Understanding gastric forces calculatedfrom high-resolution pill trackingBryan Laulichta, Anubhav Tripathib, Vincent Schlageterc, Pavel Kucerac,d,e, and Edith Mathiowitza,b,1

aDepartment of Molecular Pharmacology, Physiology, and Biotechnology, and bDivision of Engineering and Medical Science, Brown University, Providence,RI 02912; cMotilis Sárl, CH-1007 Lausanne, Switzerland; dDepartment of Physiology, University of Lausanne, CH-1015 Lausanne, Switzerland; andeDepartment of Biomedical Engineering, Czech Technical University, 166 36 Prague, Czech Republic

Edited* by Robert Langer, Massachusetts Institute of Technology, Cambridge, MA, and approved March 12, 2010 (received for review February 25, 2010)

Although other methods exist for monitoring gastrointestinalmotility and contractility, this study exclusively provides directand quantitative measurements of the forces experienced by anorally ingested pill. We report motive forces and torques calcu-lated from real-time, in vivo measurements of the movement of amagnetic pill in the stomachs of fasted and fed humans. Three-dimensional net force and two-dimensional net torque vectors asa function of time data during gastric residence are evaluated usinginstantaneous translational and rotational position data. Addition-ally, the net force calculations described can be applied to high-resolution pill tracking acquired by any modality. The fraction oftime pills experience ranges of forces and torques are analyzedand correlate with the physiological phases of gastric digestion.We also report the maximum forces and torques experienced invivo by pills as a quantitative measure of the amount of force pillsexperience during the muscular contractions leading to gastricemptying. Results calculated from human data are compared withsmall and large animal models with a translational research focus.The reportedmagnitude and direction of gastric forces experiencedby pills in healthy stomachs serves as a baseline for comparisonwith pathophysiological states. Of clinical significance, the direc-tionality associated with force vector data may be useful in deter-mining the muscle groups associated with gastrointestinaldysmotility. Additionally, the quantitative comparison betweenhuman and animal models improves insight into comparativegastric contractility that will aid rational pill design and providea quantitative framework for interpreting gastroretentive oralformulation test results.

drug delivery ∣ gastric retention ∣ gastrointestinal biophysics ∣ pill science

The question of what forces a pill experiences in the gastricenvironment is of great importance to the rational design

of pills that target drug delivery to the proximal gastrointestinal(GI) tract. Many therapeutic agents would benefit from increasedresidence time in the stomach and a number of gastroretentivetechniques for prolonging gastric residence time have beendevised and tested (1–3). The most prominent gastroretentivemethods are density mismatching, geometry-based, and bioadhe-sive doses (1–3). By calculating the forces a pill experiences inhuman stomachs, in vitro models can be designed that will aidin predicting clinical success. The net force results in this studycan also serve as baseline measurements for comparison withpathophysiological GI dysmotilities. The calculations can alsobe used to analyze differences in strength of gastric-emptyingforces amongst age groups and patient populations useful fordisease-specific oral dosage design. Additionally, understandingthe quantitative relationships among small animal, large animal,and human gastric forces provided by this work will aid in theselection of animal models and in interpreting translationalresearch results.

Previous methods of measuring gastric forces include mano-metry measurements, which can be made by placing a ballooncatheter in the stomachs of patients and monitoring pressure.Vassallo et al. added a load cell to a balloon catheter to monitor

load in the antegrade direction (4). Measurements were reportedas the cumulative load experienced by the balloon over a periodof 30 min and are the most closely related to the measurementsmade in our study (4). However, the measurements are made on a2-cm-diameter balloon, which is far larger than a typical pill (4).Additionally, the balloon catheter is tethered and thereforeunrepresentative of motive forces experienced by a pill (4).

