(Radiology. 2001;219:596-610.)
© RSNA, 2001
Practical Applications of Mach Band Theory in Thoracic Analysis1
Marvin H. Chasen, MD, MSEE
1 From the Department of Radiology, University of Texas M.D. Anderson Cancer Center, Box 57, 1515 Holcombe Blvd, Houston, TX 77030. Received March 3, 1999; revision requested April 23; revision received February 16, 2000; accepted February 23. Address correspondence to the author (e-mail: mchasen@di.mdacc.tmc .edu).
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ABSTRACT
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In this review, routine radiographs with computed tomographic (CT) correlation are used to demonstrate practical applications of Mach band theory in thoracic analysis. Mach bands represent optical psychophysiologic edge-enhancement phenomena produced by means of lateral inhibition in the retina of the eye. Visualization of Mach bands depends on a set of variables that involve primarily the contour and optical density of a structure at an interface relative to that of its surround. On the basis of their appearance, the bands are defined as positive (white) or negative (black). The concept of Mach bands contributes to a greater understanding of three-dimensional structures projected onto two-dimensional routine radiographic images of the thorax. Mach bands can help differentiate normal from abnormal anatomy and thus increase the diagnostic yield from such images. Mach bands can be seen on images that use transmitted or reflective light, including CT scout images (topograms) of the thorax.
Index terms: Images, analysis, 60.91, 60.99 • Images, interpretation, 60.91, 60.99 • Mach band • Review • Thorax, CT, 60.1211 • Thorax, radiography, 60.11
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INTRODUCTION
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Routine chest radiography remains the most often ordered study in both the initial work-up of patients and subsequent evaluations. A thorough understanding of chest anatomy is necessary to derive as much information as possible from such images. In this review, routine radiographs with computed tomographic (CT) correlation are used to demonstrate the practical applications of Mach band theory in thoracic analysis as a method of increasing the yield from such routine studies. In addition, it will be shown that this theory is directly applicable in obtaining valuable information from CT digital scout views (topograms), which are usually obtained only as the reference image to localize transverse CT images of the chest. Space limitations preclude a full analysis of all techniques that might use Mach bands in analysis (eg, conventional tomography). To the best of the author’s knowledge, there are no studies that have illustrated Mach bands on transverse CT scans or explored their potential in magnetic resonance imaging.
First described by Ernst Mach in 1865, Mach bands are optical psychophysiologic edge-enhancement phenomena produced by means of the process of lateral inhibition in the retina (1). One of the first articles to present a comprehensive approach to the principles and applications of Mach bands in radiology was written in 1976 (2). Mach bands are observed on images of numerous body systems (eg, the thorax and abdomen). They are defined as positive or negative and can be seen on routine normal and abnormal chest radiographs (Fig 1). These bands do not exist in the real sense but are perceived as real by the visual system. Their visualization depends on a set of variables that primarily involve the contour and optical density of a structure at an interface relative to that of its surround (2).
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Figure 1a. (a) Posteroanterior chest radiograph demonstrates negative (arrows) and positive (arrowheads) Mach bands along the descending aorta and the paraspinal region. (b) Lateral chest radiograph in a different patient with known tumor recurrence after left upper lobe (LUL) lobectomy demonstrates a positive Mach band (arrowheads) at the interface between aerated lower lobe and the mediastinum. Note also the negative Mach bands (arrows) around the diaphragm and breasts.
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Figure 1b. (a) Posteroanterior chest radiograph demonstrates negative (arrows) and positive (arrowheads) Mach bands along the descending aorta and the paraspinal region. (b) Lateral chest radiograph in a different patient with known tumor recurrence after left upper lobe (LUL) lobectomy demonstrates a positive Mach band (arrowheads) at the interface between aerated lower lobe and the mediastinum. Note also the negative Mach bands (arrows) around the diaphragm and breasts.
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Mach bands are not restricted to images viewed with transmitted light, as in radiography; they are also produced by reflected light in photography. Therefore, the glossy print representations of radiographic images in this article faithfully reproduce the principles behind the visualization of Mach bands, despite some loss of quality inherent in the transition from radiograph to print. Further, although digital CT images might alter contrast relationships within the image, resulting in enhancement of Mach bands, they do not appear to create these bands.
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GLOSSARY
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The following terms will be defined to better facilitate understanding of how Mach bands can improve radiographic interpretation within the thorax.
Contrast: a difference in optical density or the difference in opacity across a boundary.
Optical density: a measure of light transmission. On a routine radiograph increased blackness has a higher optical density than increased whiteness.
Line: an opacity of approximately 1 mm in thickness observed on a radiograph. It may be straight or curved in its configuration.
Stripe: a thick line.
Interface: boundaries (edges) across which contrast can be observed.
Contour: shape, as in convex versus concave or smooth versus irregular.
Projection: a two-dimensional image generated from a three-dimensional object.
Locus: a set of points, lines, or surfaces that satisfy a given condition (eg, the locus of all points equidistant from a given point is a circle).
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MACH BAND THEORY
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A useful model for illustrating Mach bands based on the concept of lateral inhibition is provided by light stimulation across the retinal elements of the arthropod Limulus (3,4). This animal has approximately 1,000 distinct visual elements interconnected by a neural network that can be experimentally stimulated as individual or multiple units. Light intensity on a single unit produces a given neural response that decreases if other units are simultaneously stimulated (Fig 2). This effect is termed lateral inhibition and is a form of negative feedback control to prevent excessive stimulation of a single element in the retina. Because the retinal elements are interconnected, the resultant response will be modulated by the number of units stimulated, the distance between the units, and the nature of the light intensity change across the elements. The closer two units are, the more they inhibit each other; conversely, the farther apart, the less they inhibit each other. Uniform stimulation results in equal inhibition, whereas a step change in light intensity results in maximal edge enhancement at the step, as illustrated in Figure 2.
