Initial commit
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redclawsystems
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//! Tissue conductivity models for FEM head modeling.
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//!
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//! Provides isotropic and anisotropic conductivity tensors
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//! for different tissue types in the head.
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use crate::error::{FemError, FemResult};
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use crate::mesh::TissueLayer;
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use nalgebra::{Matrix3, Vector3};
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use serde::{Deserialize, Serialize};
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use std::collections::HashMap;
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/// Conductivity tensor (3x3 symmetric matrix)
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#[derive(Debug, Clone, Serialize, Deserialize)]
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pub struct ConductivityTensor {
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/// Tensor components (symmetric)
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pub tensor: Matrix3<f64>,
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/// Whether this is isotropic
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pub is_isotropic: bool,
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}
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impl ConductivityTensor {
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/// Create an isotropic conductivity tensor
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pub fn isotropic(sigma: f64) -> Self {
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Self {
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tensor: Matrix3::identity() * sigma,
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is_isotropic: true,
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}
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}
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/// Create an anisotropic conductivity tensor
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pub fn anisotropic(tensor: Matrix3<f64>) -> Self {
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Self {
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tensor,
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is_isotropic: false,
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}
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}
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/// Create from principal conductivities and eigenvectors
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pub fn from_principal(sigmas: &[f64; 3], eigenvectors: &Matrix3<f64>) -> Self {
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// σ = V * diag(σ1, σ2, σ3) * V^T
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let d = Matrix3::from_diagonal(&Vector3::new(sigmas[0], sigmas[1], sigmas[2]));
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let tensor = eigenvectors * d * eigenvectors.transpose();
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Self {
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tensor,
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is_isotropic: (sigmas[0] - sigmas[1]).abs() < 1e-10
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&& (sigmas[1] - sigmas[2]).abs() < 1e-10,
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}
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}
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/// Get scalar conductivity (trace/3 for anisotropic)
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pub fn scalar(&self) -> f64 {
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(self.tensor[(0, 0)] + self.tensor[(1, 1)] + self.tensor[(2, 2)]) / 3.0
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}
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/// Get conductivity in a specific direction
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pub fn in_direction(&self, direction: &Vector3<f64>) -> f64 {
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let d = direction.normalize();
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d.dot(&(self.tensor * d))
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}
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/// Apply conductivity to electric field gradient
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pub fn apply(&self, gradient: &Vector3<f64>) -> Vector3<f64> {
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self.tensor * gradient
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}
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}
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impl Default for ConductivityTensor {
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fn default() -> Self {
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Self::isotropic(1.0)
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}
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}
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/// Anisotropy model type
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#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
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pub enum AnisotropicModel {
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/// Isotropic (no anisotropy)
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Isotropic,
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/// Volume-based constraint
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VolumeConstraint,
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/// DTI-based from diffusion tensor
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DtiBased,
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/// Fixed ratio anisotropy
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FixedRatio,
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}
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/// Configuration for tissue conductivity
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#[derive(Debug, Clone, Serialize, Deserialize)]
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pub struct TissueConfig {
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/// Tissue type
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pub tissue: TissueLayer,
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/// Isotropic conductivity (S/m)
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pub conductivity: f64,
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/// Anisotropy model
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pub anisotropy: AnisotropicModel,
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/// Anisotropy ratio (longitudinal/transverse) for non-DTI models
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pub anisotropy_ratio: f64,
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}
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impl TissueConfig {
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/// Create with isotropic conductivity
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pub fn isotropic(tissue: TissueLayer, conductivity: f64) -> Self {
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Self {
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tissue,
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conductivity,
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anisotropy: AnisotropicModel::Isotropic,
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anisotropy_ratio: 1.0,
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}
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}
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/// Create with anisotropic conductivity
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pub fn anisotropic(
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tissue: TissueLayer,
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conductivity: f64,
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model: AnisotropicModel,
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ratio: f64,
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) -> Self {
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Self {
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tissue,
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conductivity,
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anisotropy: model,
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anisotropy_ratio: ratio,
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}
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}
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}
