INVESTIGATING STOMACH MIXING AND EMPTYING FOR AQUEOUS LIQUID CONTENTS USING A COUPLED BIOMECHANICAL-SMOOTHED PARTICLE HYDRODYNAMICS MODEL

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1 Eleventh Interntionl Conference on CFD in the Minerls nd Process Industries CSIRO, Melourne, Austrli 7-9 Decemer 2015 INVESTIGATING STOMACH MIXING AND EMPTYING FOR AQUEOUS LIQUID CONTENTS USING A COUPLED BIOMECHANICAL-SMOOTHED PARTICLE HYDRODYNAMICS MODEL Simon M. HARRISON 1,2*, Pul W. CLEARY 1,2 nd Mtthew D. SINNOTT 1,2 1 CSIRO Dt61, Clyton, Victori 3169, AUSTRALIA 2 CSIRO Food nd Nutrition, Clyton, Victori 3169, AUSTRALIA *Corresponding uthor, E-mil ddress: Simon.Hrrison@csiro.u ABSTRACT The stomch is criticl orgn for food digestion ut it is not well understood how the stomch opertes, either when it is helthy or when dysfunction occurs. Stomch function depends on the timing nd mplitude of stomch contrctions, the fill level of contents nd the type of gstric contents. Using coupled iomechnicl-smoothed Prticle Hydrodynmics (B-SPH) model, we investigte how gstric dischrge is ffected y the contrction ehviour of stomch wll nd the viscosity of the contents. The results of the model provide new insights into how the content viscosity nd the numer of compression wves down the length of the stomch ffect the flow rte of the contents exiting the stomch to the duodenum. This investigtion evlutes the ility of B-SPH model for simulting complicted stomch ehviour. Gstric emptying is found to increse with greter numer of contrctile wves nd strongly decrese with incresing gstric content viscosity. Future studies will determine how ntomicl movements nd stomch contents ffect the residence time of food in the stomch. INTRODUCTION The stomch is n importnt orgn tht mixes nd comminutes the products of ingestion nd mstiction nd provides control of nutrient nd drug delivery to the intestines nd circultory system. Stomch function hs typiclly een studied using limited in vivo mesurements (Ajj et l., 2004; Ro et l., 1996) or in vitro experiments (Guerr et l., 2012; Kong nd Singh, 2010) ut the mixing nd emptying ehviour cnnot e fully chrcterised y these methods. Computtionl simultion hs the cpcity to provide understnding where mesurements re not prcticl or ethiclly llowed. Currently, studies hve focused on how the stomch mixes purely liquid contents (Pl et l., 2004, 2007; Ferru nd Singh, 2010; Kozu et l., 2010; Xue et l., 2012; Du et l., 2013; Imi et l., 2013; Clery et l., 2015) nd only one study hs considered how these contents re emptied into the intestines (Pl et l., 2007). After mstiction in the mouth, food enters the stomch from the oesophgus nd is churned y contrctions of the stomch wll. Acids nd other digestive chemicls re secreted nd mixed with the food olus to ccelerte the digestive process. After suitle mount of rekdown the food frgments re emptied through the pyloric sphincter into the smll intestine where further rekdown nd nutrient uptke occurs. Stomch function depends on the timing nd mplitude of stomch contrctions, the fill level of contents nd the lod of solid contents. It is not well understood how the stomch opertes, either when it is helthy or when dysfunction occurs. Emptying is thought to e controlled y restriction of the pyloric sphincter nd contrctions in the duodenum, which re induced y exposure of the duodenum to cid or lipids (Ro et l., 1996). Aqueous (non-lipid contining) stomch contents cn pss through the stomch without mesurele restriction from the muscles distl to the stomch, including the pyloric sphincter (Tougs et l., 1992). However, when sustntil oil (lipid) contents re detected y the duodenum, the pyloric sphincter closes nd retention time of gstric contents is much longer (Tougs et l., 1992). Using B-SPH model, we investigte stomch emptying for non-lipid contining liquids, where the pyloric sphincter is consistently fully open. Chnges to gstric flow due to chnges in the contrction ehviour of stomch wll