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Figure 2. Cross-sectional illustration of the Limulus eye demonstrates lateral inhibition of the frequency response of ommatidium A when other elements (ommatidia 1, 2, and 3) are simultaneously stimulated. This lateral inhibition is a function of distance between elements. A step function of light intensity across elements on each side of the step (top right) results in two levels of lateral inhibition (bottom right); the inhibition is maximal at the step. The response at the step is the analog in humans for positive or negative Mach bands observed on chest images. (Modified and reprinted, with permission, from reference 2.)
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Although the human retina is far more complex than that of Limulus, the underlying process that produces lateral inhibition (and hence Mach bands) is much the same. Unlike the Limulus retina, however, which appears to respond maximally to a step function of a light stimulus (see Fig 2), the human eye is more sensitive to a light stimulus from curved structures than from those that form right angles (2). Therefore, tubular or spherical structures elicit a much greater Mach band effect than do those with less curvature. In addition to curvature, however, the luminance difference must occur at a well-defined interface to produce a contrast sufficient to elicit the Mach band response. If the object has greater opacity than its surround and presents a convex contour relative to a concave surround at the interface, then a negative Mach band will result; a positive Mach band results if one of the conditions is reversed (Fig 3). If the contrast difference is excessive or insufficient across the interface, the Mach band may be partially or totally obscured at the interface, as will be demonstrated in subsequent figures.
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Figure 3. Left: Radiograph of an opaque sphere relative to a more lucent uniform background elicits a negative Mach band (arrows) around its periphery at the interface with the background. Right: A positive Mach band (arrowheads) results if the sphere is more lucent than the background. Object contour and contrast across a well-defined interface are necessary for the production of such Mach bands. (Modified and reprinted, with permission, from reference 2.)
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An important concept to understand in Figure 3 and many others in this review is that of projection as defined in the Glossary. Although the spheres in Figure 3 appear as circles, they are three-dimensional objects radiographically compressed into two dimensions. It is the luminance change across the curvature of the spheres that elicits the response at the interface, even though the spheres are imaged as a circles. Understanding the principles behind Mach bands in such compressed images allows for the interpretation of what is a true three-dimensional structure in space.
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MACH BAND MODELS
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In addition to Figure 3, it is helpful to illustrate the production of Mach bands by using ceramic models with different contours as representative of what might be imaged in a patient (Fig 4). The ceramic bowl is a structure with a convex outer contour and a concave inner one; the door knob has a contour with changing curvatures; and the tubular structure with the added flange is a simulation of the descending aorta, the paraspinal region, and an aspect of the chest wall. The radiographs of these structures produce positive or negative Mach bands, depending on the contour with respect to convexity versus concavity, opacity versus lucency, and a well-defined interface with the surround (Figs 5–7). What is not as easily understood, however, is the determination of a three-dimensional convexity versus a concavity on a two-dimensional image. The drawing in Figure 8 of a saddle in two orientations illustrates this concept. From the side, the seat of the saddle appears to be a concavity, but from a three-dimensional perspective it is actually a convexity.
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Figure 4. Three ceramic models illustrate the production of Mach bands when radiographed under different conditions (see Figs 5-7). The bowl and doorknob are objects with simple and complex radii of curvature (ie, contour), respectively. The simulated aorta (ie, the cylinder) is designed to illustrate the reflection of room air around an object that will elicit two different but parallel Mach bands when radiographed (see Fig 7). Note the tangent points of the convexity of the opaque tube (arrow) and convex lucency (arrowhead) of room air that will elicit the negative and positive Mach bands along the entire length of this tubular model, as illustrated radiographically in Figure 7.
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Figure 5. Frontal radiographs of the ceramic bowl in The bowl represents an object with an outer convexity and an inner concavity. Top: The empty bowl elicits a positive Mach band (arrowheads) at the interface of room air with the opaque concavity of the bowl. Bottom: A negative Mach band should be produced at the interface of the convex component of the bowl with room air, but excessive contrast prevents clear visualization. Placement of iodinated contrast material inside the bowl reverses the Mach band to negative (arrows) because the iodine is more opaque than the bowl. Therefore, changing a lucent convexity (air) to an opaque one (iodine) alters the Mach band at the interface with the bowl.
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Figure 6a. (a) Radiographic side view of the doorknob object in Figure 4 shows the tangent points (arrows) around the periphery of the knob. (b) En face radiograph of the knob demonstrates three Mach bands at these tangents, two of which are negative (arrows) and the inner one, positive (arrowheads). The outer negative band is more difficult to appreciate than the inner negative band because of excessive contrast at its interface with air. The positive Mach band (arrowheads) produced at the point of maximum concavity (middle arrows in a) is somewhat difficult to appreciate, not because of insufficient contrast at the points of concavity but because of insufficient contrast secondary to superimposition of the opacity of the knob. The result is a consequence of the projection onto two-dimensional images of the overlapping components of three-dimensional objects. In addition, the fact that the knob has a concavity in one aspect of its contour on the side view does not indicate that it is an actual concavity in three-dimensional space. Therefore, convexity and concavity as visualized on a single radiograph may have no meaning in the three-dimensional domain (see Figs 8, 9).
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Figure 6b. (a) Radiographic side view of the doorknob object in Figure 4 shows the tangent points (arrows) around the periphery of the knob. (b) En face radiograph of the knob demonstrates three Mach bands at these tangents, two of which are negative (arrows) and the inner one, positive (arrowheads). The outer negative band is more difficult to appreciate than the inner negative band because of excessive contrast at its interface with air. The positive Mach band (arrowheads) produced at the point of maximum concavity (middle arrows in a) is somewhat difficult to appreciate, not because of insufficient contrast at the points of concavity but because of insufficient contrast secondary to superimposition of the opacity of the knob. The result is a consequence of the projection onto two-dimensional images of the overlapping components of three-dimensional objects. In addition, the fact that the knob has a concavity in one aspect of its contour on the side view does not indicate that it is an actual concavity in three-dimensional space. Therefore, convexity and concavity as visualized on a single radiograph may have no meaning in the three-dimensional domain (see Figs 8, 9).
