code: def directional_diffusion_variance(kt, V, min_kurtosis=-3 / 7):
      r"""Calculate the apparent diffusion variance (adv) in each direction of a
      sphere for a single voxel [1]_
  
      Parameters
      ----------
      dt : array (6,)
          elements of the diffusion tensor of the voxel.
      kt : array (15,)
          elements of the kurtosis tensor of the voxel.
      V : array (g, 3)
          g directions of a Sphere in Cartesian coordinates
      min_kurtosis : float (optional)
          Because high-amplitude negative values of kurtosis are not physically
          and biologicaly pluasible, and these cause artefacts in
          kurtosis-based measures, directional kurtosis values smaller than
          `min_kurtosis` are replaced with `min_kurtosis`. Default = -3./7
          (theoretical kurtosis limit for regions that consist of water confined
          to spherical pores [2]_)
      adc : ndarray(g,) (optional)
          Apparent diffusion coefficient (adc) in all g directions of a sphere
          for a single voxel.
      adv : ndarray(g,) (optional)
          Apparent diffusion variance coefficient (advc) in all g directions of
          a sphere for a single voxel.
  
      Returns
      -------
      adv : ndarray (g,)
          Apparent diffusion variance (adv) in all g directions of a sphere for
          a single voxel.
  
      References
      ----------
      .. [1] Neto Henriques R, Correia MM, Nunes RG, Ferreira HA (2015).
             Exploring the 3D geometry of the diffusion kurtosis tensor -
             Impact on the development of robust tractography procedures and
             novel biomarkers, NeuroImage 111: 85-99
  
      """
      adv = (
          V[:, 0] * V[:, 0] * V[:, 0] * V[:, 0] * kt[0]
          + V[:, 1] * V[:, 1] * V[:, 1] * V[:, 1] * kt[1]
          + V[:, 2] * V[:, 2] * V[:, 2] * V[:, 2] * kt[2]
          + 4 * V[:, 0] * V[:, 0] * V[:, 0] * V[:, 1] * kt[3]
          + 4 * V[:, 0] * V[:, 0] * V[:, 0] * V[:, 2] * kt[4]
          + 4 * V[:, 0] * V[:, 1] * V[:, 1] * V[:, 1] * kt[5]
          + 4 * V[:, 1] * V[:, 1] * V[:, 1] * V[:, 2] * kt[6]
          + 4 * V[:, 0] * V[:, 2] * V[:, 2] * V[:, 2] * kt[7]
          + 4 * V[:, 1] * V[:, 2] * V[:, 2] * V[:, 2] * kt[8]
          + 6 * V[:, 0] * V[:, 0] * V[:, 1] * V[:, 1] * kt[9]
          + 6 * V[:, 0] * V[:, 0] * V[:, 2] * V[:, 2] * kt[10]
          + 6 * V[:, 1] * V[:, 1] * V[:, 2] * V[:, 2] * kt[11]
          + 12 * V[:, 0] * V[:, 0] * V[:, 1] * V[:, 2] * kt[12]
          + 12 * V[:, 0] * V[:, 1] * V[:, 1] * V[:, 2] * kt[13]
          + 12 * V[:, 0] * V[:, 1] * V[:, 2] * V[:, 2] * kt[14]
      )
  
      return adv
  
imports: import numpy
  import warnings
  import scipy.optimize
  import dipy.core.sphere
  from dipy.reconst.multi_voxel import multi_voxel_fit
  from dipy.reconst.dti import TensorFit, mean_diffusivity, from_lower_triangular, lower_triangular, decompose_tensor, MIN_POSITIVE_SIGNAL, nlls_fit_tensor, restore_fit_tensor
  from dipy.reconst.utils import dki_design_matrix
  from dipy.reconst.recspeed import local_maxima
  from dipy.reconst.base import ReconstModel
  from dipy.core.ndindex import ndindex
  from dipy.core.geometry import sphere2cart, cart2sphere, perpendicular_directions
  from dipy.core.optimize import PositiveDefiniteLeastSquares
  from dipy.data import get_sphere, get_fnames, load_sdp_constraints
  from dipy.reconst.vec_val_sum import vec_val_vect
  from dipy.core.gradients import check_multi_b
label_desc: Use image node_id 7 for calling a global function with example usage: directional_diffusion_variance(kt, V, min_kurtosis) and returns: adv