nd the viscosity of the contents re investigted. The model comprises iomechnicl model of the stomch wll nd n SPH representtion of queous stomch contents. The lrge ntrl contrction wves (ACWs) tht trvel down the stomch wll re prescried in the model s rigid deformtions of the stomch wll. Using this model, we investigte the emptying ehviour of the stomch nd the sensitivity of model results to input prmeters. COMPUTATIONAL MODEL Smoothed Prticle Hydrodynmics SPH is mesh-free Lgrngin prticle method for solving prtil differentil equtions. Fluid dynmics pplictions of the method re detiled in Monghn (1994, 2005) nd Clery et l. (2007). Volumes of fluid re represented y moving set of prticles, over which the Nvier Stokes equtions cn e reduced to the following ordinry differentil equtions: d mv W (1) dt dv dt P P m v 2 r r g 2 (2) where is the density of prticle, t is time, m is the mss of prticle nd v = v - v, where v nd v re the velocities of prticles nd. W is cuic-spline interpoltion kernel function tht is evluted for the Copyright 2015 CSIRO Austrli 1

2 distnce etween prticles nd. P nd re the locl pressure nd dynmic viscosity for prticle, is smll numer to mitigte singulrities when the denomintor is smll, is normlistion constnt for the kernel function nd g is the grvittionl ccelertion. A qusi-compressile formultion of the SPH method is employed. The eqution of stte for such wekly compressile fluid reltes the fluid pressure, P to the prticle density, : c (3) P 0 where c is sound speed nd the reference density is given y 0. is mteril constnt, which is equl to 7 for fluids with properties similr to wter. A mch numer of pproximtely 0.1 is used to reduce density vritions from compressiility effects to the order of 1%. A second order predictor-corrector integrtion scheme given in Monghn (1994) is used. The time step is chosen so tht it stisfies the Cournt condition with modifiction for the presence of viscosity (see Clery, 1998): 2 t min 0.5 h c (4) h This formul gurntees stility of the numericl integrtion Nodes of oundry ojects re represented s oundry SPH prticles, which re repositioned t every time step s result of oth rigid ody motion nd/or deformtion of the oundry. The wll of the stomch (descried elow) is deformed y ntrl contrction wves (ACWs) propgting down towrds the pyloric sphincter. SPH model of the stomch contents The stomch ws filled to 80% with n initilly sttionry Newtonin fluid of constnt viscosity. Stomch contents cn vry from wter with viscosity of P s to thick slurry with viscosity of 1 P s (Ferru nd Singh 2010). The effect of viscosity on mixing nd emptying ws investigted using four vlues tht spn the representtive rnge: 0.01 P.s, 0.03 P.s, 0.1 P.s nd 1.0 P.s in seprte simultions. Bck pressure on the fluid leving the stomch, due to downstrem intestinl contrctions is modelled using constnt pressure outflow oundry condition fter the pyloric sphincter. The ck pressure is ssumed to e 400 P, which is pproximtely 50% of the hydrosttic pressure t the pyloric sphincter (using n 86 mm initil depth of fluid). This is similr in mgnitude to mnometry redings for the pyloric region of the stomch (Tougs et l., 1992) during emptying. The sensitivity of model results to the choice of ck pressure is investigted using two pressure levels (400 P nd 500 P) in seprte simultions. Biomechnicl model of the contrcting stomch Figure 1 shows schemtic of the stomch model. The stomch wll is represented in the computtionl model y deforming surfce mesh. The mesh comprises 15,000 nodes, spced t n verge seprtion of 3 mm. The deformtion of the surfce mesh is kinemticlly prescried input ccording to mesurements y Ferru nd Singh (2010). The mesh is rigged to set of rings, which reduce in rdius ccording to the speed nd occlusion of ech ACW. Figure 2 shows the deformtion of the stomch model for simultion cse with three simultneous ACWs. Ech ACW trvels down the stomch t speed of 2.2 mm/s long the centreline (Ferru nd Singh, 2010). With