Studies by Kamba et al. investigated the relationship betweengastrointestinal contractility and pill crushing force by assessingthe destruction of pills with varying moduli in healthy male sub-jects (5, 6). Magnetic tracking methods can also be used to assesscrushing force, disintegration, and tablet breakability (7). Thecrushing force of the gastrointestinal tract is very useful fordesigning oral dosage forms. However, crushing force studiesdo not elucidate the net motive forces experienced by a pill.

Parkman and Jones have incorporated a miniaturized pressuresensor into a pill, which communicates real-time manometry andother data via radio telemetry during gastrointestinal transit (8).Although the manometry data alone does not yield force or tor-que data, forces and torques could be calculated and paired withthe pill data given detailed position as a function of time mea-surements. Whereas manometry measures the total contractileaction of the entire muscularis mucosae, the directional data as-sociated with force measurements in the appropriate coordinatesystem could be used to evaluate the contractility of individuallyoriented muscle layers (e.g., circumferential or longitudinal).

Biomechanics testing and manometry have been employedto investigate the contractility and motility of stomach muscle(9–11). Biomechanical measurements give great insight intothe operation of stomach muscle andmanometry techniques yieldquantitative information regarding local pressure changes duringgastrointestinal contractions (9). However, net forces experi-enced by a pill result from the pressure differences across the sur-face of a pill, its interaction with the mucosal lining, and thegastrointestinal contents. All of these factors affect the motionproducing forces experienced by pills in the gastrointestinal tract.Therefore, monitoring the motion of pills in real time is impor-tant to the accurate determination of gastric motive forces.

The method we employed for calculating instantaneous netforces experienced by model pills in the stomach began by obtain-ing high-resolution pill-tracking data. A superconducting quan-tum interference device (SQUID), radiotelemetry, ultrasound,fluoroscopy, and gamma scintigraphy are all capable of providinghigh-resolution pill location as a function of time data (8, 11–15).All of the methods are high cost and all except SQUID requireimage analysis to extract position data (15, 16). Additionally,

Author contributions: B.L., A.T., V.S., P.K., and E.M. designed research; B.L. and V.S.performed research; V.S. and P.K. contributed new reagents/analytic tools; B.L., A.T.,V.S., P.K., and E.M. analyzed data; and B.L., A.T., P.K., and E.M. wrote the paper.

The authors declare no conflict of interest.

*This Direct Submission article had a prearranged editor.1To whom correspondence should be addressed. E-mail: Edith_Mathiowitz@brown.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1002292107/-/DCSupplemental.

www.pnas.org/cgi/doi/10.1073/pnas.1002292107 PNAS ∣ May 4, 2010 ∣ vol. 107 ∣ no. 18 ∣ 8201–8206

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pill-tracking methods have primarily been used to determine gas-trointestinal tract residence time. Recently, our group and othershave reported measurements using inexpensive, highly accuratereal-time magnetic tracking (17–20). We employed a Hall arraysensor technology to inexpensively and noninvasively track theposition and orientation of magnetic model pills within thestomachs of humans, rats, and dogs without anesthesia. Forcecalculations were made using the acquired position data. Thesame force calculation technique could be applied to similar dataobtained by any methodology, including the ones listed above.Evaluating the force from pill motion enables us to answer thequestion of what forces a pill experiences in the stomach. Thedata provide a pill’s eye view of the stomach that serves as aplatform for investigating basic gastroenterological questionsof motility and contractility, as well as for establishing quantita-tive design criteria for gastroretentive dosage forms.

