T Parameter

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Figure 1: A Kratky plot of the radial intensity profile used for T parameter calculation.

The T parameter is a measure of the mean thickness of the mineral particles in bone and is calculated from a radial intensity profile. T is calculated by T parameter def.png.
Porod constant (P) and background (B) are derived from a Porod plot. The integral is solved by calculating the three areas I0, I1 and I2. I0 [0, qmin Kratky] is calculated by linear approximation, I1 [qmin Kratky, qmin Porod] is directly calculated from the radial intensity profile and I2 [qmin Porod, ∞] is approximated by I2 = P / qmin Porod.


Parameter

  • q_min Porod and q_max Porod: The region [q_min Porod, q_max Porod] is used to calculate the Porod constant (P) and the background (B). Choose the “q_min Porod” and “ q_max Porod” so that the slope of log-log plot is approximately -4.
  • q_min Kratky: Select the “q_min Kratky” as an available minimum q value in the data.
  • q_min Plot and q_max Plot: Both are used only for plot clarity to check the results.


Figure 2: Screenshot of the "T Parameter" plugin.
Figure 3: Screenshot of the example Direct Transmission File.


Inputs

  • q: The q values of the radial intensity profile.
  • I: The intensity values of the radial intensity profile.

Outputs

  • q_orig, I_orig: The radial intensity profile.
  • q_porod, I_porod: The Porod plot used to calculate Porod constant and background.
  • q^4, Iq^4: The "Porod Plot" profile.
  • q_kratky, I_kratky: The Kratky plot used to calculate Integration_1.
  • porod_cst: The calculated Porod constant.
  • laue_cst: The calculated background.
  • loglog_slope: The slope of the log-log-radial profile in the region [q_min_porod, q_max_porod]. Should be approximately -4.
  • Integration_0, Integration_1, Integration_2, Total_integration: The calculated areas I0, I1, I2 and their sum.
  • T: The T parameter.
  • q_min_porod, q_max_porod, q_min_kratky: The plugin input parameters.
  • qT, I_Gx: The G(x) curve plot data.
  • q_min Plot and q_max Plot: Used only for plot clarity to check the results.