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Figure 7. Radiograph of the tubular ceramic model in Figure 4 demonstrates a positive Mach band (arrowheads) along the length of the tube at the locus of connecting tangent points of convex room air at the interface with the opaque tubular model. The outer curvature of the tube exhibits a negative Mach band (arrows), but again excessive contrast at the interface with room air diminishes visibility. It is this model that substantiates the concept that a positive Mach band in this location is a factitious optical illusion, despite contrary suggestions that it is an actual structure in the paraspinal region (see Fig 10). Further evidence of the factitious nature of the positive Mach band can be obtained by placing a vertical strip of paper over the opaque model without covering the Mach band to observe the disappearance of the band as the strip of paper approaches the band.
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Figure 8. Illustration of a saddle in the side view (left) indicates that the seat is a concavity (arrows). However, a three-dimensional perspective view (right) proves that, in three-dimensional space, the seat is a convexity. This concept forms the basis for understanding the difficulty in differentiating convexity from concavity on two-dimensional radiographs, as well as the value of Mach bands in resolving such difficulty.
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PRACTICAL APPLICATIONS
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Convexity versus Concavity
The practical value of an understanding of Mach band concepts is illustrated in Figure 9. The convex line on the frontal radiograph is factitious and does not represent a bulging minor fissure. It actually represents a positive Mach band produced by a tangent x-ray beam at all points along an interface of convex aerated right middle lobe with a relatively opaque concavity consisting of consolidated upper lobe and a large tumor mass demonstrated on the lateral image. However, it is important to understand that the apparent convexity on the frontal image and concavity on the lateral image are factitious because of the projection of three-dimensional structures onto two-dimensional images, as noted for the doorknob model in Figure 6 and the saddle in Figure 8. Specifically, the presence of a negative Mach band on the lateral view in Figure 9 indicates that although the opacity appears concave on this image, it actually is convex in three-dimensional space. Therefore, conditions that might produce a positive Mach band on a two-dimensional image in one orientation (eg, frontal image) may actually be a convexity in three-dimensional space on an orthogonal view (ie, lateral image) because of projection.
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Figure 9a. (a) Posteroanterior radiograph shows an apparently bulging minor fissure (arrowheads) that is, in actuality, a positive Mach band produced by aerated lung reflecting off a soft-tissue mass (*), seen in part below the Mach band. (b) Lateral radiograph shows no similar bulging fissure. The positive Mach band in a is elicited by the locus of x-ray tangent points at the interface (arrows) of aerated right middle lobe with the mass and consolidated right upper lobe (RUL). Note that this interface appears to represent convex lung with concave soft tissue, and yet no positive Mach band is present along the interface. Although it is difficult to appreciate, a faint negative Mach band is present at this interface. The fact that the positive Mach band is convex in a and the negative band is concave in b is a consequence of two-dimensional imaging.
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Figure 9b. (a) Posteroanterior radiograph shows an apparently bulging minor fissure (arrowheads) that is, in actuality, a positive Mach band produced by aerated lung reflecting off a soft-tissue mass (*), seen in part below the Mach band. (b) Lateral radiograph shows no similar bulging fissure. The positive Mach band in a is elicited by the locus of x-ray tangent points at the interface (arrows) of aerated right middle lobe with the mass and consolidated right upper lobe (RUL). Note that this interface appears to represent convex lung with concave soft tissue, and yet no positive Mach band is present along the interface. Although it is difficult to appreciate, a faint negative Mach band is present at this interface. The fact that the positive Mach band is convex in a and the negative band is concave in b is a consequence of two-dimensional imaging.
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The Paraspinal Line
The practical counterpart of the paraspinal line in Figure 7 is illustrated in Figure 10a and has already been illustrated in Figure 1a. The densitometer reading across the positive Mach band at the level of the black bar shows no marked change in optical density, thus confirming its psychophysiologic nature (5). A similar result occurs at the negative Mach band along the descending aorta. The transverse CT image in Figure 10b illustrates the convex high-attenuating (opaque) aorta protruding into lung, which is responsible for the negative Mach band in Figure 10a; the reflection of convex lung at the interface with paraspinal fat results in the positive Mach band. Therefore, contour and contrast at well-defined interfaces are what produce Mach bands, as illustrated in the models in Figures 3 and 4.
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Figure 10a. (a) Supine anteroposterior radiograph of the thoracic spine demonstrates a positive Mach band (arrowheads) along the paraspinal region. This Mach band has been labeled the paraspinal line, but it is factitious, as evidenced by the lack of a marked change in the densitometer reading (black tracing) across the region at the level of the black bar (top arrowhead). Note that at the level of the osteophyte (middle arrowhead), the Mach band is affected by the overlapping opacity of bone, a consequence of projection. Portions of a negative Mach band are present along the descending aorta (short arrows). No marked change is present in the densitometer reading (long arrow) because, like the positive Mach band, this negative band is also factitious. (b) Representative transverse CT image confirms the criteria that produce negative and positive Mach bands seen in a. Convex aorta (arrow) forms an interface with concave lung, resulting in a negative Mach band; convex lung at an interface with concave paraspinal fat (arrowheads) results in the positive Mach band in a.
