Tarefa8_Modelo_Hill_Classe.ipynb

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        "<a href=\"https://colab.research.google.com/github/menezes-eduardo/BMC/blob/master/Tarefa8_Modelo_Hill_Classe.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "source": [
        "##**Tarefa 8 - Modelo Hill Classe**\n",
        "\n",
        "Eduardo de Menezes dos Santos 21065916"
      ],
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        "id": "rfn9GBAU-4tY"
      }
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    {
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      "metadata": {
        "id": "TlSACAx0xv0j"
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      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ]
    },
    {
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      "source": [
        "class Musculo:\n",
        "  \n",
        "  def __init__(self, nome, ltslack, lmopt, fmax, alpha, lm_0,dt, A0, A1):\n",
        "\n",
        "    # ft_T03\n",
        "    #--------------------------------------\n",
        "    self.nome = nome    \n",
        "    self.ltslack = ltslack\n",
        "    self.lmopt = lmopt\n",
        "    self.fmax = fmax\n",
        "    self.alpha = alpha \n",
        "    self.dt = dt\n",
        "\n",
        "    self.epst0 = 0.04\n",
        "    self.kttoe = 3\n",
        "    self.kpe = 5\n",
        "    self.epsm0 = 0.6\n",
        "    self.gammal=0.45\n",
        "    self.vmmax=10\n",
        "    self.fmlen=1.4\n",
        "    self.af=0.25\n",
        "    self.t_act= 0.015\n",
        "    self.t_deact = 0.05\n",
        "\n",
        "    self.lm = lm_0\n",
        "    self.lm_norm = lm_0/self.lmopt\n",
        "    self.a = 0.001\n",
        "    self.F = 0\n",
        "    self.lt = 0\n",
        "\n",
        "    self.A0 = A0\n",
        "    self.A1 = A1\n",
        "  \n",
        "  def fselt_T03(self, lt):\n",
        "    \"\"\"Thelen (2003) force-length relationship of tendon as function of tendon length.\n",
        "    \n",
        "    Parameters\n",
        "    ----------\n",
        "    lt  : float, optional (default=1)\n",
        "        normalized tendon length\n",
        "    ltslack  : float, optional (default=1)\n",
        "        normalized tendon slack length\n",
        "    epst0  : float, optional (default=0.04)\n",
        "        tendon strain at the maximal isometric muscle force\n",
        "    kttoe  : float, optional (default=3)\n",
        "        linear scale factor\n",
        "\n",
        "    Returns\n",
        "    -------\n",
        "    fse  : float\n",
        "        normalized force of the tendon series element\n",
        "    \"\"\"\n",
        "\n",
        "    epst = (lt-self.ltslack)/self.ltslack\n",
        "    fttoe = 0.33\n",
        "    # values from OpenSim Thelen2003Muscle\n",
        "    epsttoe =  .99*self.epst0*np.e**3/(1.66*np.e**3 - .67)\n",
        "    ktlin =  .67/(self.epst0 - epsttoe)\n",
        "    #\n",
        "    if epst <= 0:\n",
        "        fse = 0\n",
        "    elif epst <= epsttoe:\n",
        "        fse = fttoe/(np.exp(self.kttoe)-1)*(np.exp(self.kttoe*epst/epsttoe)-1)\n",
        "    else:\n",
        "        fse = ktlin*(epst-epsttoe) + fttoe\n",
        "        \n",
        "    return fse\n",
        "\n",
        "  def fpelm_T03(self, lm):\n",
        "    \"\"\"Thelen (2003) force of the muscle parallel element as function of muscle length.\n",
        "    \n",
        "    Parameters\n",
        "    ----------\n",
        "    lm  : float, optional (default=1)\n",
        "        normalized muscle fiber length\n",
        "    kpe  : float, optional (default=5)\n",
        "        exponential shape factor\n",
        "    epsm0  : float, optional (default=0.6)\n",
        "        passive muscle strain due to maximum isometric force\n",
        "\n",
        "    Returns\n",
        "    -------\n",
        "    fpe  : float\n",
        "        normalized force of the muscle parallel (passive) element\n",
        "    \"\"\"\n",
        "    \n",
        "    if lm < 1:\n",
        "        fpe = 0\n",
        "    else:\n",
        "        fpe = (np.exp(self.kpe*(lm-1)/self.epsm0)-1)/(np.exp(self.kpe)-1)\n",
        "    \n",
        "    return fpe\n",
        "\n",
        "  def flce_T03(self, lm):\n",
        "    \"\"\"Thelen (2003) force of the contractile element as function of muscle length.\n",
        "    \n",
        "    Parameters\n",
        "    ----------\n",
        "    lm  : float, optional (default=1)\n",
        "        normalized muscle fiber length\n",
        "    gammal  : float, optional (default=0.45)\n",
        "        shape factor\n",
        "\n",
        "    Returns\n",
        "    -------\n",
        "    fl  : float\n",
