Spinoff toolbox from SPM for developing, fitting and comparing single region haemodynamic models (HDMs).
NB 1: This is intended for situations where only a single brain region is being modelled. If data from multiple regions are available, then DCM is recommended (which has both hidden neural and haemodynamic states).
NB 2: This work is unpublished.
- Download the toolbox, unzip it and add the 'toolbox' directory to your Matlab path.
- In Matlab, go into the attention_example directory and run spm_hdm_demo.m
The code is arranged into a set of functions, mirroring the DCM framework:
| Function | Description |
|---|---|
| spm_hdm_specify | Create an HDM from a subject's SPM.mat and a representative timeseries (VOI) |
| spm_hdm_estimate | Fits an HDM to the data |
| spm_hdm_review | GUI for inspecting an HDM |
A default model is included, as introduced in Friston et. al 2000 and Stephan et al. 2007. It is specified in the following Matlab functions:
| Function | Description |
|---|---|
| spm_fx_hdm2 | Neurovascular / haemodynamic model |
| spm_gx_hdm2 | Observation model |
| spm_hdm_priors_hdm2 | Priors on log scaling parameters as well as the default values they scale |
The priors on parameters that can be estimated from the data are as follows:
| Section | Parameter | Default | Variance | Notes |
|---|---|---|---|---|
| Neurovascular | Efficacy | 0Hz | 1 | Efficacy of stimuli |
| Neurovascular | Decay | 0.64Hz | 1/32 | Half-life of vasoactive signal: 1/decay x log(2) |
| Neurovascular | Feedback | 0.41Hz | 0 | Period of vasoactive signal: 1/(2 x pi x sqrt(1/feedback)) |
| Vascular | Transit | 1.02Hz | 1/32 | Vascular transit rate |
| Vascular | Alpha | 0.33 | 0 | Grubb's exponent |
| Vascular | E0 | 0.40 | 0 | Resting oxygen extraction fraction |
| BOLD | V0 | 0.04 | 0 | Resting venous blood volume fraction |
| BOLD | Epsilon | 0.72 (1.5T), 0.44 (3T), 0 (7T) | 0 | Ratio of intra-to extra-vascular signal contributions |
Fixed parameters are as follows:
| Section | Parameter | Value | Notes |
|---|---|---|---|
| BOLD | r0 | 25 (1.5T), 110 (3T), 325 (7T) | Slope of intravascular relaxation rate against O2 |
| BOLD | nu0 | 28.265 * B0 | Frequency offset at the outer surface of magnetized vessels |
Notes:
- The haemodynamic priors have been changed to be log scaling parameters that multiply default values. These default values come from Figure 7 of Friston et. al 2000. The resulting prior density over parameters can be viewed with the function attention_example/view_hdm_priors.m .
- Parameters of the haemodynamic / observation models have been changed to be suitable for data of different field strengths (parameters epsilon, r0, nu0), based on recommendations from Heinzle et al. 2016 and Havlicek et al. 2015.