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Figure 10b. (a) Supine anteroposterior radiograph of the thoracic spine demonstrates a positive Mach band (arrowheads) along the paraspinal region. This Mach band has been labeled the paraspinal line, but it is factitious, as evidenced by the lack of a marked change in the densitometer reading (black tracing) across the region at the level of the black bar (top arrowhead). Note that at the level of the osteophyte (middle arrowhead), the Mach band is affected by the overlapping opacity of bone, a consequence of projection. Portions of a negative Mach band are present along the descending aorta (short arrows). No marked change is present in the densitometer reading (long arrow) because, like the positive Mach band, this negative band is also factitious. (b) Representative transverse CT image confirms the criteria that produce negative and positive Mach bands seen in a. Convex aorta (arrow) forms an interface with concave lung, resulting in a negative Mach band; convex lung at an interface with concave paraspinal fat (arrowheads) results in the positive Mach band in a.
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There has been controversy in the literature as to whether the paraspinal line observed at the interface of lung with the paraspinal anatomy may be a true line under some circumstances; some (6) believe it could represent the sum of the visceral pleura of the lung, the parietal pleura of the mediastinum, and the potential pleural space outlined by paraspinal fat medially and aerated lung laterally. However, measurements of this line have shown it to be "thicker" than might be expected given the actual widths of these membranes (5). Certainly, these membranes are included in defining the interface at which the positive Mach band shown in Figure 10 occurs, but the ceramic model in Figure 7 demonstrates a positive Mach band in the absence of such membranes. Specifically, both the positive and the negative Mach bands observed in Figure 7 are produced solely by room air surrounding the opaque convex component of the model and then reflecting off the concave simulated paraspinal area. The transverse CT image in Figure 10b has already demonstrated that contour and opacity at interfaces are what produce Mach band phenomena, and, although the visceral and parietal membranes are included as structures at the interfaces in that image, they are not primarily responsible for it. Note that in Figure 10b no line is visible in the paraspinal region, although there is fat medially and lung laterally at the interface. Perhaps the visceral and parietal membranes have insufficient thickness to produce a visible line on such images, or the mediastinal technique used precludes the observation of this line (not proved).
The practical value of Mach bands is further illustrated in Figure 11. A mass overlapping the aortopulmonary window in Figure 11b represents a new finding relative to a normal previous image in Figure 11a. The presence of a negative Mach band around the mass and a positive Mach band seen through it produced by lung reflecting off the mass are insufficient to localize the lesion on a two-dimensional frontal radiograph. The lesion was not observed on the lateral image (not shown). It is the deviation of the paraspinal line below the mass in Figure 11b that is contiguous with the positive Mach band associated with the mass that allows localization of the lesion to the vertebral region on this two-dimensional image. The vertebral location of the mass is confirmed on the supine thoracic spine image in Figure 11c. Note the poor definition of the joint space at T5-6 in Figure 11c because of partial collapse of the inferior aspect of T5 secondary to metastatic disease in this patient with a nasopharyngeal malignancy. Retrospective review of the lateral image only suggested abnormality in the region.
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Figure 11a. (a) Posteroanterior radiograph demonstrates a negative Mach band (arrows) along the course of the descending aorta. No abnormality is present in the general region of the aortopulmonary window (*), and no positive Mach band is defined in the paraspinal region. (b) Follow-up posteroanterior radiograph now shows a mass overlying the aortopulmonary window, with a negative Mach band on its outer contour (arrows) and a positive Mach band overlying the mass (top two arrowheads). Note the contiguity of this positive Mach band with a slightly deviated paraspinal line (bottom two arrowheads). Deviation of the paraspinal line indicates a paravertebral location of the mass. (c) Supine anteroposterior thoracic spine radiograph confirms the deviation of the paraspinal line by the mass at the T5 through T6 level (small arrowheads), with return to a normal configuration inferiorly (large arrowheads). Note the subtle loss of joint space at T5-6 (arrows) secondary to partial collapse of T5 because of metastatic disease. The soft-tissue component of the metastatic process is responsible for the convex mass observed in b. This mass was not observed on the lateral radiograph (not shown).
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Figure 11b. (a) Posteroanterior radiograph demonstrates a negative Mach band (arrows) along the course of the descending aorta. No abnormality is present in the general region of the aortopulmonary window (*), and no positive Mach band is defined in the paraspinal region. (b) Follow-up posteroanterior radiograph now shows a mass overlying the aortopulmonary window, with a negative Mach band on its outer contour (arrows) and a positive Mach band overlying the mass (top two arrowheads). Note the contiguity of this positive Mach band with a slightly deviated paraspinal line (bottom two arrowheads). Deviation of the paraspinal line indicates a paravertebral location of the mass. (c) Supine anteroposterior thoracic spine radiograph confirms the deviation of the paraspinal line by the mass at the T5 through T6 level (small arrowheads), with return to a normal configuration inferiorly (large arrowheads). Note the subtle loss of joint space at T5-6 (arrows) secondary to partial collapse of T5 because of metastatic disease. The soft-tissue component of the metastatic process is responsible for the convex mass observed in b. This mass was not observed on the lateral radiograph (not shown).
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Figure 11c. (a) Posteroanterior radiograph demonstrates a negative Mach band (arrows) along the course of the descending aorta. No abnormality is present in the general region of the aortopulmonary window (*), and no positive Mach band is defined in the paraspinal region. (b) Follow-up posteroanterior radiograph now shows a mass overlying the aortopulmonary window, with a negative Mach band on its outer contour (arrows) and a positive Mach band overlying the mass (top two arrowheads). Note the contiguity of this positive Mach band with a slightly deviated paraspinal line (bottom two arrowheads). Deviation of the paraspinal line indicates a paravertebral location of the mass. (c) Supine anteroposterior thoracic spine radiograph confirms the deviation of the paraspinal line by the mass at the T5 through T6 level (small arrowheads), with return to a normal configuration inferiorly (large arrowheads). Note the subtle loss of joint space at T5-6 (arrows) secondary to partial collapse of T5 because of metastatic disease. The soft-tissue component of the metastatic process is responsible for the convex mass observed in b. This mass was not observed on the lateral radiograph (not shown).
