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Swap ASE to full integral equation
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@spinicist
spinicist committed Jul 30, 2021
1 parent d2ae0d8 commit ee2b7f5
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Showing 3 changed files with 64 additions and 45 deletions.
4 changes: 2 additions & 2 deletions Python/Tests/test_perfusion.py
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Original file line number Diff line number Diff line change
Expand Up @@ -62,8 +62,8 @@ def test_oef(self):
noise=noise, verbose=vb).run()
diff_DBV = Diff(in_file='ASE_DBV.nii.gz', baseline='DBV.nii.gz',
noise=noise, verbose=vb).run()
self.assertLessEqual(diff_R2p.outputs.out_diff, 12)
self.assertLessEqual(diff_DBV.outputs.out_diff, 50)
self.assertLessEqual(diff_R2p.outputs.out_diff, 20)
self.assertLessEqual(diff_DBV.outputs.out_diff, 75)

def test_oef_fixed_dbv(self):
# Use MultiEchoFlex as a proxy for ASE
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3 changes: 2 additions & 1 deletion Source/Core/FitScaledAuto.h
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Expand Up @@ -36,7 +36,8 @@ template <typename ModelType_, typename FlagType_ = int> struct ScaledAutoDiffFi
using AutoCost = ceres::AutoDiffCostFunction<Cost, ceres::DYNAMIC, ModelType::NV>;
auto *cost = new Cost{this->model, fixed, data};
auto *auto_cost = new AutoCost(cost, this->model.sequence.size());
problem.AddResidualBlock(auto_cost, NULL, varying.data());
auto *loss = new ceres::HuberLoss(1.0);
problem.AddResidualBlock(auto_cost, loss, varying.data());
for (int i = 0; i < ModelType::NV; i++) {
problem.SetParameterLowerBound(varying.data(), i, this->model.bounds_lo[i]);
problem.SetParameterUpperBound(varying.data(), i, this->model.bounds_hi[i]);
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102 changes: 60 additions & 42 deletions Source/Perfusion/qi_ase_oef.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -11,9 +11,12 @@

#include <Eigen/Dense>

#include "NumericalIntegration.h"

// #define QI_DEBUG_BUILD

#include "Args.h"

#include "FitFunction.h"
#include "FitScaledAuto.h"
#include "ImageIO.h"
Expand All @@ -28,45 +31,52 @@ using namespace std::literals;
constexpr double kappa = 0.03; // Conversion factor
constexpr double gyro_gamma = 2 * M_PI * 42.577e6; // Gyromagnetic Ratio
constexpr double delta_X0 = 0.264e-6; // Susc diff oxy and fully de-oxy blood
constexpr double Hct = 0.34;
constexpr double Hb = Hct / kappa;

template <typename T> struct fcFunctor {
const T &dw, tau;
T operator()(const T u) const {
const auto Jterm = ceres::BesselJ0(1.5 * dw * tau * u);
return (2. + u) * sqrt(1. - u) * (1. - Jterm) / (u * u);
}
};

struct ASEModel : QI::Model<double, double, 4, 0, 1, 3> {
using SequenceType = QI::MultiEchoSequence;
const SequenceType &sequence;
const double B0;
const double B0, Hct;

const std::array<const std::string, NV> varying_names{"S0"s, "dT"s, "R2p"s, "DBV"s};
const std::array<const std::string, ND> derived_names{"Tc"s, "OEF"s, "dHb"s};

const VaryingArray start{0.98, 0., 2.0, 0.02};
const VaryingArray start{0.98, 0., 5.0, 0.025};
const VaryingArray bounds_lo{0.1, -0.1, 0.25, 0.001};
const VaryingArray bounds_hi{2., 0.1, 20.0, 0.05};
const VaryingArray bounds_hi{2., 0.1, 50.0, 0.5};

int input_size(const int /* Unused */) const { return sequence.size(); }

template <typename Derived>
auto signal(const Eigen::ArrayBase<Derived> &varying, const FixedArray & /* Unused */) const
-> QI_ARRAY(typename Derived::Scalar) {
using T = typename Derived::Scalar;
const T &S0 = varying[0];
const T &dT = varying[1];
const T &R2p = varying[2];
const T &DBV = varying[3];

const auto dw = R2p / DBV;
const auto Tc = 1.5 * (1. / dw);
using T = typename Derived::Scalar;
const T & S0 = varying[0];
const T & dT = varying[1];
const T & R2p = varying[2];
const T & DBV = varying[3];
const auto dw = R2p / DBV;

const auto aTE = (sequence.TE + dT).abs();
QI_ARRAY(T) S(sequence.size());
Eigen::Integrator<T> integrator(5);
const auto quad_rule = Eigen::Integrator<T>::GaussKronrod15;
T abs_error{1.e-9};
T rel_error{1.e-9};
const auto aTE = (sequence.TE + dT).abs();
QI_ARRAY(T) fc(sequence.size());
for (int i = 0; i < sequence.size(); i++) {
const auto tau = aTE(i);
if (tau < Tc) {
S(i) = S0 * exp(-(0.3) * (R2p * tau) * (R2p * tau) / DBV);
} else {
S(i) = S0 * exp(-tau * R2p + DBV);
}
const auto tau = aTE(i);
fcFunctor<T> functor{dw, tau};
fc[i] = (1. / 3.) * integrator.quadratureAdaptive(
functor, T{0.0}, T{1.0}, abs_error, rel_error, quad_rule);
}
QI_ARRAY(T) S = S0 * exp(-DBV * fc);
return S;
}