Results and DiscussionPill-Tracking Analysis. The motion of the model oral dosage formsin the stomachs of humans, dogs, and rats is governed by the netforces and torque it experiences. Gastric transit data provided theLagrangian position of the magnetic model pill in three transla-tional [xðtÞ, yðtÞ, zðtÞ] and two rotational [θðtÞ, φðtÞ] coordinateplanes at a rate of 10 Hz. In the human studies, the z correspondsto the cephalo-caudal, y to the dorsal-ventral, and x to the lateraldirections; whereas, in the animal studies, z corresponds to thedorsal-ventral, y to the cephalo-caudal, and x to the lateraldirections as plotted in Fig. 1A. The myoelectric slow wavethat governs the frequency of gastric contractions occurs at0.05–0.08 Hz in humans, dogs, and rats, indicating that 10 Hz datacollection rate can be assumed to provide sufficient resolution forinstantaneous velocity and acceleration calculations (6, 11, 17).We evaluated the instantaneous translational velocity compo-nents as Vx ¼ dxðtÞ∕dt, Vy ¼ dyðtÞ∕dt, Vz ¼ dzðtÞ∕dt, and theangular velocity components as νθ ¼ dθðtÞ∕dt, νφ ¼ dφðtÞ∕dt.Similarly, we evaluated the instantaneous acceleration (ax, ay,az, αθ, αΦ) of pill motion by evaluating corresponding instanta-neous time derivatives of velocity components. Given the

acceleration, magnitude of net force (jF⇀

netj) at each time point

was calculated using the equation jF⇀

netðtÞj ¼ mpill

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffia2x þ a2y þ a2z

q,

in which mpill denotes the mass of the pill. The magnitude of net

torque (j τ⇀netj) is calculated using the rotational equivalent of theforce equation, in which the pill is approximated as a cylinder,

j τ⇀netðtÞj ¼ Icylffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiα2θ þ α2ϕ

q, in which Icyl ¼ mpill l2

12.

Force and Torque Analysis. The translational components of force

F⇀

x, F⇀

y, and F⇀

z from the data acquired during one of the fastedhuman trials are plotted as a function of time in Fig. 1B. Although

the gravitational field points in the −z direction, the F⇀

z compo-nent follows the other force components with no significantdifferences in magnitude or timing. Because that holds truefor all cases studied, the gravitational component, the weightof the pill, was not factored into calculations. For studies in whichgravity pointed in a direction other than −z during testing, aCartesian coordinate transformation was performed so thatgravity was pointing in the −z direction for data analysis. Dataanalyzed in this study were from healthy subjects, establishingthe force experienced by pills under physiological conditions.In the event of gastrointestinal dysmotility, unusual force patternsalong a particular axis could indicate pathophysiological neuro-muscular activity of a particular layer of the muscularis mucosae.Specific knowledge of the muscle fibers implicated in a case ofgastrointestinal dysmotility provided by force and torquemodeling data may aid in diagnosis or in deciding the courseof treatment. Additionally, the directionality of the force vectordata is useful in analyzing the contributions of different layers ofthe muscularis mucosae to gastric emptying.

Three components of force and two components of tor-que constitute force and torque vectors. Small fluctuations inthe magnitude of force and torque (<250 dynes and<100 dynes · cm, respectively) reflect small stomach wall move-ments and noise, as shown in Fig. 1 B and Fig. S1. In previousstudies, Stathopoulos et al. (19) demonstrated that the dominantfrequencies of pill movement unrelated to measurement noisematch the respiration and heart rate. Large spikes in the magni-tude of force and torque appearing approximately 1,100 s after

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Fig. 1. (A) The solid red line shows a three-dimensional trajectory plot of the model pill in an exemplary fasted human subject. A dashed, dark-blue outline ofthe frontal projection of the stomach is superimposed to correlate the pill motion with the anatomical position. The pill resides predominantly along thegreater curvature of the stomach. At first, the pill resides more orally (position “1”) and at later times (position “2”) more aborally as expected. Ultimately,

the pill is emptied through the pylorus into the small intestines. (B) Exemplary fasted human subject axial force components in three dimensions (F⇀

x , F⇀

y , and F⇀

z)

showing no preference for the −z gravitational direction plotted with the magnitude of the net force vector (jF⇀

netðtÞj ¼ mpill

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffia2x þ a2y þ a2z

q) as a function of

time. The three largest force vectors associated with gastric emptying are labeled F⇀