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Knowledge of Mach band theory provides a greater understanding of interfaces in general, as illustrated in Figure 12. This CT scout image demonstrates a weak positive Mach band along an oblique interface in a patient with an aortic aneurysm. Two transverse CT images obtained at the upper and lower aspects of the interface confirm that the aneurysm progressively excludes lung from the paraspinal area in the craniocaudal direction, thus producing the oblique interface on this two-dimensional CT image. Note that it is the locus of connecting tangent points at all levels in the transverse plane in which the lung reflects behind the aneurysm that produces the weak Mach band along the interface on the scout image. At this point, it becomes apparent that although the CT images confirm the finding, the anatomy that produces it can be inferred from the scout image by utilizing Mach band theory.
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Figure 12. Top: CT scout image with patient supine demonstrates an oblique interface seen through an aortic aneurysm. There is a weak positive Mach band (arrowheads) at the interface of the aneurysm with aerated lung. Bottom: CT images at levels 23 (left) and 38 (right) represent the cephalic and caudal levels of this interface. Note the distance between the left aspect of the vertebral body (black dashed lines) and the paraspinal reflection of lung (arrows) behind the aorta on each of the two CT images. The distance between the dashed line and the arrow on each image is a measure of the degree of exclusion of lung from the paraspinal region by the aneurysm, thus accounting for the oblique manifestation on the scout view.
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Lines, Stripes, and Interfaces
When observed at the paraspinal interface, the paraspinal line is but one example of a positive Mach band that must be differentiated from true lines on chest radiographs. In fact, there are many interfaces that produce such factitious lines (eg, see Figs 1b and 9a). In addition, the definition of a stripe on a radiograph is often misused or confused with an interface, especially around the mediastinum (7). Examples of normal stripes include the paratracheal and pleuroesophageal stripes (8,9). Interfaces as defined in the Glossary may be normal or abnormal and are found in almost all locations within the chest, but especially around the mediastinum.
The only true lines found within the projection of the mediastinum are the anterior and posterior junction lines (10,11) (Fig 13). The visceral pleura covering aerated lung in a case of pneumothorax can be visualized as a true line and can be differentiated from skin folds that elicit negative Mach bands (Fig 14a, 14b). However, pneumothorax in the presence of consolidated lung can also produce negative Mach bands (Fig 14c), and this pitfall is to be avoided. Normal stripes, as well as those representing a pathologic condition, are usually straightforward (Fig 15).
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Figure 13. Posteroanterior radiograph shows the anterior (arrows) and posterior (arrowheads) junction lines representing apposition of four layers of pleura where the two lungs can meet in the retrosternal and retroesophageal regions, respectively. Even when allowing for the potential pleural space and minimal tissue of the mediastinum in the region, the total anatomy still manifests as a thin true line.
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Figure 14a. (a) Posteroanterior radiograph in a patient with pneumothorax shows the visceral pleura as a thin line (arrows) outlined laterally by air in the pleural space and medially by aerated lung. The arrows show that this line can be seen through bone on this two-dimensional image. (b) Posteroanterior radiograph in another patient shows a skin fold, which appears as a convexity on the chest wall outlined by room air that elicits a negative Mach band (arrowheads) at the interface. This appearance should, in most cases, exclude pneumothorax. (c) Posteroanterior radiograph in a patient with pneumothorax associated with consolidated lung elicits a negative Mach band (arrows) at the interface of the opaque lung with pleural space air, because the consolidated lung represents an opaque convexity at an interface with concave pleural space air. This manifestation should not be confused with a skin fold. Note the change in the perception of the Mach band along the contour of the interface at each of the arrows as the overall contrast is altered by the increasing opacity of the lung and its overlapping surround in the craniocaudal direction.
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Figure 14b. (a) Posteroanterior radiograph in a patient with pneumothorax shows the visceral pleura as a thin line (arrows) outlined laterally by air in the pleural space and medially by aerated lung. The arrows show that this line can be seen through bone on this two-dimensional image. (b) Posteroanterior radiograph in another patient shows a skin fold, which appears as a convexity on the chest wall outlined by room air that elicits a negative Mach band (arrowheads) at the interface. This appearance should, in most cases, exclude pneumothorax. (c) Posteroanterior radiograph in a patient with pneumothorax associated with consolidated lung elicits a negative Mach band (arrows) at the interface of the opaque lung with pleural space air, because the consolidated lung represents an opaque convexity at an interface with concave pleural space air. This manifestation should not be confused with a skin fold. Note the change in the perception of the Mach band along the contour of the interface at each of the arrows as the overall contrast is altered by the increasing opacity of the lung and its overlapping surround in the craniocaudal direction.
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Figure 14c. (a) Posteroanterior radiograph in a patient with pneumothorax shows the visceral pleura as a thin line (arrows) outlined laterally by air in the pleural space and medially by aerated lung. The arrows show that this line can be seen through bone on this two-dimensional image. (b) Posteroanterior radiograph in another patient shows a skin fold, which appears as a convexity on the chest wall outlined by room air that elicits a negative Mach band (arrowheads) at the interface. This appearance should, in most cases, exclude pneumothorax. (c) Posteroanterior radiograph in a patient with pneumothorax associated with consolidated lung elicits a negative Mach band (arrows) at the interface of the opaque lung with pleural space air, because the consolidated lung represents an opaque convexity at an interface with concave pleural space air. This manifestation should not be confused with a skin fold. Note the change in the perception of the Mach band along the contour of the interface at each of the arrows as the overall contrast is altered by the increasing opacity of the lung and its overlapping surround in the craniocaudal direction.
