to select and parameterize
 * the active stress model (see \ref ActiveStress, e.g. `strain_independent`,
 * `strain_dependent`).
 *
 * ### Usage in json configuration file
 *
 *     "chambers": [
 *        {
 *            "type": "ChamberSphere",
 *            "name": "ventricle",
 *            "values": {
 *                "rho" : 1e3,
 *                "thick0" : 0.01,
 *                "radius0" : 0.05,
 *                "eta" : 10.0
 *            },
 *            "activation_function": {},
 *            "material": {},
 *            "active_stress": {}
 *        }
 *     ]
 *
 * A chamber is connected to the rest of the circuit via valve blocks (see
 * \ref ValveTanh, \ref PiecewiseValve) referencing its `name` as their
 * `upstream_block`/`downstream_block`.
 *
 * ### Internal variables
 *
 * Names of internal variables in this block's output:
 *
 * * `radius` - Chamber radius \f$r\f$
 * * `velo` - Chamber velocity \f$\dot{r}\f$
 * * `stress` - Spherical stress \f$S\f$
 * * `tau` - Active stress \f$\tau\f$
 * * `volume` - Chamber volume \f$V\f$
 *
 * Active stress models may introduce additional internal variables (e.g.
 * `e_c`, `tau_c`, `k_c`, `omega` for the `strain_dependent` model, see
 * \ref ActiveStress).
 *
 */
class ChamberSphere : public Block {
 public:
  /**
   * @brief Local IDs of the parameters
   *
   */
  enum ParamId {
    rho = 0,
    thick0 = 1,
    radius0 = 2,
    eta = 3,
  };
 
  /**
   * @brief Construct a new ChamberSphere object
   *
   * @param id Global ID of the block
   * @param model The model to which the block belongs
   */
  ChamberSphere(int id, Model* model)
      : Block(id, model, BlockType::chamber_sphere, BlockClass::chamber,
              {{"rho", InputParameter()},
               {"thick0", InputParameter()},
               {"radius0", InputParameter()},
               {"eta", InputParameter()}}) {}
 
  /**
   * @brief Set up the degrees of freedom (DOF) of the block
   *
   * Set \ref global_var_ids and \ref global_eqn_ids of the element based on the
   * number of equations and the number of internal variables of the
   * element.
   *
   * @param dofhandler Degree-of-freedom handler to register variables and
   * equations at
   */
  void setup_dofs(DOFHandler& dofhandler) override;
 
  /**
   * @brief Update the constant contributions of the element in a sparse
   system
   *
   * @param system System to update contributions at
   * @param parameters Parameters of the model
   */
  void update_constant(SparseSystem& system,
                       std::vector<double>& parameters) override;
 
  /**
   * @brief Update the time-dependent contributions of the element in a sparse
   * system
   *
   * @param system System to update contributions at
   * @param parameters Parameters of the model
   */
  void update_time(SparseSystem& system,
                   std::vector<double>& parameters) override;
 
  /**
   * @brief Update the solution-dependent contributions of the element in a
   * sparse system
   *
   * @param system System to update contributions at
   * @param parameters Parameters of the model
   * @param y Current solution
   * @param dy Current derivate of the solution
   */
  void update_solution(
      SparseSystem& system, std::vector<double>& parameters,
      const Eigen::Matrix<double, Eigen::Dynamic, 1>& y,
      const Eigen::Matrix<double, Eigen::Dynamic, 1>& dy) override;
 
  void set_activation_function(std::unique_ptr<ActivationFunction> af) override;
 
  void set_active_stress(std::unique_ptr<ActiveStress> as) override;
 
  void set_material(std::unique_ptr<SphereMaterial> m) override;
 
 private:
  double activation_signal_ = 0.0;  // activation_function_->compute(time),
                                    // cached for use in update_solution
  std::unique_ptr<ActivationFunction> activation_function_;
 
  std::unique_ptr<ActiveStress> active_stress_;
 
  std::unique_ptr<SphereMaterial> material_;
 
  /**
   * @brief Number of triplets of element
   *
   * Number of triplets that the element contributes to the global system
   * (relevant for sparse memory reservation)
   */
  TripletsContributions num_triplets{0, 0, 18};
};
 
#endif  // SVZERODSOLVER_MODEL_ChamberSphere_HPP_