1, F⇀

2, and F⇀

3 (2,481; 3,014; and 1,236 dynes, respectively). (C) Three-dimensional force vectors plotted with their origins at the position of the pill, corresponding with position 2 in the trajectory plot, as it moves during phaseIII of digestion (1,100–1,200 s). Propulsive forces F

⇀

1, F⇀

2, and F⇀

3 generated by phasic contractions of the antrum are labeled and overlaid on a frontal projectionof the stomach marked with a longitudinal (L) and circumferential (C) curvilinear coordinate system. The directions of F

⇀

1, F⇀

2, and F⇀

3 indicate that circum-ferentially oriented muscle fibers play a large role in the gastric emptying of the magnetic model pill.

8202 ∣ www.pnas.org/cgi/doi/10.1073/pnas.1002292107 Laulicht et al.

dosing this particular fasted human correspond to the phasiccontractions associated with gastric emptying that occur just be-fore the pill exits the stomach through the pyloric sphincter intothe duodenum, as shown in Fig. 1C. We report the maximumforce and torque experienced by the model pills prior to exiting

the stomach as the gastric-emptying force jF⇀

maxj and torquej τ⇀maxj in fasted and fed humans, dogs, and rats. Plotting the mag-

nitude of the force and torque vectors (jF⇀

netj and j τ⇀netj) as a func-tion of time gives a pill’s eye view of the digestive forcesexperienced in the gastric environment (Fig. 1 and Fig. S1).

It is important to note that, in the fed state, the stomach isfilled with partially digested food mixed with gastric secretions,i.e., chyme (21). In this case, the stomach contents have theproperties of water. In the fed state, the presence of foodincreases the chyme viscosity (21–23). Experiments to determinethe exact chyme viscosity are invasive and often involve aspirationof contents or excision of the region of the gastrointestinal tractin question. Such experiments would detract from the noninva-sive nature of the study. Hence, in this study, the contribution

from viscous force on the net force jF⇀

netj was not evaluated.

Human Trials. In the fasted state, pills are the only ingested solidstomach contents, therefore minimal muscular contractions occuruntil the migrating myoelectric complex (MMC) or “housekeep-ing” wave, which occurs approximately every 90 min in fastedhumans and causes large spikes in force until the stomach is empty(24). Fig. 1 B and C depicts the components and magnitude offorces experienced by the magnetic pill over time. The highest

magnitude gastric motive forces—F⇀

1 ¼ 2481, F⇀

2 ¼ 3014, andF⇀

3 ¼ 1236 dynes, respectively (note that the gravitational forcein the z direction is always mg ¼ 667 dynes)—occurring approxi-mately 90 min after ingestion that directly precede gastric empty-ing are attributed to the migrating myoelectric complex (seen inFig. 1B). Based on the force profile observed in Fig. 1B, themotiveforces were overlaid onto the 3D trajectory of the pill onto a lateralprojection of the human stomach during the time period that cor-responds to the MMC (1,100–1,200 s). Although the majority ofthe low-magnitude forces have randomly distributed orientations,

the highest magnitude forces F⇀

1, F⇀

2, and F⇀

3 are oriented aborallywhile the pill is in the vicinity of the pyloric sphincter. In accor-

dance with GI transit, the final large magnitude force F⇀

3 priorto gastric emptying is aligned with the projected opening of thepyloric sphincter. In the exemplary fasted human data plottedin Fig. 1C, the largest magnitude force vectors point primarilyalong the cephalo-caudal and dorso-ventral axes. Motive forcesin the cephalo-caudal direction are likely associated with con-tractions of the circumferentially oriented muscularis mucosae.In the fasted state, because motion of the dense magnetic pills isinertially dominated, the motive forces are assumed to occurfrom solid-body motion rather than motion of the gastriccontents. Therefore, in the fasted state, analysis of the 3D forcevectors calculated from data collected by any high-resolutionpill-tracking data in a gastric dysmotility patient could help todistinguish if the force profile along a particular axis is dimin-ished or if all forces are diminished compared to healthy subjectsto differentiate between weakening of muscle fibers in a parti-cular orientation or of the muscularis as a whole.

