SingleVoxelFFBS {BayesDLMfMRI}

SingleVoxelFFBS

Description

This function is used to perform an activation analysis for single voxels based on the FFBS algorithm.

Usage

SingleVoxelFFBS(
  posi.ffd,
  covariates,
  ffdc,
  m0,
  Cova,
  delta,
  S0,
  n0,
  N1,
  Nsimu1,
  Cutpos1,
  Min.vol,
  r1
)

Arguments

posi.ffd

the position of the voxel in the brain image.

covariates

a data frame or matrix whose columns contain the covariates related to the expected BOLD response obtained from the experimental setup.

ffdc

a 4D array (ffdc[i,j,k,t]) that contains the sequence of MRI images that are meant to be analyzed. (i,j,k) define the position of the observed voxel at time t.

m0

the constant prior mean value for the covariates parameters and common to all voxels within every neighborhood at t=0 (m=0 is the default value when no prior information is available). For the case of available prior information, m0 can be defined as a \(p\times q\) matrix, where \(p\) is the number of columns in the covariates object and \(q\) is the cluster size.

Cova

a positive constant that defines the prior variances for the covariates parameters at t=0 (Cova=100 is the default value when no prior information is available). For the case of available prior information, Cova can be defined as a \(p\times p\) matrix, where \(p\) is the number of columns in the covariates object.

delta

a discount factor related to the evolution variances. Recommended values between 0.85<delta<1. delta=1 will yield results similar to the classical general linear model.

S0

prior covariance structure among voxels within every cluster at t=0. S0=1 is the default value when no prior information is available and defines an \(q\times q\) identity matrix. For the case of available prior information, S0 can be defined as an \(q\times q\) matrix, where \(q\) is the common number of voxels in every cluster.

n0

a positive hyperparameter of the prior distribution for the covariance matrix S0 at t=0 (n1=1 is the default value when no prior information is available). For the case of available prior information, n0 can be set as n0=np, where np is the number of MRI images in the pilot sample.

N1

is the number of images (2<N1<T) from the ffdc array employed in the model fitting. N1=NULL (or equivalently N1=T) is its default value, taking all the images in the ffdc array for the fitting process.

Nsimu1

is the number of simulated on-line trajectories related to the state parameters. These simulated curves are later employed to compute the posterior probability of voxel activation.

Cutpos1

a cutpoint time from where the on-line trajectories begin. This parameter value is related to an approximation from a t-student distribution to a normal distribution. Values equal to or greater than 30 are recommended (30<Cutpos1<T).

Min.vol

helps to define a threshold for the voxels considered in the analysis. For example, Min.vol = 0.10 means that all the voxels with values below to max(ffdc)*Min.vol can be considered irrelevant and discarded from the analysis.

r1

a positive integer number that defines the distance from every voxel with its most distant neighbor. This value determines the size of the cluster. The users can set a range of different r1 values: \(r1 = 0, 1, 2, 3, 4\), which leads to \(q = 1, 7, 19, 27, 33\), where \(q\) is the size of the cluster.

Details

This function allows the development of an activation analysis for single voxels. A multivariate dynamic linear model is fitted to a cluster of voxels, with its center at location (i,j,k), in the way it is presented in (Cardona-Jiménez and de B. Pereira 2021).

Value

a list containing a vector (Evidence) with the evidence measure of activation for each of the p covariates considered in the model, the simulated online trajectories related to the state parameter, the simulated BOLD responses, and a measure to examine the goodness of fit of the model \((100 \ast |Y[i,j,k]_t - \hat{Y}[i,j,k]_t |/ \hat{Y}[i,j,k]_t )\) for that particular voxel (FitnessV).

References

Cardona-Jiménez J, de B. Pereira CA (2021). “Assessing dynamic effects on a Bayesian matrix-variate dynamic linear model: An application to task-based fMRI data analysis.” Computational Statistics & Data Analysis, 163, 107297. ISSN 0167-9473, doi:10.1016/j.csda.2021.107297, https://www.sciencedirect.com/science/article/pii/S0167947321001316.

Cardona-Jiménez J (2021). “BayesDLMfMRI: Bayesian Matrix-Variate Dynamic Linear Models for Task-based fMRI Modeling in R.” arXiv e-prints, arXiv–2111.

Examples

## Not run: 
# This example can take a long time to run.
fMRI.data  <- get_example_fMRI_data()
data("covariates", package="BayesDLMfMRI")
res.indi <- SingleVoxelFFBS(posi.ffd = c(14, 56, 40), 
                            covariates = Covariates,
                            ffdc =  fMRI.data, 
                            m0 = 0, Cova = 100, delta = 0.95, S0 = 1, 
                            n0 = 1, Nsimu1 = 100, N1 = FALSE, Cutpos1 = 30, 
                            Min.vol = 0.10, r1 = 1)


## End(Not run)