Apparent Diffusion Coefficient Calculator

Calculate apparent diffusion coefficient, b-value, signal intensity, or baseline signal from the other three using the MRI diffusion equation.

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Apparent Diffusion Coefficient Formula

The apparent diffusion coefficient calculation is based on the monoexponential diffusion-weighted MRI signal model:

S = S₀ * e⁽ - b * ADC)

Rearranged forms used to solve for each missing value are:

ADC = - ln(S / S₀) / b

b = - ln(S / S₀) / ADC

S₀ = S / e⁽ - b * ADC)

S = signal intensity measured at the selected b-value
S₀ = baseline signal intensity, usually measured at b = 0 or a very low b-value
b = diffusion weighting factor, commonly entered in s/mm²
ADC = apparent diffusion coefficient, commonly expressed in mm²/s
ln = natural logarithm
e = Euler’s number, used in exponential decay calculations

The calculator lets you enter any three values and solves for the fourth. If ADC is missing, it uses the ratio between the measured signal and baseline signal. If signal intensity is missing, it applies exponential decay from the baseline signal. If the b-value is missing, it solves for the amount of diffusion weighting needed to produce the observed signal drop. If baseline signal is missing, it reverses the decay equation to estimate S₀.

Common ADC and b-Value Reference Ranges

ADC values depend on scanner settings, tissue type, acquisition method, and region of interest placement. The table below gives broad reference ranges for checking whether a result is in a plausible order of magnitude.

Result range	ADC in mm²/s	Common interpretation
Low ADC	About 0.0004 to 0.0008	Greater diffusion restriction, depending on tissue and context
Intermediate ADC	About 0.0008 to 0.0015	Often seen in many normal soft tissues and mixed tissue regions
High ADC	Above about 0.0015	Less restricted diffusion or more free water contribution

b-value range	Typical use	Effect on signal
0 to 100 s/mm²	Baseline or low diffusion weighting	Signal remains close to S₀
400 to 800 s/mm²	Moderate diffusion weighting	Signal decreases more noticeably
800 to 1000+ s/mm²	High diffusion weighting	Signal drop is stronger and ADC differences are emphasized

Example Calculations

Example 1: Calculate ADC

Suppose the signal intensity is 450, the baseline signal intensity is 1000, and the b-value is 800 s/mm².

ADC = - ln(450 / 1000) / 800

ADC = 0.000998 mm² / s

The apparent diffusion coefficient is approximately 0.0010 mm²/s.

Example 2: Calculate Signal Intensity

Suppose the baseline signal intensity is 1200, the b-value is 1000 s/mm², and the ADC is 0.0009 mm²/s.

S = 1200 * e⁽ - 1000 * 0.0009)

S = 487.9

The estimated signal intensity is approximately 487.9.

FAQ

What units should I use for ADC and b-value?

ADC is commonly entered in mm²/s, and b-value is commonly entered in s/mm². These units pair naturally because multiplying b by ADC gives a unitless exponent. If you use cm-based units, make sure the b-value and ADC units are consistent.

Why does signal intensity decrease as the b-value increases?

A higher b-value applies stronger diffusion weighting. In the formula, the term e^{-b × ADC} becomes smaller as b increases, so the measured signal intensity decreases relative to the baseline signal intensity.

Can ADC be negative?

In normal physical interpretation, ADC should not be negative. A negative result usually means the entered signal intensity is greater than the baseline signal intensity, the values are noisy, or the baseline and diffusion-weighted measurements were not entered consistently.