centreline length of 13.3 cm, the ACW durtion is 60 s. The effect of vrying the numer of ACWs ws investigted y considering three different inter-wve periods: 20 s (giving 3 simultneous wves t different loctions in the stomch), 40 s (2 simultneous wves) nd 60 s (one wve t time). Figure 1: The ntomicl model of the stomch which is hollow digestive orgn. The food olus enters from the oesophgus t the crdi. The superior section is the fundus nd is often not filled with liquid/solids; the middle section is the ody (or corpus); nd the inferior section is the pylorus. Once mixing nd digestion hve occurred the contents leve the stomch through the pyloric sphincter into the duodenum, which leds to the smll intestine. RESULTS AND DISCUSSION Figure 3 shows the mixing flow of fluid in centrl cross-sectionl plne through the stomch during dischrge for inter-acw periods of 20 s, 40 s nd 60 s. The contrction wves strt t the top nd propgte downwrds. In regions of high contrction, the fluid is forced to move quickly wy from the converging stomch surfces. At 30 s (Figure 3) the pek contrction is out 2/3 of the wy down the stomch. Fluid is firly quiescent ove this ut flows quickly within nd wy from the constricted re. The contrctile stte of the stomch is the sme for ech of the three wve periods (shown in Figure 3 s columns) t this time so the flow is very similr for the three cses. At 60 s (Figure 3) the stomch contrction hs dissipted for the period=60 s cse (left) nd so the fluid velocities hve sustntilly slowed. Higher speed flow is only oserved ner the pyloric sphincter. In contrst, the contrction in the period=40 s cse (middle column) hs resonle flow speeds throughout much of the content. For the period=20 s cse (right column) the contrction hs lmost reched the lower end of the stomch nd flow speeds re high throughout. The free surfce level declines through ech simultion due to the dischrge generted y the contrction of the stomch. The mount of emptying visily increses with the decrese in contrction period (since there is more contrctile ctivity driving the flow). At 90 s, (Figure 3c) the second wve for the period=60 s cse is now in the sme loction s for the first wve (Figure 3) nd genertes similr intensity flow ut with lower free surfce due to the dischrge. The period=20 s cse shows the contrctile wve just rriving t the loction of the pyloric sphincter nd there is strong nd coherent flow out through the end of the stomch into the smll intestine. Figures 3d nd e show the stte of the stomch nd contents for nother hlf nd one full contrction cycle for the period=60 s cse. Copyright 2015 CSIRO Austrli 2

3 () 0.0 s () 20 s (c) 40 s (d) 60 s Figure 2: Model representtion of ntrl contrctile wves (ACWs) moving down the stomch towrds the pyloric sphincter. The wve occurs every 20 s (resulting in three wves eing present t different loctions in the stomch t ny point in time). These re inputs into the model. The multiple overlpping contrctile wves (period=20 s cse) re very effective t creting dischrge flow nd lowering the level of fluid content in the stomch. As generl oservtion, high fluid speeds occur elow the regions of pek contrction of the stomch wll nd this flow is comintion of dischrge flow out of the stomch nd vortex induced mixing within the stomch contents. Figure 4 shows the mss flow rte through the pyloric sphincter for inter-acw periods of 20 s, 40 s nd 60 s for viscosity of 0.01 P.s. In ll cses there re high frequency fluctutions driven y the detils of the fluid flow in the lower stomch which re not importnt. The underlying flow rte for the period=20 s cse (with 3 simultneous wves) declines linerly with time due to the decresing pressure hed s the stomch content empties. However s the inter-acw period increses nd the numer of simultneous wves decreses then long period coherent cyclic vritions re oserved in the flow rte. For n inter- ACW period of 40 s (2 simultneous wves) the mss flow rte hs minim corresponding to the