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Simulated Random Spatially Patterned Kidney Datasets

Source: R/data.R
simRanPatternRasts.Rd

A list of 100 simulated SpatialExperiment objects representing kidney-shaped datasets, each containing one independently generated spatially patterned gene with no correlation between datasets. For each dataset, \(N = 5000\) cells were simulated in the unit square, and the 1201 to 1381 cells within a kidney-shaped region were kept, with spatial coordinates and expression values generated from Gaussian random fields.

Usage

simRanPatternRasts

Format

A list of length 100, where each element is a SpatialExperiment object containing:

assays

Matrix of simulated expression values named "pixelval".

colData

Data frame of per-pixel metadata: the number and IDs of the cells in the pixel, the pixel shape and resolution, and its geometry.

spatialCoords

Matrix of spatial \((x, y)\) coordinates.

Source

Simulated by the STcompare development team.

Details

Each simulated dataset was generated as follows:

  • Cell coordinates \((x, y)\) were uniformly sampled within a bounding box from \(x, y \in [0,1]\).

  • A Matern covariance matrix \(Cov_{ij}\) of size \(N \times N\) was computed as: $$ Cov_{ij} = \frac{2^{1-\nu}}{\Gamma(\nu)} \left(\frac{h \sqrt{2\nu}}{\kappa}\right)^{\nu} K_\nu \left(\frac{h \sqrt{2\nu}}{\kappa}\right) $$ where \(h = \sqrt{(x_i - x_j)^2 + (y_i - y_j)^2}\), \(\nu = 0.5\), \(\kappa = 0.1\), \(\Gamma\) is the gamma function, and \(K_\nu\) is the modified Bessel function of the second kind. For diagonal elements (\(i = j\)), \(Cov_{ij} = 1\).

  • The covariance matrix was used to generate a multivariate normal vector \(W_i\) with mean 0 via MASS::mvrnorm.

  • Independently and identically distributed noise \(Z_i\) was sampled using stats::rnorm with mean 0 and standard deviation \(\sqrt{0.3}\).

  • The simulated gene expression for each cell was computed as: $$G_i = W_i + Z_i + 10$$

  • To form a kidney-shaped spatial pattern, each cell position was transformed to \((x, y) = (6x - 3, 6y - 3)\) and retained only if its Euclidean distance from the origin satisfied: $$\sqrt{x^2 + y^2} \le 1 - 2\sin(\theta) + \cos(\theta^2)$$ where \(\theta = \mathrm{atan2}(y, x)\).

Each element of simRanPatternRasts is a SpatialExperiment object with:

  • One simulated gene (1 row)

  • 272 to 288 spatial pixels (columns)

  • An assay named "pixelval" containing expression values

  • colData with columns: num_cell, cellID_list, type, resolution, geometry, and sample_id

  • Spatial coordinates (x, y)

See also

SpatialExperiment, mvrnorm, rnorm

Examples

data(simRanPatternRasts)
simRanPatternRasts[[1]]
#> class: SpatialExperiment 
#> dim: 1 280 
#> metadata(0):
#> assays(1): pixelval
#> rownames(1): 1
#> rowData names(0):
#> colnames(280): pixel151 pixel152 ... pixel588 pixel589
#> colData names(6): num_cell cellID_list ... geometry sample_id
#> reducedDimNames(0):
#> mainExpName: NULL
#> altExpNames(0):
#> spatialCoords names(2) : x y
#> imgData names(0):
SummarizedExperiment::assays(simRanPatternRasts[[1]])$pixelval[1, 1:5]
#>  pixel151  pixel152  pixel153  pixel154  pixel169 
#>  9.947299 10.203625  9.442802  8.277710 10.923103