Computed tomography has long been one of medicine’s most powerful windows into the human body, but a fundamental limitation has always lurked beneath its grayscale images. Conventional CT measures how much X-rays are attenuated as they pass through tissue, a property tied mainly to electron density. That means materials with similar electron densities — different tissues, different tumors, different stone compositions — can look frustratingly alike on a standard scan. A new study published in Heliyon by Sebastian Horstmeier, Felix Sebastian Thomsen and Jan Borggrefe now shows how to squeeze far more chemical information out of a modern clinical scanner, computing maps of mass density and effective atomic number directly from images that hospitals already generate every day.
The key to the approach lies in a piece of physics that dates back to 1976, when Robert Alvarez and Albert Macovski showed that X-ray attenuation in the diagnostic energy range can be described as the sum of just two effects: the photoelectric effect and Compton scattering. The photoelectric contribution depends strongly on the atomic number of the material, while the Compton contribution depends mainly on electron density. If attenuation can be measured at several different X-ray energies, the two contributions can be mathematically separated, and from them the material’s mass density and its effective atomic number — a weighted average of the atomic numbers of the elements it contains — can be calculated. This formalism underlies virtually every spectral CT technique in use today, from virtual non-contrast imaging to material decomposition.
What has historically made such calculations difficult in the clinic is that the raw projection data needed for them are locked away inside proprietary scanner software. Manufacturers guard the sinograms, the scanner geometry, the beam-hardening corrections and the spectral detector response functions that a from-scratch reconstruction would require. The German team sidestepped this obstacle elegantly: instead of raw data, they used virtual monoenergetic images, or VMIs, which the scanner’s own software already produces. VMIs simulate what a CT image would look like if the X-ray beam consisted of photons at a single energy, and because the manufacturer has already corrected them for beam hardening, beam quality and detector efficiency, they arrive ready for quantitative analysis. No knowledge of the bow-tie filter or the tube spectrum is needed.
The scanner in question was the Naeotom Alpha from Siemens Healthineers, the first clinically approved photon-counting CT system, released in 2021. Unlike conventional detectors that merely count photons in aggregate, photon-counting detectors register each X-ray photon individually and sort them by energy, providing spectral data intrinsically with every scan and without any additional radiation dose to the patient. From a single acquisition, the researchers generated virtual monoenergetic reconstructions at six energies — 40, 50, 60, 80, 100 and 150 kiloelectronvolts — using the scanner’s Syngo.Via software, and then imported these image sets into their own Python-based analysis pipeline.
The mathematics at the heart of the method is disarmingly compact. Following the Alvarez-Macovski model, the linear attenuation coefficient at each energy is written as a photoelectric term, scaling with density, effective atomic number and an inverse power of the energy, plus a Compton term described by the Klein-Nishina function. Substituting two composite coefficients reduces the problem to a linear system: with attenuation measured at two or more energies, the coefficients can be solved by linear regression, and from them density and effective atomic number follow directly. Using six energies rather than the minimum of two gives the regression extra robustness against the noise that inevitably contaminates real CT data, producing more stable values in the final maps.
Before the algorithm could touch a scanner, its four free parameters had to be calibrated. The team fitted the model to reference attenuation data from the NIST XCOM database for sixteen elements spanning effective atomic numbers from 5, boron, to 20, calcium — precisely the range occupied by the elements that make up human tissue, and a range conveniently free of the abrupt K-edge absorption features that would complicate the fit. The calibration, performed over 40 to 200 keV, yielded parameters remarkably close to those reported by earlier groups, with a coefficient of determination of 0.9996. A verification step then confirmed that the calibrated model reproduces the literature values for density and atomic number with slopes of almost exactly one, small residual deviations being folded in as correction factors.
To test the method on real scanner output, the researchers prepared a series of alcohol-water mixtures — ethanol at 0, 25, 50, 75 and 95 percent by volume, and isopropanol at 0, 10, 35, 60 and 70 percent. These humble mixtures were chosen deliberately: their densities and effective atomic numbers fall squarely in the soft-tissue range of the human body, they are cheap, safe and easy to prepare, and their expected properties can be calculated from published reference data. The tubes were mounted in a custom epoxy-resin phantom nested inside a larger PMMA ring to mimic the scattering conditions of a human torso, and scanned five times at 140 kilovolts so that image noise could be reduced by averaging.