When fed, the ingested food undergoes muscular contractionsfor a greater portion of the gastric residence time of the pill, whilethe food grinds and mixes until it has been sufficiently digested topass through the pyloric sphincter. In the human gastric environ-ment, the time fraction histogram of the magnitude of force(jF⇀

netj) suggests that the MMC wave accounts for a small fractionof the total gastric residence time in the fasted state (24). When

fed, the time fraction jF⇀

netj histogram indicates a greater percen-tage of time spent in digestive contractions that produce forceshigher than biorhythms in the fasted state. The motive forces ex-perienced by the model pills are in the low range (<3% of theweight of the pill, where the gravitational force in the z directionis mg ¼ 667 dynes) during 94.5� 1.9% of the gastric residencetime in the fasted state and 68.3� 12.1% in the fed (Fig. 2A).

Torque (j τ⇀j) histograms are statistically similar in the fastedand fed states indicating that the presence of food minimallyaffects the rotational forces experienced by the pills (Fig. 2A).

Although the time fraction jF⇀

netj and j τ⇀j histograms describethe distribution of forces experienced by pills during the quiescentstages of digestion, quantifying the peristaltic forces andtorques that lead to the ejection of the model pills from thestomach are of great utility to the assessment of gastric functionand for the rational design of gastroretentive pills. The maximumforce and torque experience during gastric residence is plotted inboth the fasted and fed states in Fig. 2B. The average human

gastric-emptying force (jF⇀average

net j) is 414� 194 dynes (62% ofthe weight of the pill) (N ¼ 3) in the fasted state, which isstatistically insignificantly lower than in the fed state,657� 84 dynes (99% of the weight of the pill) (N ¼ 3). Average

Human Mean Force and Torque Histograms

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Fig. 2. (A) Frequency histogram of the magnitude of force (jF⇀j) experienced

by pills in the stomachs of fasted and fed human subjects (N ¼ 3 each). In thefed state, the histogram curve shifts to the right reflecting greater timefraction of gastric residence that the pill experiences forceful contractionsassociated with the gastric grinding and mixing of ingested food (phase IIand III of digestion). The * indicates p < 0.05 between the fasted and fedcases. Frequency histogram of the magnitude of torque (jτ⇀j) experiencedby pills in the stomachs of fasted and fed human subjects (N ¼ 3 each) plottedin gray. No difference in torque distribution is observed between the fastedand fed states. (B) Plot shows the average maximummagnitude of force andtorque experienced by the pills during gastric residence. The values corre-spond to the gastric-emptying forces experienced in phase III of digestionthat lead to the passage of the pills from the stomach to the small intestines.No statistically significant difference appears between feed states in eitherforce or torque, although there is a trend toward increased mean gastric-emptying force and torque in the fed state. All error bars depict the SEM.

Laulicht et al. PNAS ∣ May 4, 2010 ∣ vol. 107 ∣ no. 18 ∣ 8203

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human gastric-emptying torque shows a similar trend in thatfasted and fed show little difference, 2; 525� 5 and 2; 582�39 dynes · cm, respectively. The insignificant differences in fedand fasted gastric-emptying forces and torques in humansindicates that the motive forces exerted upon pills are similar inboth the fasted and fed states. In light of the emptying forcesimilarities and because the pills are too large to pass throughthe pyloric sphincter during the grinding and mixing of ingestedfood, the MMC wave is likely responsible for gastric emptyingof the pills in both fasted and fed states.

For comparison with the uniaxial cumulative force resultsreported by Camilleri and Prather, calculated forces were nor-malized by the cross-sectional area of a sphere with equivalentvolume to the pill (in the units of mechanical stress) (25). Theaverage cumulative stress summed over the 30 min period priorto gastric emptying is 160; 000� 70; 000 dynes∕cm2 fasted and520; 000� 270; 000 dynes∕cm2 fed, 42% and 1.5 times the cumu-lative uniaxial area-normalized forces (or stresses) measured bythe force traction catheter, respectively. The area-normalizedforces (or stresses) results from both studies demonstrate nostatistically significant difference (p > 0.05) and are thereforeare in good agreement (24).