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Figure 15. Air in both the peritoneal cavity and in normal aerated lung demonstrates the diaphragm as a soft-tissue stripe on this posteroanterior radiograph. There is a negative Mach band (straight arrows) along the contour of the liver, a weak positive Mach band (curved arrows) on the undersurface of the diaphragm, and a weak negative Mach band (arrowheads) along the superior surface of the diaphragm. The diaphragmatic stripe is of insufficient thickness and opacity to elicit stronger Mach bands at the interface with air. The negative Mach band over the liver is a result of the convex opacity of the liver relative to the concave air in the peritoneal space. The positive Mach band is a result of convex peritoneal air relative to the concave undersurface of the diaphragm. The negative Mach band over the superior surface of the diaphragm is a consequence of the convexity of the diaphragm relative to the concave aerated lung. The Mach band over the liver is not organ specific, because a similar band would be present over a normal diaphragm (as in Fig 1b). It should be noted that the overall thickness of the diaphragm includes the peritoneal membrane on its undersurface and the visceral and parietal pleurae with the potential pleural space on its superior surface.
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Although the walls of vessels are rarely, if ever, seen on routine chest images, they can be observed on studies obtained with iodinated contrast material (eg, angiographic studies) when their visualization is aided by the presence of Mach bands (Fig 16). Note also in Figure 16 that regions of excessive or insufficient contrast at some interfaces prevent the formation of Mach bands. It is important to emphasize again that on two-dimensional images, the interface is defined by the optical density difference (ie, contrast) across the interface and is affected by the optical density of the entire surround. In addition, complex transitions from lines to stripes may not be fully understood on routine two-dimensional images (Fig 17). Interfaces must be clearly understood, to avoid confusion in analysis (Fig 18). The negative Mach band that outlines the right-hand border of the heart in Figure 18a confirms that the pneumonia is not in direct contiguity with the heart; in Figure 18b, the apparent "thick" lucency between the right-hand heart border and a branch of the right pulmonary artery is the sum of two negative Mach bands produced by the heart and tubular vessel and does not represent a pneumomediastinum (12). Mach bands cannot create Mach bands because they are psychophysiologic in nature rather than real structures in space (2).
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Figure 16. On this aortogram, an aspect of the outer wall of the descending aorta (including the visceral and parietal pleurae and potential pleural space) is demonstrated as a soft-tissue stripe because of a negative Mach band (white arrows) along the lateral wall of this structure. It is the opacity of the stripe that produces this outer Mach band rather than the intense iodinated contrast material opacity within the lumen of the aorta. In fact, the opaque iodine within the aorta elicits a negative Mach band (large arrowheads) at the interface with the lumen; the Mach band actually encroaches on the true width of the wall. Note that a Mach band is not elicited inferiorly along the descending aorta because of insufficient contrast in the region, nor is one apparent more superiorly because of excessive contrast. Although a negative Mach band (black arrows) is present along the ascending aorta, no aortic wall is visualized because the background opacity of the vertebral bodies contributes to the surround, thus producing insufficient contrast to elicit a negative Mach band that might demonstrate the wall. However, it is possible that the wall of the ascending aorta is not tangent to the x-ray beam, precluding its observation. Note that negative Mach bands (small arrowheads) are also present along the lumen of the brachiocephalic artery. A further observation is the apparent concave manifestation of the descending aorta on this two-dimensional image, although this structure is a convexity in three-dimensional space—a consequence of projection.
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Figure 17. Pneumopericardium is present on a posteroanterior radiograph. The line represents the combined anatomy of the parietal and fibrous pericardium, the parietal pleura of the mediastinum, the potential pleural space, and the visceral pleura of the lung. The positive Mach band (arrowheads) on the inner aspect of the stripe appears as a straight edge but in reality represents a curvature in space. Air in the pericardial sac can elicit a positive Mach band at the interface only if convex air forms the interface with concave soft tissue. The negative Mach band (arrows) on the outer aspect of the stripe is formed by convex soft tissue of the mediastinum at an interface with the concave air of the lung. The thickness of the soft-tissue stripe is explained by tangents that define the interfaces of the stripe in different sagittal planes on this two-dimensional image.
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Figure 18a. (a) Posteroanterior radiograph shows a negative Mach band around the right border of the heart (arrows), which proves that the pneumonia (*) present in this patient cannot be in contiguity with the heart border. The lateral projection (not shown) confirmed pneumonia in the lower lobe. The minor fissure (arrowheads) is faintly depicted as further proof of sparing of the middle lobe. (b) Posteroanterior radiograph in a different patient shows that the lucent rim (arrows) around the right border of the heart is thicker than expected for the usual negative Mach band in this location, as shown in a. The medial aspect of the convex pulmonary artery branch (arrowheads) to the lower lobe elicits a second and parallel negative Mach band in the same region. This double Mach band should not be confused with a pneumomediastinum, nor should it be thought that one Mach band can generate another.
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Figure 18b. (a) Posteroanterior radiograph shows a negative Mach band around the right border of the heart (arrows), which proves that the pneumonia (*) present in this patient cannot be in contiguity with the heart border. The lateral projection (not shown) confirmed pneumonia in the lower lobe. The minor fissure (arrowheads) is faintly depicted as further proof of sparing of the middle lobe. (b) Posteroanterior radiograph in a different patient shows that the lucent rim (arrows) around the right border of the heart is thicker than expected for the usual negative Mach band in this location, as shown in a. The medial aspect of the convex pulmonary artery branch (arrowheads) to the lower lobe elicits a second and parallel negative Mach band in the same region. This double Mach band should not be confused with a pneumomediastinum, nor should it be thought that one Mach band can generate another.