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/// Default conductivities for different tissue types (S/m)
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pub fn default_conductivity(tissue: TissueLayer) -> f64 {
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match tissue {
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TissueLayer::Scalp => 0.43,
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TissueLayer::Skull => 0.0042,
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TissueLayer::Csf => 1.79,
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TissueLayer::GrayMatter => 0.33,
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TissueLayer::WhiteMatter => 0.14,
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TissueLayer::Air => 1e-12,
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}
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}
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/// Default anisotropy ratio for tissues
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pub fn default_anisotropy_ratio(tissue: TissueLayer) -> f64 {
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match tissue {
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TissueLayer::Skull => 10.0, // Radial/tangential
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TissueLayer::WhiteMatter => 9.0, // Along/perpendicular to fibers
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_ => 1.0, // Isotropic
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}
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}
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/// Tissue conductivity model for FEM
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#[derive(Debug, Clone, Serialize, Deserialize)]
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pub struct TissueConductivity {
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/// Per-tissue configurations
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configs: HashMap<TissueLayer, TissueConfig>,
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/// Per-element conductivity tensors (if computed)
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element_tensors: Option<Vec<ConductivityTensor>>,
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}
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impl TissueConductivity {
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/// Create with default isotropic conductivities
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pub fn default_isotropic() -> Self {
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let mut configs = HashMap::new();
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for tissue in [
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TissueLayer::Scalp,
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TissueLayer::Skull,
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TissueLayer::Csf,
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TissueLayer::GrayMatter,
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TissueLayer::WhiteMatter,
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] {
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configs.insert(
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tissue,
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TissueConfig::isotropic(tissue, default_conductivity(tissue)),
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);
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}
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Self {
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configs,
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element_tensors: None,
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}
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}
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/// Create with default anisotropic conductivities
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pub fn default_anisotropic() -> Self {
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let mut configs = HashMap::new();
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// Isotropic tissues
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for tissue in [
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TissueLayer::Scalp,
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TissueLayer::Csf,
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TissueLayer::GrayMatter,
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] {
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configs.insert(
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tissue,
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TissueConfig::isotropic(tissue, default_conductivity(tissue)),
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);
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}
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// Anisotropic skull
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configs.insert(
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TissueLayer::Skull,
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TissueConfig::anisotropic(
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TissueLayer::Skull,
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default_conductivity(TissueLayer::Skull),
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AnisotropicModel::FixedRatio,
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default_anisotropy_ratio(TissueLayer::Skull),
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),
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);
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// Anisotropic white matter
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configs.insert(
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TissueLayer::WhiteMatter,
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TissueConfig::anisotropic(
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TissueLayer::WhiteMatter,
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default_conductivity(TissueLayer::WhiteMatter),
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AnisotropicModel::VolumeConstraint,
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default_anisotropy_ratio(TissueLayer::WhiteMatter),
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),
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);
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Self {
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configs,
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element_tensors: None,
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}
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}
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/// Set conductivity for a tissue
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pub fn set_conductivity(&mut self, tissue: TissueLayer, sigma: f64) {
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if let Some(config) = self.configs.get_mut(&tissue) {
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config.conductivity = sigma;
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} else {
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self.configs
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.insert(tissue, TissueConfig::isotropic(tissue, sigma));
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}
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self.element_tensors = None; // Invalidate cached tensors
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}
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/// Set anisotropy model for a tissue
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pub fn set_anisotropy(&mut self, tissue: TissueLayer, model: AnisotropicModel, ratio: f64) {
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if let Some(config) = self.configs.get_mut(&tissue) {
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config.anisotropy = model;
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config.anisotropy_ratio = ratio;
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}
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self.element_tensors = None;
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}
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/// Get configuration for a tissue
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pub fn get_config(&self, tissue: TissueLayer) -> Option<&TissueConfig> {
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self.configs.get(&tissue)
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}
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/// Get conductivity tensor for a tissue at a position
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pub fn tensor_at(
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&self,
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tissue: TissueLayer,
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position: &Vector3<f64>,
