Investigation of the relationship between linear attenuation coefficients and CT Hounsfield units using radionuclides for SPECT

Abstract

This study has investigated the relationship between linear attenuation coefficients (μ) and Hounsfield units (HUs) for six materials covering the range of values found clinically. Narrow-beam μ values were measured by performing radionuclide transmission scans using ^99mTc, ¹²³I, ¹³¹I, ²⁰¹Tl and ¹¹¹In. The μ values were compared to published data. The relationships between μ and HU were determined. These relationships can be used to convert computed tomography (CT) images to μ-maps for single photon emission computed tomography (SPECT) attenuation correction.

Introduction

Single photon emission computed tomography (SPECT) is an imaging modality used to visualise the biological uptake and distribution of an injected radionuclide. Photons produced through radioactive decay interact with soft tissue and bone inside the patient before reaching an external detector. The probability that a photon will undergo an interaction while passing through a unit thickness of material is defined by the linear attenuation coefficient (μ), which has units of cm⁻¹. The linear attenuation coefficient is dependent on the composition of the attenuating material and the photon energy. For a mono-energetic narrow beam of photons, intensity I, the exponential attenuation law states

$$I=I_0·\exp (-\mu x)\text{,}$$

where I₀ is the initial intensity of the incident beam and x is the thickness of material which the beam passes through.

Fusing SPECT and computed tomography (CT) images has been shown to be a useful clinical method of spatially localising radionuclide uptake within organs and tumour volumes, giving both anatomical and functional information (Roach et al., 2006). X-ray CT data have previously been used to improve the accuracy of a SPECT image by creating a patient specific attenuation map for photon attenuation correction (Fleming, 1989). CT image data are dependent on the density of tissues and the beam energy, where each image pixel is assigned a Hounsfield unit (HU). HU is directly related to μ at the effective energy (E_CT) of the CT scanner:

$$\mathrm{HU}=1000·\left[\frac{\mu (E_{\mathrm{CT}})-{\mu }_{\mathrm{w}}(E_{\mathrm{CT}})}{{\mu }_{\mathrm{w}}(E_{\mathrm{CT}})}\right]\text{,}$$

where μ_w is the linear attenuation coefficient of water.

Linear attenuation coefficients are referred to as being narrow-beam or broad-beam depending on whether they contain scattered transmission photons or not. Narrow-beam linear attenuation coefficients should be used for SPECT attenuation correction when combined with an explicit correction for scattered photons (Bailey, 1998).

A previous investigation (Bai et al., 2003) produced a simple mathematical model for calculating linear attenuation coefficients of a given material from CT numbers by introducing a material dependent conversion factor that categorised materials into either having an HU less than zero (“water–air assumption”) or having an HU greater than zero (“water–bone assumption”). This model was based on the piecewise bilinear fitting technique developed by Blankespoor et al. (1996), with a linear fit between the lowest density material (air with an HU of −1000) and water (HU of 0) and a second linear fit between water and the highest density material (cortical bone with an HU>1000). In order to use this bilinear model proposed by Bai et al. (2003) for materials with a density greater than water, a sample of cortical bone equivalent material must be CT scanned at each required kVp for accurate conversion of the CT numbers to linear attenuation coefficients.

This study aims to quantify the relationship between linear attenuation coefficients and CT HU by performing radionuclide transmission scans using a selection of clinically relevant radionuclides and a selection of materials with densities that span the entire Hounsfield scale (Table 1). These mathematical relationships could be used to accurately convert CT numbers to linear attenuation coefficients for SPECT attenuation correction without having to scan a sample of cortical bone at the required CT kVp.