Understanding ibidi Chemotaxis Metrics

Introduction

Chemotaxis—the directed migration of cells in response to chemical gradients—is fundamental to immune responses, wound healing, cancer metastasis, and embryonic development. Quantifying chemotaxis requires more than just measuring how far cells move; we need to understand whether they’re moving toward the chemoattractant and how efficiently they navigate.

The ibidi Chemotaxis Tool has become a standard in the field, providing a well-defined coordinate system and metrics for analyzing cell migration in chemotaxis assays. This guide explains these metrics, how they’re calculated, and what they tell you about your cells.

The ibidi Coordinate System

Before diving into metrics, it’s crucial to understand the ibidi coordinate system, which differs from standard image coordinates.

Image Coordinates vs. ibidi Coordinates

Standard Image Coordinates:

Origin at top-left corner
X increases rightward
Y increases downward
No inherent biological meaning

ibidi Chemotaxis Coordinates:

Origin at cell starting position (M_start)
Y-axis (parallel): Points toward the chemoattractant (direction of gradient)
X-axis (perpendicular): Perpendicular to gradient (90° clockwise from Y-axis)
Biologically meaningful: Y measures chemotaxis, X measures random drift

Reservoir Locations

The ibidi μ-Slide Chemotaxis chambers have reservoirs that establish chemical gradients. The reservoir location determines coordinate transformation:

Reservoir Position	Forward Direction (Y)	Perpendicular Direction (X)
Bottom	Downward (0, +1)	Rightward (+1, 0)
Top	Upward (0, -1)	Leftward (-1, 0)
Right	Rightward (+1, 0)	Downward (0, +1)
Left	Leftward (-1, 0)	Upward (0, -1)

Key Rule: X-axis is always 90° clockwise from the Y-axis gradient direction.

Core Metrics Explained

1. Forward Migration Index (FMI)

FMI quantifies how much of a cell’s movement is directed along a specific axis, normalized by the total path length.

Formula:

FMI = Σ(displacement_along_axis) / AccumulatedDistance

Two Components:

yFMI (Parallel FMI):

Measures movement along the gradient (toward/away from chemoattractant)
Range: -1 to +1
+1: Perfect directed movement toward attractant
0: Random walk (no net directionality)
-1: Movement away from attractant (chemorepulsion)

xFMI (Perpendicular FMI):

Measures drift perpendicular to gradient
Range: -1 to +1
Should be ≈0 for true chemotaxis (random lateral drift)
Non-zero values indicate bias or assymetric conditions

Example Interpretation:

yFMI = 0.75, xFMI = 0.05

✓ Strong chemotaxis (75% of movement toward attractant)
✓ Minimal lateral drift (random walk perpendicular to gradient)

yFMI = 0.15, xFMI = 0.60

✗ Weak chemotaxis (only 15% toward attractant)
✗ Strong lateral bias (possibly due to flow, gravity, or damage)

2. Center of Mass (CoM)

The average endpoint of all tracked cells, relative to their starting positions.

Components:

CoM X: Mean perpendicular displacement (µm)
CoM Y: Mean parallel displacement (µm)
CoM Length: Euclidean distance from origin: √(X² + Y²)

Interpretation:

CoM Length measures population-level net displacement
For true chemotaxis: CoM Y >> CoM X
Large CoM X suggests external bias or assymetry

Relationship to FMI:

CoM Length ≈ MeanEuclideanDistance
yFMI ≈ CoM Y / MeanAccumulatedDistance

3. Directness (Directionality)

Directness measures how straight cells move from start to finish.

Formula:

Directness = EuclideanDistance / AccumulatedDistance

Where:

EuclideanDistance: Straight-line distance from start to end
AccumulatedDistance: Total path length traveled

Interpretation:

1.0: Perfectly straight line
0.8-0.95: Fairly direct migration (typical for chemotaxis)
0.5: Meandering path (significant random walk)
<0.3: Highly convoluted, exploratory behavior

Important: High directness alone doesn’t prove chemotaxis—a cell could walk straight in the wrong direction. Always check yFMI alongside directness.

4. Velocity vs. Speed

These terms are often confused but measure different things:

Mean Velocity (µm/min):

Velocity = EuclideanDistance / Duration

Net displacement rate (start → end)
Affected by directness
Lower than speed for meandering cells

Mean Speed (µm/min):

Speed = AccumulatedDistance / Duration

Total path length rate
Represents actual locomotion capability
Higher than velocity for random walkers

Example:

A cell travels 200 µm over 20 minutes but ends up only 120 µm from its start:

Speed: 200 µm / 20 min = 10 µm/min
Velocity: 120 µm / 20 min = 6 µm/min
Directness: 120 / 200 = 0.6 (meandering path)

5. Rayleigh Test

A statistical test for whether cell migration directions are randomly distributed or show a preferred direction.

Interpretation:

p < 0.05: Significant directional bias (reject random walk hypothesis)
p > 0.05: Directions are randomly distributed (consistent with random walk)

For chemotaxis experiments, you want p < 0.05 in the treatment group but p > 0.05 in the control (no gradient).

Practical Guidelines

What Makes Good Chemotaxis?