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normal: Option<&Vector3<f64>>,
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) -> ConductivityTensor {
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let config = match self.configs.get(&tissue) {
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Some(c) => c,
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None => return ConductivityTensor::isotropic(default_conductivity(tissue)),
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};
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match config.anisotropy {
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AnisotropicModel::Isotropic => ConductivityTensor::isotropic(config.conductivity),
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AnisotropicModel::VolumeConstraint => {
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// Volume-preserving anisotropy
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self.volume_constraint_tensor(config, position, normal)
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}
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AnisotropicModel::FixedRatio => {
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// Fixed ratio along normal direction
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self.fixed_ratio_tensor(config, normal)
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}
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AnisotropicModel::DtiBased => {
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// Would need DTI data - fall back to isotropic
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ConductivityTensor::isotropic(config.conductivity)
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}
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}
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}
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/// Compute tensor with volume constraint
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fn volume_constraint_tensor(
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&self,
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config: &TissueConfig,
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position: &Vector3<f64>,
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_normal: Option<&Vector3<f64>>,
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) -> ConductivityTensor {
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let sigma = config.conductivity;
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let ratio = config.anisotropy_ratio;
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// Get principal direction (radial from center for spherical)
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let r = position.norm();
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let radial = if r > 1e-10 {
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position / r
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} else {
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Vector3::new(0.0, 0.0, 1.0)
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};
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// Volume constraint: σ_l * σ_t^2 = σ_iso^3
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// With ratio = σ_l / σ_t
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let sigma_t = (sigma.powi(3) / ratio).powf(1.0 / 3.0);
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let sigma_l = sigma_t * ratio;
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// Build tensor: σ = σ_t * I + (σ_l - σ_t) * r ⊗ r
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let tensor =
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Matrix3::identity() * sigma_t + (sigma_l - sigma_t) * radial * radial.transpose();
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ConductivityTensor::anisotropic(tensor)
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}
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/// Compute tensor with fixed ratio along normal
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fn fixed_ratio_tensor(
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&self,
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config: &TissueConfig,
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normal: Option<&Vector3<f64>>,
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) -> ConductivityTensor {
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let sigma = config.conductivity;
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let ratio = config.anisotropy_ratio;
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let default_normal = Vector3::new(0.0, 0.0, 1.0);
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let n = normal.unwrap_or(&default_normal);
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let n = n.normalize();
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// σ_radial = sigma * ratio, σ_tangential = sigma / sqrt(ratio)
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let sigma_n = sigma * ratio.sqrt();
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let sigma_t = sigma / ratio.sqrt();
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let tensor = Matrix3::identity() * sigma_t + (sigma_n - sigma_t) * n * n.transpose();
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ConductivityTensor::anisotropic(tensor)
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}
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/// Compute conductivity tensors for all elements
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pub fn compute_element_tensors(&mut self, mesh: &crate::mesh::HeadMesh) -> FemResult<()> {
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let n_elements = mesh.n_elements();
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let mut tensors = Vec::with_capacity(n_elements);
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for elem in &mesh.elements {
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let centroid = elem.centroid(&mesh.nodes);
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let normal = Some(centroid.normalize()); // Radial for spherical
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let tensor = self.tensor_at(elem.tissue, ¢roid, normal.as_ref());
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tensors.push(tensor);
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}
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self.element_tensors = Some(tensors);
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Ok(())
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}
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/// Get pre-computed element tensor
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pub fn element_tensor(&self, element_idx: usize) -> Option<&ConductivityTensor> {
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self.element_tensors.as_ref()?.get(element_idx)
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}
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/// Get all element tensors
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pub fn element_tensors(&self) -> Option<&[ConductivityTensor]> {
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self.element_tensors.as_deref()
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}
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}
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impl Default for TissueConductivity {
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fn default() -> Self {
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Self::default_isotropic()
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}
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}
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/// DTI-based conductivity model
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#[derive(Debug, Clone)]
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pub struct DtiConductivity {
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/// Diffusion tensors per voxel
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pub diffusion_tensors: Vec<Matrix3<f64>>,
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/// Voxel positions
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pub positions: Vec<Vector3<f64>>,
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/// Conversion factor from diffusion to conductivity
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pub d2c_factor: f64,
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/// Minimum eigenvalue ratio
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pub min_ratio: f64,
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}
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impl DtiConductivity {
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/// Create from diffusion tensor data
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pub fn new(
