[Paper Review] Relationship between mass density, electron density, and elemental composition of body tissues for Monte Carlo simulation in radiation treatment planning

Nobuyuki Kanematsu|arXiv (Cornell University)|Aug 2, 2015

Advanced Radiotherapy Techniques25 references17 citations

TL;DR

This study formulates invariant polyline relationships between mass density, electron density, and elemental composition of human tissues to enable accurate Monte Carlo radiotherapy treatment planning without additional CT-number calibration. By using mass-weighted averages of standard tissues from ICRP Publication 110, the method provides consistent, patient-specific tissue models across density ranges, with high accuracy except for C, N, and O in low-density spongiosa tissues.

ABSTRACT

Purpose: For Monte Carlo simulation of radiotherapy, x-ray CT number of every system needs to be calibrated and converted to mass density and elemental composition. This study aims to formulate material properties of body tissues for practical two-step conversion from CT number. Methods: We used the latest compilation on body tissues that constitute reference adult male and female. We formulated the relations among mass, electron, and elemental densities into polylines to connect representative tissues, for which we took mass-weighted mean for the tissues in limited density regions. We compared the polyline functions of mass density with a bi-line for electron density and broken lines for elemental densities, which were derived from preceding studies. Results: There was generally high correlation between mass density and the other densities except of C, N, and O for light spongiosa tissues occupying 1% of body mass. The polylines fitted to the dominant tissues and were generally consistent with the bi-line and the broken lines. Conclusions: We have formulated the invariant relations between mass and electron densities and from mass to elemental densities for body tissues. The formulation enables Monte Carlo simulation in treatment planning practice without additional burden with CT-number calibration.

Motivation & Objective

• To eliminate the need for repeated CT-number calibration in Monte Carlo treatment planning by establishing invariant tissue density relationships.
• To improve accuracy and consistency in tissue modeling for radiotherapy simulations using standardized ICRP 110 tissue data.
• To address limitations in existing conversion functions that are system-specific and not transferable across CT scanners.
• To enable practical two-step conversion from CT number to electron density, then to tissue-specific effective densities for accurate dose calculation.

Proposed method

• Used ICRP Publication 110 data for 53 standard tissues in reference male and female phantoms to derive mass, electron, and elemental densities.
• Defined regional representative tissues via mass-weighted averaging of tissue properties within density intervals (e.g., 0.90–1.00 g/cm³, 1.00–1.07 g/cm³).
• Constructed polyline functions to relate mass density to electron density and elemental densities (H, C, N, O, P, Ca), replacing previous bi-line and broken-line approximations.
• Modelled tissue mixtures in regions of variable density using linear interpolation between representative tissues, ensuring continuity across density segments.
• Incorporated residual mass and mean residual atomic number (Z_res) to account for minor elements not explicitly tracked in major element analysis.
• Validated the polyline functions against existing SBS and Hünemohr models, assessing agreement across tissue types and density ranges.

Experimental results

Research questions

• RQ1 Can a consistent, system-independent conversion from CT number to tissue properties be achieved using mass-weighted tissue data?
• RQ2 How do the relationships between mass density, electron density, and elemental composition vary across different human tissue types and density ranges?
• RQ3 To what extent do existing bi-linear and broken-line models for electron and elemental densities match the latest ICRP 110 tissue data?
• RQ4 What is the impact of low-mass, low-density tissues (e.g., spongiosa) on the accuracy of density conversion functions?
• RQ5 Can a two-step conversion process (CT number → electron density → tissue-specific effective density) be reliably implemented without additional calibration?

Key findings

• The polyline functions for electron density and elemental densities showed high consistency with the SBS broken-line and Hünemohr bi-line models across most tissue types and density ranges.
• The highest deviation from the bi-line model occurred at 0.90 g/cm³ (fat) and 2.75 g/cm³ (tooth), with errors of -1.7% and -1.3% respectively, which the polyline resolved via continuity.
• The correlation between mass and electron density was strong except for carbon, nitrogen, and oxygen in tissues with spongiosa content (1% of body mass), where inconsistencies arose due to undifferentiated inclusion.
• Residual mass and mean residual atomic number (Z_res) varied from 12.0 (tooth) to 20.6 (thyroid), with a global mean of 15.95, close to sulfur (S), indicating reasonable approximation of minor elements.
• The formulation enables direct use in Monte Carlo simulations without recalibration for different CT systems, significantly reducing setup burden in clinical treatment planning.
• The method supports accurate, patient-specific volumetric modeling by enabling conversion from electron density to full elemental composition using the derived polyline functions.