A strong chemotactic response typically shows:

yFMI: 0.6-0.9 (60-90% of movement toward attractant)
xFMI: -0.2 to +0.2 (minimal lateral bias)
Directness: >0.7 (fairly straight paths)
Rayleigh p-value: <0.05 (significant directionality)

Red Flags in Your Data

High xFMI (>0.3):

Check for flow in the chamber
Verify chamber is level (no gravity effects)
Look for damage/assymetry in chamber

Low Directness (<0.5) with High yFMI:

Cells are moving toward attractant but taking inefficient paths
May indicate weak gradient or competing signals
Normal for some cell types (e.g., dendritic cells)

Negative yFMI:

Possible chemorepulsion
Or cells were placed on wrong side of chamber
Or gradient direction was misidentified

Common Pitfalls

Wrong Reservoir Location: Choosing “Bottom” when gradient is from “Top” will invert yFMI sign
Insufficient Track Duration: Minimum 5 minutes recommended; longer is better for statistical power
Too Few Cells: Need ≥20 tracked cells for reliable statistics
Mixing Active and Inactive Tracks: Only include cells tracked for minimum duration
Ignoring Calibration: Always set µm/pixel and seconds/frame correctly

Metric Reference Table

Metric	Symbol	Range	Ideal Chemotaxis	Random Walk	Chemorepulsion
Parallel FMI	yFMI	-1 to +1	0.6-0.9	≈0	-0.6 to -0.9
Perpendicular FMI	xFMI	-1 to +1	≈0	≈0	≈0
Directness	d	0 to 1	>0.7	0.3-0.6	>0.7
Velocity	v	≥0 µm/min	Moderate-High	Low	Moderate-High
Speed	s	≥0 µm/min	Always ≥ velocity	≈velocity	Always ≥ velocity
Rayleigh p	p	0 to 1	<0.05	>0.05	<0.05

Example Analysis

Experiment: Neutrophil response to fMLP gradient

Results:

Chemotaxis Metrics (n=47 cells):
  FMI Parallel (yFMI):        0.721
  FMI Perpendicular (xFMI):   -0.043
  Center of Mass Y:           185.3 µm
  Center of Mass X:           -12.1 µm
  Mean Directness:            0.823
  Mean Velocity:              8.7 µm/min
  Mean Speed:                 10.6 µm/min
  Rayleigh Test p-value:      0.0001

Interpretation:

✓ Strong chemotaxis: yFMI = 0.72 means 72% of neutrophil movement is directed toward fMLP
✓ No lateral bias: xFMI ≈ 0 indicates no systematic drift perpendicular to gradient
✓ Efficient migration: Directness = 0.82 shows fairly straight paths
✓ Statistically significant: p < 0.001 strongly rejects random walk hypothesis
✓ Active locomotion: Speed = 10.6 µm/min is typical for activated neutrophils

Conclusion: Neutrophils exhibit robust, directed chemotaxis toward fMLP with minimal random walk component.

Implementation Notes

When implementing ibidi metrics in software:

1. Coordinate Transformation

// Example: Bottom reservoir (gradient pointing down)
double gradientX = 0, gradientY = 1;  // Forward direction
double perpX = 1, perpY = 0;          // 90° clockwise: (gradY, -gradX)

// For any reservoir, perpendicular is always:
perpX = gradientY;
perpY = -gradientX;

2. Track Filtering

// Recommended minimum track criteria:
int minDetections = 3;              // At least 3 time points
double minDuration = 300;           // At least 5 minutes (300 seconds)
double minMovement = 2.0;           // At least 2 µm total displacement

3. Metric Calculation Order

Transform coordinates (image → ibidi)
Normalize tracks (set start position to origin)
Calculate per-track metrics
Aggregate across population
Compute statistical tests

Summary

ibidi chemotaxis metrics provide a standardized, biologically meaningful framework for quantifying directed cell migration:

FMI (yFMI, xFMI): Direction and bias of movement
Center of Mass: Population-level displacement
Directness: Path efficiency
Velocity/Speed: Migration rates
Rayleigh Test: Statistical significance

Understanding these metrics enables rigorous quantification of chemotactic responses, comparison across experiments, and publication-quality analysis.

When analyzing your data, always consider metrics together—no single value tells the complete story. A strong chemotactic response shows high yFMI, near-zero xFMI, reasonable directness, and significant Rayleigh p-value.

About MetaVi Labs: We develop automated image analysis tools for life science research, including implementation of ibidi-compatible chemotaxis analysis in our FastTrackAI platform.

Questions or feedback? Contact us at support@metavilabs.com

Last updated: December 30, 2025

Understanding ibidi Chemotaxis Metrics

Introduction

The ibidi Coordinate System

Image Coordinates vs. ibidi Coordinates

Reservoir Locations

Core Metrics Explained

1. Forward Migration Index (FMI)

Formula:

Two Components:

Example Interpretation:

2. Center of Mass (CoM)

Components:

Interpretation:

Relationship to FMI:

3. Directness (Directionality)

Formula:

Interpretation:

4. Velocity vs. Speed

Mean Velocity (µm/min):

Mean Speed (µm/min):

Example:

5. Rayleigh Test

Interpretation:

Practical Guidelines

What Makes Good Chemotaxis?

Red Flags in Your Data

Common Pitfalls

Metric Reference Table

Example Analysis

Experiment: Neutrophil response to fMLP gradient

Implementation Notes

1. Coordinate Transformation

2. Track Filtering

3. Metric Calculation Order

Further Reading

Summary