Geometric Factors in the Silhouette Sign.

The Geometric Factors in the Generation of an Image of the Chest, using X-rays.

There are some assumptions in any reasoned argument about the chest X-ray. Some of these geometric factors are indicated below.

The relation between density and tissue thickness.

Put simply, we can equate the thickness of a soft tissue in the chest with its perceived density. (Here, we Radiologists mean whiteness on our negative images). The argument in simple reasoning is that the mathematical process involved in the assessment of radiation absortion, film blackening and perception is logarithmic. Those who are unfamiliar with this concept should consider compound interest or amortisation of a mortgage.

Light absorbed in a substance is a fixed ratio of incident radiation. Film blackening is proportional to this. Effectively, the reasoning concerning incremental steps in the processes of radiation absorption, film blackening and perception involves processes like: 'third of a third of a third'. Students of Calculus use incremental steps in their analysis.

THE SMALLEST PERCEIVABLE SENSATION IS A FIXED RATIO ABOVE EXISTING LEVELS OF THAT SENSATION. (simplification of Webber-Fechner Law)

All entirely normal anatomy within the patient's chest is soft tissue density and either contains some air or lies adjacent to some air. Any denser object will exceed the greyscale perception threshold and always be visible. Calcification is an example.

Felsen's original example was to look at the image resulting from the passage of X-rays through boxes, which contained wedges of wax and added mineral oil. He attempted to demonstrate the low contrast densities lying adjacent or projected by each other. The image shows a ground plan of the experiment alongside its projection.

Tuddenham made a slightly different model with curved surfaces.

In fact, the geometry is more complex, since an xray is generated effectively from a Point source. This means that the shadows generated would have margins nearly as sharp as the edges of the original structures. The penumbra effect in the diagram is minimised by the large distance between source and patient, for a chest X-ray.

Since x-rays are shadow pictures, the direction of a beam imposes an obvious limitation on the final image. The generation of an X-ray image imposes a reduction in the potential sub-set of information to be stored in the image of the patient. The information is collected as the radiation beam passes through the patient and each point in the image records only that amount of Xray absorption in the direction of the beam.

The boundary must be tangential to the majority of the incident beam. The changes in greyscale in the final image that record changes in X-ray absorption are recorded as changes at right angles to the beam. The normal boundary must be long enough at the tangent to produce a density difference which is perceivable in the chest X-ray.

The shadows of lumps of wax may have a sharp margin, but consolidation rarely conforms, except at a pleural boundary.

The CT scanner has made clear the location of consolidation that blurs anatomical boundaries. The two densities indicated are of roughly similar grey scale. Where any two densities lie in contact their boundary density changes have to merge. With non-contact, the change of grey scale is sudden , even if very small. The silhouette sign depends on this small difference being visible. The contrast change occurs over a line on the image and the observer's retina and visual system are well-suited for its detection.

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Ian Maddison, Nov 1994, revised Sept 2007