Dog Trials. In the fasted and fed, force and torque histograms, nostatistically significant difference is observed between the fastedand fed state (Fig. 3 A). One possible explanation for theobserved lack of differentiation may be that the canine stomachis very muscular and the contractions are similarly forcefulindependent of the gastric contents (6, 25). In keeping withthe supposition that the canine stomach undergoes very forcefuldigestive contractions, the average gastric-emptying force in thefasted state is 2; 633� 78.7 dynes (3.95 times the weight of thepill) and in the fed state is 2; 483� 161.5 dynes (3.73 timesthe weight of the pill). Average gastric-emptying force is 6%higher fasted than fed, and there is no statistically significantdifference between the values. Also, no statistically significantdifference is observed between the fasted and fed gastric-empty-ing torques, 2; 610� 41.27 and 2; 518� 12.77 dynes · cm, respec-tively. The lack of dependence of gastric-emptying force on feedstate may be attributed to the nonerodible pill being large enoughto require emptying by the MMC wave independent of feed state.

Rat Trials. Themass of themodel pills dosed to rats is much smallerthan those dosed to humans and dogs due to differences in size.The presence of food had no significant affect upon the averagefraction of gastric residence time spent in specific ranges of forceor torque (Fig. 4). The average gastric-emptying force and torqueexperienced show a trend toward increasing in the fed state values,which are 7.4 and 2.1 times the fasted averages, respectively. Theaverage gastric-emptying force is 0.43� 0.05 fasted (6% of theweight of the pill, mg ¼ 6.8 dynes) and 3.2� 1.9 dynes (47% ofweight of the pill) fed. The average gastric-emptying torque is0.05� 0.05 fasted and 0.12� 0.01 dynes∕cm fed (N ¼ 2 fastedand N ¼ 2 fed). Although there is a trend toward increasing gas-tric-emptying force and torque, it is not statistically significant.

Interspecies Comparison and Implications. Results indicate that feddogs and humans produce statistically similar gastric-emptyingforces and as such would be a significantly better preclinical mod-el for gastroretentive dosage forms than rats. However, the fastedaverage canine gastric-emptying forces are roughly five timesgreater than those of human subjects indicating that, in the fastedstate, canine stomachs may not provide a good gastric-emptyingmodel for humans.

Because the dog and human model pills are identical, the com-parison of forces and torques does not require size normalization.However, the rat model pills scale with the size of the animal andso, to compare the gastric environments, results were normalized

by the cross-sectional area of spheres with equivalent volumes tothe sphero-cylindrical pills to yield units of mechanical stress.Size-normalized gastric-emptying stresses in the fed rats are onthe order of fed and fasted humans and an order of magnitudelower than dogs (Table 1). Fasted rats exhibit average normalizedgastric-emptying forces an order of magnitude lower thanhumans and two orders of magnitude lower than dogs. Therefore,if rats are used as a preclinical gastric-emptying model forhumans, it is likely best to perform experiments in the fed state.Fasted and fed dogs exhibit more similar gastric-emptying forcesand torques to humans and dogs can accept human-size pills,therefore, although dogs exhibit higher gastric-emptying forcesin general than humans, they are better preclinical models ofhuman gastric emptying than rats.

Researchers and clinicians can utilize the force and stresscalculations presented in this paper as quantitative guidelinesfor approaching the active research topic of achieving prolongedgastric residence time to improve the therapeutic benefit ofpill-based therapies. It is important to note that the pills usedin this study are models in that their size and mass approximatethose typically dosed to humans, dogs, and rats. In the event thatdosage forms or feeding conditions are altered from the standard,the method of using pill-tracking data to monitor force can beemployed to calculate more accurate forces and stresses forthose doses.