strt of ech wve (t 40 s, 80 s etc). For n inter-acw period of 60 s (1 wve t time) the mss flow rte reduces sustntilly fter the first 20 s of wve trnsit. The flow speeds inside the stomch content decline nd the fluid ecomes sustntilly quiescent. It would pper tht overlpping of the ACWs is le to eliminte the long period cyclic ehviour nd produce nerly liner dischrge rte. The verge dischrge rte from the stomch (given in Tle 1) decreses stedily with incresing inter-acw period. Since this period is often oserved to e round 20 s (Ferru nd Singh, 2010), it is possile tht this wve frequency is in sense optiml for stedy emptying of the stomch. Figure 5 shows the mixing nd dischrge of fluid in centrl cross-section of the stomch for viscosities of low (0.01 P.s) nd high (1.0 P.s) viscosities. Flow speeds re significntly reduced y stronger viscous forces with the mixing flow in the min volume of the stomch prticulrly strongly ffected. Dischrge flow through the pyloric sphincter is still oserved ut it is much gentler. Figure 6 shows the mss flow rte through the pyloric sphincter for viscosities of 0.01 P.s, 0.03 P.s, 0.1 P.s nd 1.0 P.s. The rte is strongly proportionl to viscosity. The pttern of time vrition is similr for the different viscosities. The verge mss flow rte for the different viscosities is shown in Tle 2 nd shows tht the dischrge rte increses logrithmiclly with decresing viscosity. Finlly, Figure 7 shows the mss flow rte through the pyloric sphincter for duodenl ck pressures of 400 nd 500 P. There re only very smll differences in the short time scle fluctutions with the underlying mss flow rte eing insensitive to viscosity nd oth the mgnitude nd the long term vrition eing the sme for the two pressures. The verge mss flow rtes re given in Tle 3 nd show tht there is little chnge with the fluid ck pressure. This shows tht the dischrge dynmics re entirely controlled y the pressures nd flow generted within the stomch s result of the nture of the contrction ehviour, the fill level nd the fluid viscosity. Future work will focus on model verifiction nd vlidtion. Sensitivity of results to model prmeters such s prticle size nd stomch wll deformtion specifictions will e determined using sensitivity study. Model outputs will e vlidted ginst mesurements where ville. Notly, the mesurement of flow rtes is difficult nd needs to e done in tndem with chrcteristion of stomch contrctile ptterns to llow suitle comprison with the stomch model. Copyright 2015 CSIRO Austrli 3

4 () 30 s () 60 s (c) 90 s (d) 120 s (e) 150 s Figure 3: Fluid flow in cross-sectionl plne through the centre of the stomch showing progressive emptying. Flow velocities re represented y vectors with velocity dependent lengths nd coloured y fluid speed (lue low, green intermedite nd red is fst). The period etween ACWs re: (left) period = 60 s; (middle) period = 40 s; nd (right) period = 20 s. Copyright 2015 CSIRO Austrli 4

5 This stomch model llows prediction of gstric mixing nd emptying of the stomch for ny prescried contrctile wve nd content fill level nd rheology. The presence of prticulte solids nd ny non-newtonin ehviour of the content will chnge these ehviours to some degree. This will e explored in future work. Tle 1: Mss flow rte through the pyloric sphincter for different inter-acw periods. Inter ACW period (s) Mss flow rte (g / s) Figure 4: Mss flow rte through the pyloric sphincter for viscosity of 0.01 P.s nd inter-acw periods of 20, 40, nd 60 s. Tle 2: Vrition of verge mss flow rte through the pyloric sphincter with the viscosity of the gstric content. Viscosity (P s) Mss flow rte (g/s) Tle 3: Vrition in the verge mss flow rte through the pyloric sphincter for different ck pressures. Bck pressure (P) CONCLUSION Mss flow rte (g/s) A coupled B-SPH model of gstric emptying for nonlipid contents is presented. Using detiled model of stomch contrction, simultions were performed of the mixing nd dischrge flow ehviour of gstric contents within