Expand All @@ -76,9 +86,11 @@ struct ASEModel : QI::Model<double, double, 4, 0, 1, 3> {
const auto &R2p = varying[2];
const auto &DBV = varying[3];

const auto dw = R2p / DBV;
const auto Tc = 1.5 * (1. / dw);
const auto OEF = dw / ((4. * M_PI / 3.) * gyro_gamma * B0 * delta_X0 * Hct);
const auto dw = R2p / DBV;
const auto Tc = 1.5 * (1. / dw);
const auto OEF =
std::clamp(dw / ((4. * M_PI / 3.) * gyro_gamma * B0 * delta_X0 * Hct), 0., 1.);
const auto Hb = Hct / kappa;
const auto dHb = OEF * Hb;

derived[0] = Tc;
Expand All @@ -91,14 +103,14 @@ using ASEFit = QI::ScaledAutoDiffFit<ASEModel>;
struct ASEFixDBVModel : QI::Model<double, double, 3, 0, 1, 3> {
using SequenceType = QI::MultiEchoSequence;
const SequenceType &sequence;
const double B0, DBV;
const double B0, Hct, DBV;

const std::array<const std::string, NV> varying_names{"S0"s, "dT"s, "R2p"s};
const std::array<const std::string, ND> derived_names{"Tc"s, "OEF"s, "dHb"s};

const VaryingArray start{0.98, 0., 1.0};
const VaryingArray start{0.98, 0., 5.0};
const VaryingArray bounds_lo{0.1, -0.1, 0.25};
const VaryingArray bounds_hi{2., 0.1, 20.0};
const VaryingArray bounds_hi{2., 0.1, 50.0};

int input_size(const int /* Unused */) const { return sequence.size(); }

Expand All @@ -110,18 +122,21 @@ struct ASEFixDBVModel : QI::Model<double, double, 3, 0, 1, 3> {
const T & dT = varying[1];
const T & R2p = varying[2];
const auto dw = R2p / DBV;
const auto Tc = 1.5 * (1. / dw);

const auto aTE = (sequence.TE + dT).abs();
QI_ARRAY(T) S(sequence.size());
Eigen::Integrator<T> integrator(5);
const auto quad_rule = Eigen::Integrator<T>::GaussKronrod15;
T abs_error{1.e-9};
T rel_error{1.e-9};
const auto aTE = (sequence.TE + dT).abs();
QI_ARRAY(T) fc(sequence.size());
for (int i = 0; i < sequence.size(); i++) {
const auto tau = aTE(i);
if (tau < Tc) {
S(i) = S0 * exp(-(0.3) * (R2p * tau) * (R2p * tau) / DBV);
} else {
S(i) = S0 * exp(-tau * R2p + DBV);
}
const auto tau = aTE(i);
fcFunctor<T> functor{dw, tau};
fc[i] = (1. / 3.) * integrator.quadratureAdaptive(
functor, T{0.0}, T{1.0}, abs_error, rel_error, quad_rule);
}
QI_ARRAY(T) S = S0 * exp(-DBV * fc);

return S;
}

Expand All @@ -131,8 +146,10 @@ struct ASEFixDBVModel : QI::Model<double, double, 3, 0, 1, 3> {
const auto &R2p = varying[2];
const auto dw = R2p / DBV;
const auto Tc = 1.5 * (1. / dw);
const auto OEF = dw / ((4. * M_PI / 3.) * gyro_gamma * B0 * delta_X0 * Hct);
const auto dHb = OEF * Hb;
const auto OEF =
std::clamp(dw / ((4. * M_PI / 3.) * gyro_gamma * B0 * delta_X0 * Hct), 0., 1.);
const auto Hb = Hct / kappa;
const auto dHb = OEF * Hb;

derived[0] = Tc;
derived[1] = OEF;
Expand All @@ -149,6 +166,7 @@ int ase_oef_main(args::Subparser &parser) {

QI_COMMON_ARGS;
args::ValueFlag<double> B0(parser, "B0", "Field-strength (Tesla), default 3", {'B', "B0"}, 3.0);
args::ValueFlag<double> Hct(parser, "HCT", "Hematocrit (default 0.34)", {'h', "Hct"}, 0.34);
args::ValueFlag<double> DBV(parser, "DBV", "Fix DBV and only fit R2'", {'d', "DBV"}, 0.0);

parser.Parse();
Expand All @@ -157,7 +175,7 @@ int ase_oef_main(args::Subparser &parser) {

if (simulate) {
if (DBV) {
ASEFixDBVModel model{{}, sequence, B0.Get(), DBV.Get()};
ASEFixDBVModel model{{}, sequence, B0.Get(), Hct.Get(), DBV.Get()};
QI::SimulateModel<ASEFixDBVModel, false>(input,
model,
{},
Expand All @@ -168,7 +186,7 @@ int ase_oef_main(args::Subparser &parser) {
threads.Get(),
subregion.Get());
} else {
ASEModel model{{}, sequence, B0.Get()};
ASEModel model{{}, sequence, B0.Get(), Hct.Get()};
QI::SimulateModel<ASEModel, false>(input,
model,
{},
Expand All @@ -188,11 +206,11 @@ int ase_oef_main(args::Subparser &parser) {
fit_filter->WriteOutputs(prefix.Get() + "ASE_");
};
if (DBV) {
ASEFixDBVModel model{{}, sequence, B0.Get(), DBV.Get()};
ASEFixDBVModel model{{}, sequence, B0.Get(), Hct.Get(), DBV.Get()};
ASEFixDBVFit fit{model};
process(fit);
} else {
ASEModel model{{}, sequence, B0.Get()};
ASEModel model{{}, sequence, Hct.Get(), B0.Get()};
ASEFit fit{model};
process(fit);
}
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