        "        normalized force of the muscle contractile element\n",
        "    \"\"\"\n",
        "    \n",
        "    fl = np.exp(-(lm-1)**2/self.gammal)\n",
        "    \n",
        "    return fl\n",
        "\n",
        "  def vmfce_T03(self, fm, flce):\n",
        "    \"\"\"Thelen (2003) velocity of the force-velocity relationship as function of CE force.\n",
        "    \n",
        "    Parameters\n",
        "    ----------\n",
        "    fm  : float\n",
        "        normalized muscle force\n",
        "    flce  : float, optional (default=1)\n",
        "        normalized muscle force due to the force-length relationship\n",
        "    lmopt  : float, optional (default=1)\n",
        "        optimal muscle fiber length\n",
        "    a  : float, optional (default=1)\n",
        "        muscle activation level\n",
        "    vmmax  : float, optional (default=1)\n",
        "        maximum muscle velocity for concentric activation\n",
        "    fmlen  : float, optional (default=1.4)\n",
        "        normalized maximum force generated at the lengthening phase\n",
        "    af  : float, optional (default=0.25)\n",
        "        shape factor\n",
        "\n",
        "    Returns\n",
        "    -------\n",
        "    vm  : float\n",
        "        velocity of the muscle\n",
        "    \"\"\"\n",
        "    \n",
        "    a = self.a\n",
        "    if fm <= a*flce:  # isometric and concentric activation\n",
        "        b = a*flce + fm/self.af\n",
        "    else:             # eccentric activation\n",
        "        b = (2 + 2/self.af)*(a*flce*self.fmlen - fm)/(self.fmlen - 1) \n",
        "    vm = (0.25  + 0.75*a)*self.vmmax*(fm - a*flce)/b\n",
        "    \n",
        "    return vm\n",
        "\n",
        "  def fce(self, Ft, Fpe):\n",
        "    \"\"\"Hill model contractile element computation.\n",
        "      \n",
        "    Parameters\n",
        "    ----------\n",
        "    Ft  : float\n",
        "        normalized tendon force\n",
        "    Fpe  : float\n",
        "        normalized passive paralel element force\n",
        "    alpha  : float\n",
        "        pennation angle\n",
        "    \n",
        "    Returns\n",
        "    -------\n",
        "    Fce  : float\n",
        "        normalized contractile element force\n",
        "    \"\"\"\n",
        "    Fce = (Ft - Fpe*np.cos(self.alpha))/np.cos(self.alpha)\n",
        "    return Fce\n",
        "\n",
        "  def act_1(self, u):\n",
        "    \"\"\" \n",
        "    Funçao de ativação do músculo\n",
        "    \n",
        "    Parametros\n",
        "    ----------\n",
        "    t : float\n",
        "      tempo em que ocorre a ativação\n",
        "    a : float\n",
        "      aticação múscular\n",
        "    t_act: float\n",
        "      tempo que demora para ativação o músculo\n",
        "    t_deact: float\n",
        "      tempo que demora para desativar o músculo\n",
        "\n",
        "    Saída\n",
        "    -----\n",
        "    adot : float\n",
        "      velocidade de ativação/derivada da ativação em função do tempo\n",
        "    \"\"\"\n",
        "    \n",
        "    # [s] , tempo de ativação\n",
        "    a = self.a\n",
        "    if u>a:\n",
        "      adot = (u-a)/(self.t_act*(0.5 + 1.5*a))\n",
        "\n",
        "    else:\n",
        "      adot = (u-a)/((self.t_deact)/(0.5+1.5*a))\n",
        "\n",
        "    return adot\n",
        "\n",
        "  def integra_musculo(self, u , Lmt):\n",
        "\n",
        "    adot = self.act_1(u=u)\n",
        "    self.a = self.a + adot*self.dt\n",
        "    self.lt = Lmt-self.lm*np.cos(self.alpha)\n",
        "    lt_norm = self.lt/self.lmopt\n",
        "    Ft_norm = self.fselt_T03(lt=lt_norm)\n",
        "    Fpe_norm = self.fpelm_T03(lm=self.lm_norm)\n",
        "    Fce_norm = self.fce(Ft_norm, Fpe_norm)\n",
        "    flce = self.flce_T03(lm=self.lm_norm)\n",
        "    vm_norm = self.vmfce_T03(Fce_norm, flce=flce)\n",
        "    self.lm_norm = self.lm_norm + self.dt*vm_norm\n",
        "    self.lm = self.lm_norm*self.lmopt\n",
        "    self.F = Ft_norm*self.fmax\n",
        "\n",
        "    \n",
        " \n",
        "  "
      ],
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        "id": "7IdeMBtOxxCY"
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      "execution_count": null,
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      "cell_type": "code",
      "source": [
        "def excitation(t, u_max=0.9 , u_min=0.5, t0=0.1, t1=10):\n",
        "  \"\"\"\n",
        "      Função da excitação senoidal\n",
        "\n",
        "      Parametros\n",
        "      ----------\n",
        "      t : float\n",
        "        tempo em que ocorre a excitação\n",
