Surface area values for the human stomach including changes in length and diameter or width with meal volume

To quantify the amount of solid, liquid or gas that can be adsorbed on to a surface, the surface area must be known. Equations were developed to calculate the macroscopic surface area of the adult human stomach in vivo, at any given meal volume. For a meal volume of V≈0-2000 cm 3 , the surface area SA≈113-1030 cm 2 and by using a cylinder-shaped stomach model, the diameter D≈2.4-10.3 cm, length L≈27-32 cm and width W≈ 7.5-32 cm. The cylinder model found for a given volume, the standard deviation in average surface area values may result from fluctuations in both length, diameter and width, indicating the stomach, by changing shape, changes surface area. Graphical Abstract The in vivo changes in the stomach average diameter, width, length, macroscopic surface area with standard deviation values and the surface area/ gastric volume ratio, including 3 stomach regions, with meal volume. Using a cylinder model, the diameter is shown as a top view of the fundus region which is then un-rolled together with the cylinder caps and flattened to form a rectangle of width and length. Data adapted from Bertoli et al. 2023 [1].


Introduction
Knowledge of the surface area (SA) of the human stomach and the SA of solid food consumed during a meal, can allow quantification of liquid or solid adsorption on both surfaces, which can be applied to research in how dietary factors could influence symptoms of gastroesophageal reflux [2].An in vivo magnetic resonance imaging (MRI) study of 12 healthy volunteers determined the SA of the human stomach, at baseline and on consuming 500 cm 3 of soup, also reporting that no standard reference values of SA could be found in the literature [1].A typical meal has a meal volume (VM) of VM≈1000cm 3 with a maximum VM ≈1500cm 3 [3].This report adapts and extends the numerical SA and V data from the MRI study to generate equations that estimate the SA for any VM and by using a cylinder model for the stomach, calculate changes in length (L) and width (W) on consumption or digestion [1].A cylinder model is used as some stomachs are reported to be cylindrical in shape and has less complex geometry than the more common J shape.In a study of the stomachs from 50 adult cadavers, 58% had a J shape, 20% cylindrical, 14% crescentic and 8% reverse L [4].
In another study with 24 adult cadavers and 46 post-mortem specimens, 71% of stomachs had a J shape, 7% cylindrical, 7% crescentic and 15% reverse L [5].Models of digestion processes generally refer to the more common J shape [3,6].

Calculation of the surface area for all meal volumes and 3 compartmental regions of the stomach
From a MRI study [1], after consuming a meal with VM≈500 cm 3 , it was found the stomach contained a total liquid volume (VL) with standard deviation (SD) of VL≈516(30) cm 3 and so it is assumed: Total gastric volume (VT) includes both VL, gas (VG) and the stomach wall (VW) such that: At baseline or pre-meal, VT≈140(32) cm 3 , higher than VL≈39(23) cm From eq. ( 3), VM≈VL=0 cm 3 , before a meal had begun, VT ≈ 113 ≈ VG + VW.
The change in gastric SA and VT, with SD values included as described previously for VL and VT, show a line of best fit, Figure 1B: Equation ( 4) can be used to calculate the change in SA≈ 200-1032 cm 2 for VM ≈ 0-2000 cm 3 , using eqs (1) and (3) from the VT ≈113-2233 cm 3 values, Table 1.The SD in the SA values can be added (or subtracted) from the average SA values, showing a line of best fit, Figure 1C: SA(+SD) ≈ 0.99SA + 37 and SA(-SD) ≈1.01SA -37 Equation ( 5) can be used to calculate the SD in the SA values and is shown for SA≈0-2000 cm 2 , with the largest SD values at low VM or VL, Figure 1C, Table 1.
An in vitro ultrasonography study with 8 adults reported a single value for the inner stomach SA≈196 cm 2 and V≈277 cm 3 , showing a SA/V ratio similar to that for a sphere, which has the minimum possible SA/V ratio, Figure 1B [8].Normalized gastric compartmental SA and VT data for the fundus, corpus and antrum are also shown using values from the MRI study for VT ≈140-669 cm 3 extended using power eqs. to VT ≈0-2000 cm 3 , Figure 2 [1].

A cylindrical model showing changes in length and width on consumption or digestion
Taking the square root of known or calculated SA values from eq. ( 4) gives values for length (L) and width (W) as LxW where L=W as SA ≈ √200-√1032 ≈ 14x14 cm -32x32 cm for VM ≈ 0-2000 cm 3 .To determine changes in the L and W of the stomach where L may not necessarily be equal to W, with changes in VM, a cylindrical model to describe the stomach shape was used.Geometric shapes like spheres or cylinders have a V and SA defined by their radius (r) and height (h) from well-known equations such that for the volume of a sphere (VS): VS = (4πr 3 )/3 (6) and SA of a sphere (SAS): For cylinder volume (VC): and cylinder SA (SAC): with h=L and diameter (D) as D=2r.
( 3), (4) (derived from the experimental values) generates VT and SA values which can both be used in eqs.( 8), ( 9) and on solving simultaneous, generating cylinder L and D values, Table 1.Solutions to the simultaneous equations give values for the cylinder L≈26-28 cm which do not increase continuously with increasing D values, with D increasing from D≈2.4-10.3cm, Table 1, Figure 3B.8), (9) and solved simultaneously show an almost constant value of L≈ 26-28 cm with D≈2.4-10.3cm with L declining for D≥6-7 cm, Table 1.When both the cylinder caps radii are included in the L then it is extended by 2r, the extend cylinder LCTB ≈29-37 cm show the expected increase with D≈2.5-10.5 cm. C. The cylinder can be opened and flattened to form a rectangle increasing L by r, with LE increasing with W value, Table 1.Average value [2] V(T)=140 cm^3 SD  with r=D/2 resulting in LE ≈27-32 cm and W≈ 7.5-32.5 cm for VM≈ 0 -2000 cm 3 , Figure 3C, Table 1.Note LCTB was extended by 2r for the cylinder while LE for the rolled and flattened cylinder to form a rectangular shape, was only extended by r.
The maximum LCTB≈37 cm and LE≈32 cm for the cylinder model were comparable to the maximum greater curvature values for J shaped stomachs, with L≈30-34 cm, which includes both the length and radius of the stomach at D≈10 cm [3,6].