The results were strikingly accurate. Across both mixture series, the measured mass densities deviated from the expected values by an average of just 1.0 percent, while the effective atomic numbers deviated by 0.84 percent. Pure water yielded an effective atomic number of 7.49 against an expected 7.47, and even the most concentrated alcohol solutions tracked their reference values almost perfectly. The maps themselves visually distinguished every concentration in both series. The accuracy is comparable to that reported by earlier image-domain approaches, such as the work of Heismann and colleagues, which required far more complex preprocessing of raw data to achieve deviations of similar magnitude.
The method is not without limits. The Zeff maps proved noisier than the density maps, because Compton scattering depends only weakly on attenuation in this energy range, leaving the atomic-number estimate more vulnerable to image noise, and residual beam-hardening effects produced a gentle gradient across the phantom. The algorithm is also valid only for materials with effective atomic numbers between 5 and 20 and densities up to about 2.0 grams per cubic centimeter — a range that comfortably covers biological tissue, including cortical bone at roughly 1.8 to 2.0, but excludes denser materials such as metal implants. Strong artifacts that distort Hounsfield units, such as severe beam hardening, will propagate into erroneous map values, since the entire method rests on the fidelity of the underlying image data.
Even so, the study lands at a moment of rapid momentum in quantitative spectral imaging. Recent work by Zimmerman and Poludniowski and by Lustermans and colleagues has demonstrated photon-counting CT’s potential for radiotherapy-related material characterization, while other groups are pursuing physics-informed deep-learning approaches to the same problem. Against those data-hungry machine-learning methods, the new algorithm offers a complementary virtue: it is analytically derived, transparently calibrated against tabulated reference data, computationally light, and runs entirely on image data that any clinical workstation can export. The authors suggest it could support applications from radiation therapy planning, where density and atomic number inform dose calculations, to oncology, where tissue characterization may distinguish tumor from benign lesions, or the identification of uric acid stones. Future studies, they note, must validate the approach across different phantoms, protocols, dose levels and realistic tissue compositions — but the demonstration that hospital-ready images alone can yield quantitative chemical maps marks a meaningful step toward making spectral material analysis a routine part of clinical CT.
Subject of Research: Calculation of mass density and effective atomic number maps from virtual monoenergetic photon-counting CT images
Article Title: Computation of the effective atomic number and mass density from virtual monoenergetic photon-counting CT reconstructions
Article References: Horstmeier, S., Thomsen, F. S., & Borggrefe, J. (2026). Computation of the effective atomic number and mass density from virtual monoenergetic photon-counting CT reconstructions. Heliyon, 12(14), Article e45404. https://doi.org/10.1016/j.heliyon.2026.e45404
Image Credits: AI Generated
DOI: Not provided
Keywords: photon-counting CT, effective atomic number, mass density, virtual monoenergetic imaging, spectral CT, Alvarez-Macovski model, material decomposition, radiation therapy, tissue characterization, Heliyon, X-ray attenuation, quantitative imaging
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Drew Townsend. (September 12, 2026). Photon-Counting CT Now Yields Density and Atomic Number Maps. Scienmag. https://scienmag.com/photon-counting-ct-now-yields-density-and-atomic-number-maps/
Drew Townsend. “Photon-Counting CT Now Yields Density and Atomic Number Maps.” Scienmag, 12 September 2026, https://scienmag.com/photon-counting-ct-now-yields-density-and-atomic-number-maps/. Accessed 12 September 2026.
Drew Townsend. “Photon-Counting CT Now Yields Density and Atomic Number Maps.” Scienmag. September 12, 2026. https://scienmag.com/photon-counting-ct-now-yields-density-and-atomic-number-maps/
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Tags: advanced CT technologyAlvarez-Macovski modelatomic number imagingchemical composition analysisCompton scattering in CTdensity mappingeffective atomic numberelectron density measurementHeliyonmass densitymaterial decompositionmaterial differentiation in medical scansMedical Imagingmulti-energy CT imagingphotoelectric effect in imagingphoton-counting computed tomographyphoton-counting CTquantitative imagingradiation therapyspectral CTtissue characterizationvirtual monoenergetic imagingX-ray attenuationX-ray attenuation physics
