Example Vessel Density Data for Stereology Analysis

Simulated dataset of vessel density measurements using stereology methods in tissue samples from patients with different diagnoses. This dataset demonstrates quantitative histopathology using systematic grid-based sampling.

Usage

stereology_vessel_data

Format

A data frame with 50 observations and 13 variables:

image_id

Character. Unique image identifier

diagnosis

Factor. Diagnosis group (Normal, Benign, Malignant)

tissue_type

Character. Type of structure quantified (Blood Vessels)

intersections

Integer. Number of grid intersections with vessels

total_points

Integer. Total number of grid points examined (100)

boundary_intersections

Integer. Grid line intersections with vessel boundaries

object_count

Integer. Number of discrete vessels counted

reference_area

Numeric. Total reference area examined (μm²)

grid_spacing

Numeric. Distance between grid lines (μm)

section_thickness

Numeric. Histological section thickness (μm)

Aa

Numeric. Calculated area density (fraction)

Vv

Numeric. Calculated volume density (fraction)

Source

Simulated data based on stereology principles from: Kayser et al. (2009) Diagnostic Pathology 4:6. Realistic vessel density values based on published tumor angiogenesis studies.

Details

Study Design:

• 50 histological images from 3 diagnostic groups

• Systematic 10×10 grid overlay (100 points per image)

• Grid spacing: 10 μm

• Reference area: 1000×1000 μm (1 mm²)

• Section thickness: 5 μm (standard histology)

Clinical Context: Vessel density is a critical parameter in tumor pathology. Malignant tumors often show increased angiogenesis (new blood vessel formation) to support rapid growth. Stereology provides unbiased quantification of vessel density from 2D histological sections without requiring 3D reconstruction.

Vessel Density by Diagnosis:

• Normal tissue: Low vessel density (Aa ~ 0.05-0.10)

• Benign tumors: Moderate vessel density (Aa ~ 0.15-0.25)

• Malignant tumors: High vessel density (Aa ~ 0.30-0.50) due to angiogenesis

Stereological Parameters:

1. Area Density (Aa)

   • Formula: Aa = intersections / total_points

   • Meaning: Fraction of tissue area occupied by vessels

   • Use: Primary measure of vessel density

2. Volume Density (Vv)

   • Formula: Vv = Aa (for isotropic random sections)

   • Meaning: Fraction of tissue volume occupied by vessels

   • Use: 3D estimate from 2D sections

3. Boundary Density (Ba)

   • Formula: Ba = (2 × boundary_intersections) / line_length

   • Meaning: Vessel boundary length per unit area

   • Use: Measure of vessel complexity

4. Numerical Density (Na)

   • Formula: Na = object_count / reference_area

   • Meaning: Number of vessels per unit area

   • Use: Vessel count density

5. Surface Density (Sv)

   • Formula: Sv = 2 × Ba

   • Meaning: Vessel surface area per unit volume

   • Use: Exchange surface quantification

Example Analysis:

# Load data
data(stereology_vessel_data, package = "ClinicoPath")

# Basic stereology analysis
stereology(
  data = stereology_vessel_data,
  intersections = 'intersections',
  totalPoints = 'total_points',
  referenceArea = 'reference_area',
  gridSpacing = 'grid_spacing',
  calculateAa = TRUE,
  calculateVv = TRUE,
  showConfidenceIntervals = TRUE
)

# Group comparison by diagnosis
stereology(
  data = stereology_vessel_data,
  intersections = 'intersections',
  totalPoints = 'total_points',
  referenceArea = 'reference_area',
  gridSpacing = 'grid_spacing',
  groupVar = 'diagnosis',
  showGroupComparison = TRUE
)

# Advanced analysis with all parameters
stereology(
  data = stereology_vessel_data,
  intersections = 'intersections',
  totalPoints = 'total_points',
  boundaryIntersections = 'boundary_intersections',
  objectCount = 'object_count',
  referenceArea = 'reference_area',
  gridSpacing = 'grid_spacing',
  tissueType = 'vessels',
  calculateAa = TRUE,
  calculateVv = TRUE,
  calculateBa = TRUE,
  calculateNa = TRUE,
  calculateSv = TRUE,
  showConfidenceIntervals = TRUE,
  bootstrapIterations = 1000
)

Why Stereology is Needed:

• Provides unbiased estimates of 3D parameters from 2D sections

• No need for complex 3D reconstruction

• Well-established statistical properties

• Reproducible across laboratories

• Applicable to any histological structure

Expected Results:

• Malignant tumors show significantly higher vessel density (Aa ~ 0.39)

• Benign tumors have intermediate density (Aa ~ 0.20)

• Normal tissue has lowest density (Aa ~ 0.07)

• Statistical tests should show significant differences between groups

Quality Control:

• Grid spacing appropriate for vessel size (10 μm)

• Adequate number of points per image (100 points)

• Multiple images per diagnosis (16-17 per group)

• Systematic random sampling approach

See also

• stereology() for stereology analysis function

• Kayser et al. (2009) for theoretical framework

• Gundersen & Jensen (1985, 1986) for stereology methodology

Examples

# \donttest{
# Load data
data(stereology_vessel_data, package = "ClinicoPath")

# Summary by diagnosis
aggregate(Aa ~ diagnosis, data = stereology_vessel_data,
          FUN = function(x) c(mean = mean(x), sd = sd(x)))
#>   diagnosis    Aa.mean      Aa.sd
#> 1    Normal 0.07352941 0.02422323
#> 2    Benign 0.20411765 0.02693947
#> 3 Malignant 0.39375000 0.08754999

# Visualize vessel density distribution
boxplot(Aa ~ diagnosis, data = stereology_vessel_data,
        main = "Vessel Area Density by Diagnosis",
        xlab = "Diagnosis", ylab = "Area Density (Aa)",
        col = c("lightblue", "lightgreen", "lightcoral"))


# Test for differences
summary(aov(Aa ~ diagnosis, data = stereology_vessel_data))
#>             Df Sum Sq Mean Sq F value Pr(>F)    
#> diagnosis    2  0.852  0.4260   147.3 <2e-16 ***
#> Residuals   47  0.136  0.0029                   
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
# }