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diffusion_tensors: Vec<Matrix3<f64>>,
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positions: Vec<Vector3<f64>>,
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) -> FemResult<Self> {
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if diffusion_tensors.len() != positions.len() {
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return Err(FemError::DimensionMismatch(
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"Tensors and positions must have same length".into(),
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));
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}
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Ok(Self {
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diffusion_tensors,
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positions,
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d2c_factor: 0.736, // Tuch 2001: σ = 0.736 * D
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min_ratio: 0.1,
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})
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}
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/// Get conductivity tensor at a position (nearest neighbor interpolation)
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pub fn tensor_at(&self, position: &Vector3<f64>) -> ConductivityTensor {
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if self.positions.is_empty() {
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return ConductivityTensor::isotropic(default_conductivity(TissueLayer::WhiteMatter));
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}
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// Find nearest DTI voxel
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let mut min_dist = f64::MAX;
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let mut nearest_idx = 0;
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for (i, pos) in self.positions.iter().enumerate() {
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let dist = (pos - position).norm_squared();
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if dist < min_dist {
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min_dist = dist;
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nearest_idx = i;
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}
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}
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// Convert diffusion to conductivity
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let d = &self.diffusion_tensors[nearest_idx];
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let sigma = d * self.d2c_factor;
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// Ensure positive definiteness
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let eigendecomp = sigma.symmetric_eigen();
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let mut eigenvalues = eigendecomp.eigenvalues;
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// Clamp eigenvalues
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let max_ev = eigenvalues.max();
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for ev in eigenvalues.iter_mut() {
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*ev = ev.max(max_ev * self.min_ratio);
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}
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let d_clamped = Matrix3::from_diagonal(&eigenvalues);
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let tensor = eigendecomp.eigenvectors * d_clamped * eigendecomp.eigenvectors.transpose();
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ConductivityTensor::anisotropic(tensor)
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}
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}
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#[cfg(test)]
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mod tests {
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use super::*;
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#[test]
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fn test_isotropic_tensor() {
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let tensor = ConductivityTensor::isotropic(0.33);
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assert!(tensor.is_isotropic);
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assert!((tensor.scalar() - 0.33).abs() < 1e-10);
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// Same in all directions
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let dir1 = Vector3::new(1.0, 0.0, 0.0);
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let dir2 = Vector3::new(0.0, 1.0, 0.0);
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assert!((tensor.in_direction(&dir1) - tensor.in_direction(&dir2)).abs() < 1e-10);
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}
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#[test]
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fn test_anisotropic_tensor() {
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let sigmas = [0.4, 0.2, 0.2];
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let eigenvectors = Matrix3::identity();
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let tensor = ConductivityTensor::from_principal(&sigmas, &eigenvectors);
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assert!(!tensor.is_isotropic);
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// Higher conductivity along x
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let dir_x = Vector3::new(1.0, 0.0, 0.0);
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let dir_y = Vector3::new(0.0, 1.0, 0.0);
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assert!(tensor.in_direction(&dir_x) > tensor.in_direction(&dir_y));
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}
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#[test]
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fn test_default_conductivities() {
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assert!((default_conductivity(TissueLayer::GrayMatter) - 0.33).abs() < 1e-10);
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assert!((default_conductivity(TissueLayer::Skull) - 0.0042).abs() < 1e-10);
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assert!((default_conductivity(TissueLayer::Csf) - 1.79).abs() < 1e-10);
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}
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#[test]
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fn test_tissue_conductivity() {
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let conductivity = TissueConductivity::default_isotropic();
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let config = conductivity.get_config(TissueLayer::GrayMatter).unwrap();
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assert!((config.conductivity - 0.33).abs() < 1e-10);
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assert_eq!(config.anisotropy, AnisotropicModel::Isotropic);
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}
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#[test]
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fn test_anisotropic_conductivity() {
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let conductivity = TissueConductivity::default_anisotropic();
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let wm_config = conductivity.get_config(TissueLayer::WhiteMatter).unwrap();
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assert_eq!(wm_config.anisotropy, AnisotropicModel::VolumeConstraint);
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let skull_config = conductivity.get_config(TissueLayer::Skull).unwrap();
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assert_eq!(skull_config.anisotropy, AnisotropicModel::FixedRatio);
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}
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#[test]
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fn test_tensor_at() {
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let conductivity = TissueConductivity::default_anisotropic();
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let pos = Vector3::new(0.05, 0.0, 0.0);
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let tensor = conductivity.tensor_at(TissueLayer::WhiteMatter, &pos, None);
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assert!(!tensor.is_isotropic);
|
||||
assert!(tensor.scalar() > 0.0);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_set_conductivity() {
|
||||
let mut conductivity = TissueConductivity::default_isotropic();
|
||||
|
||||
conductivity.set_conductivity(TissueLayer::Skull, 0.01);
|
||||
let config = conductivity.get_config(TissueLayer::Skull).unwrap();
|
||||
assert!((config.conductivity - 0.01).abs() < 1e-10);
|
||||
}
|
||||
}
|
||||
Reference in New Issue
Block a user