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. 2020 Jun;222(6):602.e1–602.e15. doi: 10.1016/j.ajog.2020.01.012

Table 6.

Equations for parameters and computations of z scores and centiles for 3 umbilical artery Doppler indices according to GA, in weeks

Parameter Equation
Skewness Pulsatility index
λ(GA) = –0.0768617
Resistance index
λ(GA) = 0.0172944
Systolic/diastolic ratio
λ(GA) = –0.2752483
Mean Pulsatility index
μ(GA) = 1.02944 + 77.7456*GA–2 – 0.000004455*GA3
Resistance index
μ(GA) = 0.674914 + 25.3909*GA–2 – 0.0000022523*GA3
Systolic/diastolic ratio
μ(GA) = 2.60358 + 445.991*GA–2 – 0.0000108754*GA3
Coefficient of variation Pulsatility index
σ(GA) = –0.00645693 + 254.885*ln(GA)*GA–2 – 715.949*GA–2
Resistance index
σ(GA) = 0.0375921 + 60.7614*ln(GA)*GA–2 – 183.336*GA–2
Systolic/diastolic ratio
σ(GA) = –0.503202 + 1268.37*ln(GA)*GA–2 – 3417.37*GA–2
z score z = λ–1∗{exp[(y-µ)∗ λ∗ σ–1]–1}
Centile c = normal(z) * 100

GA, Gestational age in exact weeks; ln, natural logarithm; y, Doppler index value.

Example: calculating the pulsatility index centile at a certain GA

Measurement: pulsatility index = 1.00 at GA 36+4
  • Calculations:
  • y = 1.00
  • 36+4 = 256 days
  • GA = 256 / 7 = 36.571429 (exact weeks)
  • λ = –0.0768617
  • μ = 1.02944 + 77.7456*(36.571429)–2 – 0.000004455*(36.571429)3 =
  • 1.02944 + 77.7456*0.00074768 – 0.000004455*48913.168 =
  • 1.02944 + 0.05812883 – 0.21790816 =
  • 0.869660
  • σ = –0.00645693 + 254.885*ln(36.571429)* (36.571429)–2 – 715.949*(36.571429)–2 =
  • –0.00645693 + 254.885*3.5992673*0.00074768 – 715.949*0.00074768 =
  • 0.144163
  • Z = λ–1*{exp[(y-μ)* λ* σ–1] – 1} =
  • (–0.0768617)–1*{exp[(1.00-0.86966067)* –0.0768617*(0.14416339)–1] – 1} =
  • –13.010381*{exp[0.13033933*–0.0768617*6.9365738] – 1} =
  • –13.010381*{exp[-0.06949131] – 1} =
  • –13.010381*{0.93286824– 1} =
  • 0.87340977
  • c = normal(0.87340977)* 100 =
  • 80.9
  • Conclusion: A pulsatility index value of 1.00 measured at 36+4 gestational weeks has a z score of 0.87 and is placed at the 80.9th centile of the distribution.

Drukker et al. International gestational age-specific centiles for umbilical artery Doppler indices: a longitudinal prospective cohort study of the INTERGROWTH-21st Project. Am J Obstet Gynecol 2020.