the stomch nd out through the pyloric sphincter. Shorter periods etween ntrl contrctile wves (AWCs) led to higher nd stedier dischrge mss flow from the stomch. This occurs ecuse the first 20 s of the wve propgtion ppers to contriute the most to generting the flow tht leds to dischrge. As the wve period increses the flow generted y ech wve is le to sustntively decline efore the rrivl of the next wve leding to strong cyclic vrition in the dischrge rte. Gstric emptying ws found to e strongly dependent on the viscosity ut insensitive to ck pressures in sensile rnge of 400 to 500 P. Future extensions of the model will include mixed solid nd liquid contents nd dynmic or sttic constrictions of the pyloric sphincter for mixing of lipid-contining contents. REFERENCES AJAJ, W., LAUENSTEIN, T., PAPANIKOLAOU, N., HOLTMANN, G., GOEHDE, S.C., RUEHM, S.G., DEBATIN, J.F., Rel-time high-resolution MRI for the ssessment of gstric motility: Pre- nd post phrmcologicl stimuli. J. Mgn. Reson. Imging 19, doi: /jmri CLEARY, P.W., Modelling confined multimteril het nd mss flows using SPH. Applied Mthemticl Modelling 22, CLEARY, P.W., PRAKASH, M., HA, J., STOKES, N. nd SCOTT, C Smooth prticle hydrodynmics: Sttus nd future potentil. Prog. Comput. Fluid Dyn. 7, CLEARY, P.W., SINNOTT, M.D., HARI, B., BAKALIS, S., HARRISON, S.M., Modelling food digestion, in: Fryer, S.B.K.J. (Ed.), Modeling Food Processing Opertions, Woodhed Pulishing Series in Food Science, Technology nd Nutrition. Woodhed Pulishing, pp DU, P., O GRADY, G., GAO, J., SATHAR, S., CHENG, L.K., Towrd the virtul stomch: progress in multiscle modeling of gstric electrophysiology nd motility. Wiley Interdiscip. Rev. Syst. Biol. Med. 5, doi: /wsm.1218 FERRUA, M. J., SINGH, R. P., Modeling the Fluid Dynmics in Humn Stomch to Gin Insight of Food Digestion. J. Food Sci. 75, R151 R162. doi: /j x GUERRA, A., ETIENNE-MESMIN, L., LIVRELLI, V., DENIS, S., BLANQUET-DIOT, S., ALRIC, M., Relevnce nd chllenges in modeling humn gstric nd smll intestinl digestion. Trends Biotechnol. 30, doi: /j.titech IMAI, Y., KOBAYASHI, I., ISHIDA, S., ISHIKAWA, T., BUIST, M., YAMAGUCHI, T., Antrl recircultion in the stomch during gstric mixing. Am. J. Physiol. - Gstrointest. Liver Physiol. 304, G536 G542. doi: /jpgi KONG, F., SINGH, R.P., A Humn Gstric Simultor (HGS) to Study Food Digestion in Humn Stomch. J. Food Sci. 75, E627 E635. doi: /j x KOZU, H., KOBAYASHI, I., NAKAJIMA, M., UEMURA, K., SATO, S., ICHIKAWA, S., Anlysis of Flow Phenomen in Gstric Contents Induced y Humn Gstric Peristlsis Using CFD. Food Biophys. 5, doi: /s y MONAGHAN, J.J Simulting free surfce flows with SPH. J. Comput. Phys. 110, MONAGHAN, J.J SPH without tensile instility. J. Comput. Phys. 159, Copyright 2015 CSIRO Austrli 5

6 PAL, A., BRASSEUR, J.G., ABRAHAMSSON, B., A stomch rod or Mgenstrsse for gstric emptying. J. Biomech. 40, doi: /j.jiomech PAL, A., INDIRESHKUMAR, K., SCHWIZER, W., ABRAHAMSSON, B., FRIED, M., BRASSEUR, J.G., Gstric flow nd mixing studied using computer simultion. Proc. R. Soc. Lond. B Biol. Sci. 271, doi: /rsp RAO, S., LU, C., SCHULZE-DELRIEU, K., Duodenum s immedite rke to gstric outflow: A videofluoroscopic nd mnometric ssessment. Gstroenterology 110, doi: /gst.1996.v110.pm TOUGAS, G., ANVARI, M., DENT, J., SOMERS, S., RICHARDS, D., STEVENSON, G.W., Reltion of pyloric motility to pyloric opening nd closure in helthy sujects. Gut 33, doi: /gut XUE, Z., FERRUA, M.J., SINGH, P., Computtionl Fluid Dynmics Modeling of Grnulr Flow in Humn Stomch. Aliment. Hoy 21, () 30 s () 60 s (c) 120 s Figure 5: Fluid flow in cross-section of the stomch for n AWC period of 30 s. The vectors hve length nd colour depending on the fluid speed. The viscosity is: (left) 0.01 P.s; nd (right) 1.0 P.s. Copyright 2015 CSIRO Austrli 6

7 Figure 6: Mss flow rte through the pyloric sphincter for (left) viscosities of 0.01, 0.03, 0.1 nd, 1.0 P.s, nd (right) ck pressure conditions of 400 P nd 500 P. Copyright 2015 CSIRO Austrli 7