Approximations and limitations
Modelling changes of stomach SA with V in vivo is a complex process and it is not surprising few results are available and over a limited ranges of V [1,8].Any model developed to describe the stomach requires many approximations including the shape, stomach wall thickness, what points to use for the measurement of L, D and the greater or lesser curvatures values, due to a lack of precise anatomical boundaries [1, 3,6].In this study, the main approximation was that the trends in SA and V values measures from consuming VM≈500 cm 3 of soup, could be extended to VM ≈500-2000 cm 3 [1].

Conclusion
Equations have been developed to allow the calculation of the SA of the stomach in vivo for any given VM.For SA ≈200-1030 cm 2 at VM≈0-2000 cm 3 with a cylindrical model, when opened and flattened to form a rectangle, showing L ≈ 27-32 cm with W ≈7.5-32 cm.The cylinder model also shows that for any given V, by changing L and D, multiple values for the SA are possible, indicating that the stomach, by changing shape, changes SA.
Figure 3A.From eq. (8), for a given VT value, a range of possible cylinder L and D values and therefor SA (eq.(9)) values are possible.For a specific VT and SA value, only one L and D value can be calculated from simultaneous equations where L>D.The solution to the simultaneous equations shows scattered L and D values due to the SD in VT and SA, possibly the result of volume changes during digestion.Variations in the SA may also be the result of variations in the stomach L and D during digestion, indicated by many of the experimentally determined SA values closely aligned to the lines showing possible L/D values at any given VT, Figure 3A.The standard deviation in average surface area values may result from fluctuations in both length and diameter, rather than be an error of measurement.The range of possible SA values for VT =140 cm 3 , where the SD values are included, areshown with SA ≈193-246 cm 3 for L≈18-32.3 cm and D≈2.3-3.2 cm, Figure3A.A change in shape at a constant V, may provide the stomach some control over SA and presumably the adsorption rates of gastric components, with more tube-like shapes (L>D for example L=9D)

Figure 1 T (cm 3 )Figure 2 .
Figure 1 Changes in the in vivo volume (VT), total liquid volume (VL) and surface area (SA), with standard deviation (SD) values shown [1]. A. The change in VT with VT>VL due to the presence of VG+VW (eq (1)).B. The change in the gastric SA values with VT values from the MRI results (MRI, SD MRI) [1] compared to the SA/V values calculated for cylinders with L=(3, 6, 9)D with the line of best fit as power equations.A single in vivo SA/V value from ultrasonography indicates a spherical shaped stomach as the SA/V data point is on the SA/V curve for a sphere which has the minimum possible SA/V ratio with SA≈800 cm 2 when VT≈2000 cm 3 [8].C. The SD for the average SA values can be added or subtracted from the 6 SA values with the line of best fit used to obtain equations to calculate SD for SA≈0-2000 cm 2 .Data adapted from Bertoli et al. 2023 [1].

Figure 3 .
Figure 3. A. The 6 SA and VT values including the SD values, from the MRI study are used in eqs.(8), (9) to form simultaneous equations which on solving give the L and D values [1].For any given VT value, multiple L and D values are possible generating multiple SA values as shown for V = 140 cm 3 with D and L values expressed as (D, L) coordinates showing SA≈193-246 cm 2 for L≈18-32.3 cm and D≈2.3-3.2 cm, Figure 2A.The line of best fit only includes the 6 averaged VT/SA values.B. From the 16 hypothetical VM≈0-2000 cm 3 , calculated VT and SA values from eqs. (3), (4) included in eqs.(8), (9) and solved simultaneously show an SA and solved simultaneously to give L and D values.The calculated L values do not show an increasing trend with VM or VT.On rolling out and flattening the cylinder to form a rectangle, the L values are adjusted to include the area from the cylinder caps, giving an extended length (LE) at increasing VM and VT.The LE and W multiplied together give a value for the SA of the stomach.If the cylinder is opened and flattened and includes the area of the circular cylinder caps, a new flat rectangular surface can be created with width (W) defined by the circumference (C): W = C =2πr = πD (11) with L now requiring an extend length (LE) to include the additional length (LA) from the circular top and base: LE = L + LA (12) with the new flattened area (LAxW) equal to the area of the 2 circular caps (2πr 2 ): LAW = 2(πr 2 ) or LA = 2πr 2 /2πr = r such that: LE = L + r (13)