        "      u_max : float\n",
        "        valor mínimo da excitação\n",
        "      t0 : float\n",
        "        tempo inicial\n",
        "      t1: float\n",
        "        tempo final\n",
        "\n",
        "      Saída\n",
        "      -----\n",
        "      u : float\n",
        "        valor da excitação no tempo t\n",
        "      \n",
        "\n",
        "    \"\"\"\n",
        "  u = u_min\n",
        "  if t >= t0 and t <= t1:\n",
        "    u = 0.7 + 0.2 * (np.sin(2*(np.pi)/0.2*t))\n",
        "    \n",
        "  return u\n"
      ],
      "metadata": {
        "id": "G-BwniZ_uOE5"
      },
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    },
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      "cell_type": "code",
      "source": [
        "def lmt(theta, musculo):\n",
        "  '''\n",
        "  theta:radian\n",
        "  '''\n",
        "\n",
        "  theta = np.rad2deg(theta)\n",
        "\n",
        "  Lmt = musculo.A0 + musculo.A1*theta\n",
        "  Lmt = Lmt/100  \n",
        "  return Lmt"
      ],
      "metadata": {
        "id": "Cyu44uV6y9rM"
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      "execution_count": null,
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      "source": [
        "    # Valores ótimos retirados do livro (muscle soleus)\n",
        "lopt = 0.05\n",
        "ltslack_norm = 8.3\n",
        "fmax = 1750\n",
        "alpha = np.deg2rad(14)\n",
        "    #------------------------------------------\n",
        "\n",
        "dt = 0.0001\n",
        "t = np.arange(0, 10, dt)\n",
        "\n",
        "lm = 1* lopt\n",
        "lm_norm = lm/lopt\n",
        "\n",
        "u_max = 1\n",
        "u_min = 0.001\n",
        "\n",
        "t0 = 0.1\n",
        "t1 = 10\n",
        "\n",
        "#------------------------------------------------------------------------------\n",
        "\n",
        "    # Ativação\n",
        "    # Vetor de Ativação e entrada degrau\n",
        "act = np.zeros_like(t)\n",
        "force = np.zeros_like(t)\n",
        "exc = np.zeros_like(t)\n",
        "muscle_length = np.zeros_like(t)\n",
        "tendon_length = np.zeros_like(t)\n",
        "Lmt = np.zeros_like(t)\n",
        "Lmt = np.zeros_like(t)\n",
        "\n",
        "a = 0.001\n",
        "# Determinaçao do tempo de ativação\n",
        "t_deact = 0.05 # escolhendo tempo de desativação de 1 segundo temos\n",
        "t_act = 0.015 # [s] , tempo de ativação\n",
        "\n",
        "gt = Musculo('Gastrocnemius', ltslack=7.5, lmopt=0.057, fmax=1750,\n",
        "             alpha=9.9, lm_0=0.0575, dt=dt, A0=46.4, A1=7.48e-2) #Gastrocen\n",
        "sol = Musculo('Soleus', ltslack=5.9, lmopt=0.049, fmax=3150, \n",
        "              alpha=28.3, lm_0=0.03, dt=dt, A0=32.3, A1=0.0722)\n",
        "\n",
        "    #------------------------------------------------------------------------------\n",
        "\n",
        "for i in range(len(t)):\n",
        "  theta =0\n",
        "  u = 1#excitation(t[i], u_max=0.9, u_min=0.5, t0=0.1, t1=4)\n",
        "  Lmt_gt = lmt(theta, gt)  \n",
        "  Lmt_sol = lmt(theta, sol)\n",
        "\n",
        "  gt.integra_musculo(u, Lmt_gt)\n",
        "  sol.integra_musculo(u, Lmt_sol)\n",
        "  Lmt[i] = Lmt_gt\n",
        "  #Lmt[i] = Lmt_sol\n",
        "  exc[i] = u\n",
        "  act[i] = gt.a\n",
        "  force[i] = gt.F\n",
        "  muscle_length[i] =gt.lm\n",
        "  tendon_length[i] = gt.lt\n",
        "\n",
        "plt.figure()\n",
        "plt.plot(t, force)\n",
        "plt.title('Músculo GT - Força em função do tempo')\n",
        "plt.show()\n",
        "\n",
        "plt.figure()\n",
        "plt.plot(t, muscle_length, 'r', label = 'Muscle')\n",
        "plt.plot(t, tendon_length, 'b', label = 'Tendon')\n",
        "plt.title('Músculo GT - Comprimento do Músculo (vermelho) e comprimento do tendão (azul)')\n",
        "plt.show()\n",
        "\n",
        "plt.figure()\n",
        "plt.plot(t, Lmt)\n",
        "plt.title('Musculo GT - Comprimento Músculo Tendão do Músculo Soleus')\n",
        "\n",
        "plt.figure()\n",
        "plt.plot(t, act, label = 'act')\n",
        "plt.plot(t, exc, label = 'exc')\n",
        "plt.title('Musculo GT - Excitação e Ativação em função do tempo')\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ],
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              "<Figure size 432x288 with 1 Axes>"
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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Musculo GT - Excitação e Ativação em função do tempo')"
            ]
          },
          "metadata": {},
          "execution_count": 35
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "n8lHvrNp3UcU"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}