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Pleural-based Masses
Masses that originate within the chest wall (eg, lipomas) but protrude into lung are extrapleural in nature because they arise outside the parietal pleura. Therefore, all mediastinal masses, by definition, are extrapleural. Lesions that are found within the pleural space might originate from either the visceral or the parietal pleura (eg, fibrous tumors of the pleura). Pleural effusions are truly within the pleural space. Difficulty arises when intraparenchymal masses (eg, bronchogenic carcinoma) abut the visceral pleura or invade through the visceral and parietal pleurae to involve the chest wall or the mediastinum. Further, mediastinal masses (eg, certain thymic tumors) might invade through the mediastinal pleura (ie, the parietal pleura) and visceral pleura to involve the lung but still have well-defined contours. Therefore, it is difficult to find an accurate term for all cases, and the term "pleural-based" is used in the generic sense to describe the spectrum of many but not all such observations. Mach band theory cannot be used to accurately determine actual invasion in every case but can contribute to a greater understanding of certain observations on routine chest images. One such example of utilizing Mach band theory to localize a lesion that protrudes into the lung but is extrapleural in origin has already been illustrated in Figure 11. Two additional cases where Mach bands contribute to further understanding of such lesions are presented in Figures 19 and 20 (13).
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Figure 19a. (a) Posteroanterior radiograph shows two interfaces of lung with soft tissue that elicit weak positive Mach bands (arrowheads), which can be visualized through a pleural-based mass. The medial interface (bottom arrowheads) is better defined than the lateral one (top arrowhead) because of more optimal contrast. These interfaces represent pleural involvement by the mass, which was confirmed at CT. (b) Transverse CT image demonstrates that the mass in cross section is pleural based, with the two tangential interfaces observed in a formed by convex lung reflecting around soft-tissue concavities at the chest wall (dashed lines). The mass is almost spherical in contour, indicating that it likely is a lung lesion, and invasion of the chest wall (arrows) is only suggested. Note that with a, one cannot determine which of the two interfaces is more anterior, but the CT image clearly shows that it is the lateral one. Bronchogenic carcinoma with pleural invasion and minimal chest wall involvement was found at surgery. Therefore, observation of positive Mach bands is an important clue that the pleura was involved in this case. (Modified and reprinted, with permission, from reference 13.)
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Figure 19b. (a) Posteroanterior radiograph shows two interfaces of lung with soft tissue that elicit weak positive Mach bands (arrowheads), which can be visualized through a pleural-based mass. The medial interface (bottom arrowheads) is better defined than the lateral one (top arrowhead) because of more optimal contrast. These interfaces represent pleural involvement by the mass, which was confirmed at CT. (b) Transverse CT image demonstrates that the mass in cross section is pleural based, with the two tangential interfaces observed in a formed by convex lung reflecting around soft-tissue concavities at the chest wall (dashed lines). The mass is almost spherical in contour, indicating that it likely is a lung lesion, and invasion of the chest wall (arrows) is only suggested. Note that with a, one cannot determine which of the two interfaces is more anterior, but the CT image clearly shows that it is the lateral one. Bronchogenic carcinoma with pleural invasion and minimal chest wall involvement was found at surgery. Therefore, observation of positive Mach bands is an important clue that the pleura was involved in this case. (Modified and reprinted, with permission, from reference 13.)
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Figure 20a. (a) Lateral radiograph demonstrates a pleural-based mass either in the immediate retrosternal region or in a parasternal location. The negative Mach band (arrows) around the sharp contour with lung might indicate a mediastinal mass. Note the vertical interface enhanced by a positive Mach band (arrowheads), which can be seen through the mass, indicating lung that is convex toward the mass. A posteroanterior radiograph (not shown) confirmed a left parasternal location but provided no further information. (b) Transverse CT scan confirms that the mass is pleural based at the chest wall in a left parasternal location. The convexity of the more opaque mass relative to concave lung at the tangential interface (long arrow) produces the negative Mach band in a; the convexity of the lung relative to the concave opaque tissue at the tangential interface of the more medial aspect of the mass (short arrow) produces the positive Mach band in a. The splaying (arrowhead) of the anterior junction line around the mass indicates a lesion in the pleural space. The region of interest ( ) in the mass was of water attenuation, and at surgery a mesothelial cyst of the parietal pleura was resected. In this case, a routine lateral chest radiograph is sufficient to accurately predict the well-defined nature of the mass and the lung reflecting around it, if one utilizes Mach band theory. (Modified and reprinted, with permission, from reference 13.)
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Figure 20b. (a) Lateral radiograph demonstrates a pleural-based mass either in the immediate retrosternal region or in a parasternal location. The negative Mach band (arrows) around the sharp contour with lung might indicate a mediastinal mass. Note the vertical interface enhanced by a positive Mach band (arrowheads), which can be seen through the mass, indicating lung that is convex toward the mass. A posteroanterior radiograph (not shown) confirmed a left parasternal location but provided no further information. (b) Transverse CT scan confirms that the mass is pleural based at the chest wall in a left parasternal location. The convexity of the more opaque mass relative to concave lung at the tangential interface (long arrow) produces the negative Mach band in a; the convexity of the lung relative to the concave opaque tissue at the tangential interface of the more medial aspect of the mass (short arrow) produces the positive Mach band in a. The splaying (arrowhead) of the anterior junction line around the mass indicates a lesion in the pleural space. The region of interest () in the mass was of water attenuation, and at surgery a mesothelial cyst of the parietal pleura was resected. In this case, a routine lateral chest radiograph is sufficient to accurately predict the well-defined nature of the mass and the lung reflecting around it, if one utilizes Mach band theory. (Modified and reprinted, with permission, from reference 13.)
