Tennis Courts in the Human Body: A Review of the Misleading Metaphor in Medical Literature

Medical literature is home to fancy descriptions, poetic metaphors, and ingenious comparisons. However, some comparisons can disguise the knowledge gap. Large surfaces in the human body, like the alveolar surface for gas exchange, villi for food absorption, and the endothelial lining of blood vessels, are frequently compared to a “tennis court.” This narrative review explores this metaphor in detail, the discrepancies and factual inaccuracies across medical literature. It highlights the inappropriate use of Euclidean geometry and introduces fractal geometry, a language to define roughness.


Introduction And Background
Medical literature is home to fancy descriptions, poetic metaphors, and ingenious comparisons. No physician can relish anchovy sauce without being reminded of the pus in amebic liver abscess. The dark sky with bright twinkling stars reminds a radiologist of hepatic parenchyma and a pathologist of Burkitt lymphoma [1]. Poetic comparison evokes the reader's imagination and ingrains itself in the long-term memory. Nevertheless, such comparisons can sometimes mask the gap in knowledge or understanding. One such intriguing instance encountered repetitively in literature is likening large surface areas to tennis courts. The surface area of the lungs available for gas exchange, the intestinal villi for the absorption of food particles, and the endothelial lining of blood vessels are all compared to the size of tennis courts.
The disparity in the estimated values of physiological surface areas and the discordance with the real dimensions of a tennis court is particularly interesting and worth investigating. The inconsistency of estimates is so stark that a popular textbook, "Berne & Levy Physiology," provides two different estimates for the surface area available for gas exchange in two different chapters. It is approximated to be 85 m 2 in Chapter 20 and 70 m 2 in Chapter 22; a comparison to tennis courts is drawn both times [2]. However, the actual dimensions of a tennis court are 195.71 m 2 for a match of singles and 260.86 m 2 for doubles games ( Figure 1) [3]. Neither of the comparisons, even approximately, equates to the area of a real tennis court.

FIGURE 1: The dimensions of a real-life tennis court.
The actual dimensions of a tennis court are 195.71 m 2 for a match of singles and 260.86 m 2 for doubles games [3]. Figure 2 illustrates the three widely used instances of this metaphor in the medical literature. This narrative review explores this phenomenon and deconstructs the discrepancies in these physiological mismeasurements. It also addresses the inappropriate use of Euclidean geometry in describing shapes that are irregular or fractal. In the latter half, the article provides an intuitive introduction to fractal geometry as a language to describe roughness and irregularity.

Review
We performed a cursory search on PubMed and Google Scholar for the term "tennis courts," and selected relevant articles. Besides, we also conducted an in-text search for "tennis courts" within popular textbooks. The sentences comparing body surfaces to tennis courts were enlisted verbatim and referenced.

The alveoli
Historically, numerous experiments have tried to square in on the exact surface area available for gas exchange. From histological techniques to radiological approximations, all the methods that have been employed in the process have failed in reaching a consensus. In 1967, Thurlbeck reported that the area of emphysematous lungs ranged from 40 to 100 m 2 , normally averaging around 63 m 2 [4]. Hasleton in 1972 estimated that the pulmonary surface area ranged from 23.56 to 68.76 m 2 [5]. Weibel provided three values at three different points in time: 150-180 m 2 in 1980, 80 m 2 in 1993, and 130 m 2 in 2009 [6,7].

NO SOURCE ANALOGY AREA(m 2 ) REFERENCE
1 Berne & Levy physiology The lungs are contained in a space with a volume of approximately 4 L, but they have a surface area for gas exchange that is the size of a tennis court (∼85 m2).  The human lung has a large surface area, which for an average-size person approximates half a doubles tennis court, thus maximizing the approximation and apposition of capillaries to the epithelial surface. 6 The lung epithelium has a surface area approximately the size of a tennis court and represents the largest epithelial surface in the body. 7 Fishman's Pulmonary

Diseases and Disorders
Because this small mass of tissue is spread over an enormous areanearly the size of a tennis court -the tissue framework of the lung must be extraordinarily delicate 5 8 To this end a very large area of contact between air and blood must be established; for the human lung it is sometimes compared with the area of a tennis court in size 9 The preceding section considered the overall size of the gas exchanger of the entire lung to compare it with the global performance of this organ. In reality, the surface the size of a tennis court is subdivided into some 400 million gas-exchange units.

Textbook of Histology
It has been estimated that the total surface area of all alveoli available for gas exchange exceeds 140 m 2 (the approximate floor space of an averagesized two-bedroom apartment or the size of a singles tennis court).

Endothelial Cell Mechano-Metabolomic
Coupling to Disease States in the Lung

Microvasculature
The lung has a prominent place in the microvasculature, as its estimated capillary surface area (as defined by diameter of a vessel 10 μm or less) is roughly 50-70 m 2 , which is one-fourth the size of a tennis court 50-70 16 17 Lung Parenchymal

Mechanics
The parenchymal structure is thus a huge collection of tiny and fine balloons that pack an enormous surface area (close to that of a tennis court) into the chest cavity 17 18 Lung Structure and the Intrinsic Challenges of Gas Exchange The model for structure-function correlation of the pulmonary gas exchanger so far discussed considered the whole lung: a gas-exchanging surface the size of a tennis court in humans with a capillary network containing ~200 mL of blood. 18 19 Smaller is better-but not too small: A physical scale for the design of the mammalian pulmonary acinus To exchange oxygen and carbon dioxide, blood and air must be brought into close contact over a large surface area, nearly the size of a tennis court, in the human lung 19