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Nodules
Pulmonary nodules may be well circumscribed or poorly defined. They may be clearly visible within the lung parenchyma or completely obscured by overlapping anatomy. Lesions hidden by osseous structures, the mediastinum, or the diaphragm may be impossible to detect. However, well-defined nodules surrounded by air within the lung may elicit negative Mach bands around their periphery that permit visualization despite the presence of overlapping structures (Fig 21). In Figure 21, the inherent optical density of the larger noncalcified nodule would not be expected to be observed through the overlapping density of the liver. Most of the smaller nodule is observed through the liver and a rib. The surrounding negative Mach band produced in the lower lobe by the interface of the spherical opaque nodules with aerated lung facilitates visualization of the nodules. However, it is not necessary that the lung provide the total lucency to aid in visualization of a nodule if another lucent structure overlaps the nodule on a two-dimensional image (Fig 22).
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Figure 21. Posteroanterior radiograph shows two pulmonary nodules (*), which can be observed through the overlapping opacity of the liver and a rib. Negative Mach bands around the periphery of the nodules permit visualization despite the superimposition of structures.
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Figure 22. The solitary nodule on this lateral radiograph is better defined posteriorly than anteriorly because of the presence of a negative Mach band (arrows). However, air in the trachea provides added lucency to the general surround, thus enhancing depiction of the Mach band. Other aspects of the nodule are not as well defined because background structures overlapping the nodule in this region result in insufficient contrast to elicit a Mach band.
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Mach Bands on CT Scout Images
The value of Mach bands on CT scout images of the chest was introduced in Figure 12. As noted in the introduction to this review, scout images are full-thickness digital views that might alter contrast relationships at interfaces, resulting in enhancement of Mach bands. However, one should be aware when evaluating these images that such changing contrast levels do not, in and of themselves, create the phenomenon.
These images are usually obtained with the patient in the supine position but can be generated in the prone, oblique, or decubitus orientation as necessary. Generally, they are used as references for obtaining transverse CT images, but they can provide much the same or, at times, more information than a supine anteroposterior chest image obtained with an analog technique. This capability is demonstrated in the scout image in Figure 23, where negative Mach bands illustrate the venous anomaly of hemiazygos-to-azygos continuation of the inferior vena cava. Figure 24 is an example of positive and negative Mach bands along the paraspinal region bilaterally in a patient with abundant paraspinal fat confirmed on transverse CT images. The correlation between the supine scout image of the chest and the supine transverse CT image accurately depicts why the more high-attenuating (opaque) convex fat relative to low-attenuating (lucent) concave lung at the interface produces negative Mach bands. The subsequent reflection of the lung along the paraspinal area produces positive Mach bands because the convex low-attenuating (lucent) lung forms an interface with more high-attenuating (opaque) concave fat. The unusual length of the Mach bands on the scout view should alert the observer to the differential possibilities of anatomy or pathologic conditions that might manifest over such lengths, triggering the realization that lipomatosis in this large patient was a likely possibility. Note that at no time does the aortic border form on the CT image. The presence of paraspinal fat is common and often forms such contours on routine chest radiographs (5).
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Figure 23. CT scout image demonstrates negative Mach bands (short arrows) along the course of tubular structures that represent hemiazygos-to-azygos continuation of the inferior vena cava. A negative Mach band (long arrows) is also present along the descending aorta. Note the positive Mach band (arrowheads) in association with the hemiazygos vein, where lung behind the vein is convex toward the paraspinal area. This paraspinal line is no different in concept than the one in Figure 10a. The azygos vein (*) is enlarged in the paratracheal region as a result of the increased blood flow within the anomaly.
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Figure 24a. (a) CT scout image shows negative (arrows) and positive (arrowheads) Mach bands bilaterally along the paraspinal region. This indicates the presence of convexities and concavities in three-dimensional space, confirmed at CT. (b) Transverse CT image at the approximate level of the hemidiaphragms shows that fat is responsible for the observations in a. The convex aspect of the fat (arrows), which is high attenuating relative to low-attenuating concave lung, elicits the negative Mach bands in a; the convex lung (arrowheads) in the paraspinal region relative to the more high-attenuating concave fat elicits the positive Mach bands in a. Note that the aorta does not manifest with a tangential interface on the image and cannot account for the negative Mach bands. It should also be noted that the closeness of the positive and negative Mach bands on the left aspect of the frontal image in a is because the sagittal planes representing the lateral aspects of these structures are so close to each other. This is confirmed with b by noting the position of the left arrow relative to the left arrowhead.
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Figure 24b. (a) CT scout image shows negative (arrows) and positive (arrowheads) Mach bands bilaterally along the paraspinal region. This indicates the presence of convexities and concavities in three-dimensional space, confirmed at CT. (b) Transverse CT image at the approximate level of the hemidiaphragms shows that fat is responsible for the observations in a. The convex aspect of the fat (arrows), which is high attenuating relative to low-attenuating concave lung, elicits the negative Mach bands in a; the convex lung (arrowheads) in the paraspinal region relative to the more high-attenuating concave fat elicits the positive Mach bands in a. Note that the aorta does not manifest with a tangential interface on the image and cannot account for the negative Mach bands. It should also be noted that the closeness of the positive and negative Mach bands on the left aspect of the frontal image in a is because the sagittal planes representing the lateral aspects of these structures are so close to each other. This is confirmed with b by noting the position of the left arrow relative to the left arrowhead.
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This case again illustrates that Mach bands are elicited on the basis of specific criteria of contour, contrast, and interface and are not necessarily organ specific. This is further shown in Figure 25, where CT analysis in the supine orientation relative to an upright chest study leads to findings based on mobility of fluid in the pleural space manifesting in a paraspinal location. The lateral displacement of a Mach band after transition from upright to supine should alert the observer to the presence of pleural fluid (14). The concept of mobility of structures and/or pathologic conditions based on changes in patient orientation may lead to errors in diagnosis (15). Therefore, the observation of a change in position of Mach bands in association with a change in patient position contributes to increased diagnostic accuracy for such images.
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ABSTRACT
INTRODUCTION