The villi
The surface area of the intestinal carpet available for absorption also has been under much debate. In 1967, Wilson first illustrated the surface area of mucosa per unit serosal length as 1.58 m 2 /m between the duodenojejunal flexure and the ileocecal valve (5.5 m). Therefore, his estimate turns out to be around 8.7 m 2 [20]. In a discussion regarding drug absorption, Niazi stated that the intestinal surface area is about 120 m 2 [21]. A recent review of morphometric data computed that the actual intestinal surface area is just around 32 m 2 , almost a 10-fold underestimation, and concluded that the area is half the size of a badminton court and not that of a tennis lawn [22].
Most sources in our literature search provide the range of estimates between 200 m 2 and 400 m 2 and have been listed in Table 2 along with the parallel drawn to tennis courts [8,[23][24][25][26][27][28][29]. Thus, the combination of the folds of Kerckring, the villi, and the microvilli increases the total absorptive area of the mucosa perhaps 1000-fold, making a tremendous total area of 250 or more square meters for the entire small intestine-about the surface area of a tennis court.

The endothelium
The vascular endothelium is another instance of repetitive analogies to tennis courts. In 1929, Krogh estimated that the cumulative surface area summed up to 6,300 m 2 [30]. On the other end of the spectrum, Pries et al. asserted that the blood-endothelium interface measured about 350 m 2 [31]. Table 3 shows the endothelial surface [24,[32][33][34][35][36][37][38][39][40][41][42].  Although it is a monolayer that covers the inner surface of the entire vascular system, its total weight is more than a liver and has a mass equal to several hearts or, if it is extended, covers a various tennis courts surface area. The average capillary density in the body is 600 vessels/mm 3 tissue with around 1000m 2 surface area available for exchange of materials, which is equivalent to the surface area of almost four tennis courts. In an adult human, the surface area of the entire endothelium is 3,000 m 2 which is equivalent to at least six tennis courts 3000 41

ANALOGY AREA(m 2 ) REFERENCE
12 Holland-Frei Cancer Medicine An angiogenic focus appears as only a tiny fraction or a small "hot spot" of proliferating and migrating endothelial cells that arise from a monolayer of resting endothelium of approximately 1000 m 2 , an area the size of a tennis court.

Discussion
Across the literature, there is a 20-fold variation (350 m 2 to 7,000 m 2 ) in the estimated endothelial surface area and around two-fold variation in the alveolar surface area (70 m 2 to 140 m 2 ). The intestinal surface area (32 m 2 to 400 m 2 ) displays a variation 12.5 times the lowest estimate ( Figure 3). Such large-scale discrepancies are unlikely to result from the variability in processing and measuring techniques or the nutritional state of the human subject. This myriad of mismeasurements is attributable to the nature of these surfaces. They are irregular patterns called fractals. Fractals are irregular geometric patterns. Euclidian shapes like a perfect square or a sphere are hardly ever found naturally. Whereas fractals are present everywhere in nature: from the branching of trees to river networks, the pattern of stars in the galaxy to whirlwinds. "Clouds are not spheres, mountains are not cones, and lightning does not travel in a straight line," says Benoit Mandelbrot, the scientist who described the language of fractal geometry. Fractals are a result of a process that is iterated or repeated multiple times. They exhibit symmetry across different scales, known as self-similarity. Although the level of magnification changes, the degree of their roughness or irregularity remains fairly constant, which can be characterized by a number called the fractal dimension [43,44].
Understanding the concept of "dimension" is necessary before venturing into fractals or fractional dimensions. Geometry deals with "objects" and "spaces." Therefore, the dimension of an object is distinct from the dimension of the space in which it lives or exists. The dimension of the space is the number of axes in which an object can move freely (degrees of freedom). For instance, a histological slide can be regarded as a plane with a dimension of two; the world we live in has a dimension of three. However, the dimension of an object reflects how the object fills up the space within which it exists [45]. Let us take an example of a tree ( Figure 4). It exists in three-dimensional space; however, it does not completely fill up the volume in all three dimensions, like a cuboid. A tree, therefore, fills up more space than a rectangle but not as much as that of a cuboid. Thus, the dimension of the tree would lie somewhere between two and three. This can be conceptualized as the fractal dimension of the tree.

FIGURE 4: A tree is a fractal.
Fractals are a signature of any process that is chaotic, non-linear, and dynamic. So are all biological processes. The human body is a conglomeration of a multitude of chaotic processes occurring in synchrony, good enough to keep us alive. The branching of the tracheobronchial tree, the intricate network of blood vessels, the system of ducts collecting hormones, the retinal vasculature are some instances of geometric fractals in the body [46]. Mathematical fractals are infinite; however, biological entities display the properties of fractals within a definite "scaling window," which is determined by physical constraints. For instance, in the tracheobronchial tree, the surface properties of the mucus limit further branching.

Conclusions
It is challenging to explain the prevalence of the "tennis court" metaphor across medical literature, and in most cases, it is not factually based. The language of fractals is what nature understands, and it is appropriate to define natural surfaces in terms of fractal geometry. Although biological entities behave as fractals within the confines of a window, it is inappropriate to apply Euclidian geometry for quantification. Mathematical modeling, based on radiological measurements can provide a more accurate estimate of these surface areas. Nonetheless, finding the exact value in terms of accuracy is out of contention.

Conflicts of interest:
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