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Fig. 3. (A) Frequency histogram of the magnitude of force experienced bypills in the stomachs of fasted and fed canine subjects (N ¼ 3 each). There isno appreciable difference in the magnitude of force distribution betweenthe fasted and fed states. Frequency histogram of the magnitude of torqueexperienced by pills in the stomachs of fasted and fed canine subjects (N ¼ 3

each) plotted in gray. No significant difference in torque distribution isobserved between the fasted and fed states. (B) Although there is no statis-tically significant difference between feed states in either gastric-emptyingforce or torque, canine gastric-emptying forces are considerably higher thanin the human in the fed state (p < 0.05). Additionally, the average coefficientof variance in the canine gastric-emptying forces is small (5%) compared tohumans (30%). Error bars depict the SEM.

8204 ∣ www.pnas.org/cgi/doi/10.1073/pnas.1002292107 Laulicht et al.

Discussion. Monitoring inertial net forces in real time has beenmade possible by the advent of increasingly high-resolutionpill-tracking methods including Hall array magnet positiontracking and radiotelemetry. This manuscript presents a quanti-tative analysis of inertial net forces experienced by magneticmodel pills during gastric residence in humans and two preclinicalanimal models both fasted and fed as tracked by Hall arraysensors. Calculations of maximal force experienced in the

stomach, or gastric-emptying forces, can serve as guidelines forthe rational design of standard pill dosage forms as a guidefor minimum hardness, frangibility, and crushing strength. Thestandard tablet parameters of crush strength and breakabilitycan be easily tested against the in vivo force and torque data.The method and calculations could readily be applied to yieldinertial force data for any oral dosage form in nearly any species,even if the pill differs significantly in size or mass from thosereported in the study.

In particular, for pills designed to achieve increased gastricresidence time, quantifying inertial forces is essential to therational design of pills that will overcome gastric-emptying forcesto remain in the stomach for extended periods of time. Gastro-retentive pills have been investigated for decades becauseincreasing the residence time of pills in the stomach would greatlybenefit the numerous narrow absorption window therapeuticsthat are primarily absorbed in the proximal small intestines(1–3). Therefore, by retaining the pill in the stomach, proximalto the site of absorption, more of the drug could achieve uptake,and time-release formulations could be developed.

The most prevalent strategies for achieving gastric retentionare density mismatching, geometry-based, and bioadhesive pills(1–3). The dense pill used in this study is an excellent modelfor dense pills that are meant to reside on the greater curvatureof the stomach avoiding the pylorus for longer than pills that areof similar density to ingested food. Floating pills, another densitymismatching technique, could be analyzed with the same techni-que by using less dense materials in pill fabrication and calcula-

tions and the gravitational component (F⇀

buoyancy ¼ ΔρV⇀

g⇀)

would be designed to be greater than the gastric-emptying force.Numerous swelling or unfolding pills have been developed

with the intention of being easily swallowed and then changingshape upon introduction into the stomach such that they aretoo large to pass through the pyloric sphincter (1–3). For swellingtablets, the forces calculated in this manuscript could be used as aguideline in designing tablets with a sufficiently high compressivestrength to overcome the gastric-emptying forces when swollen.Similarly, for unfolding films such as the Accordian Pill™, gastric-emptying forces can be used to inform the minimum bendingmodulus of the unfolded film necessary for gastric retention (26).

Finally, for bioadhesive dosage forms, the gastric-emptyingforces calculated indicate how strong the tensile bioadhesivebond strength must be to achieve gastric retention (1–3). Inbioadhesive doses, the cohesive strength of the loosely adherentmucus must also be taken into account (27).

In addition to pharmaceutical design, gastric net force calcula-tions set forth in this manuscript can be used to assess gastroin-testinal motility pathophysiologies and differences in gastricforces experienced by pills in different age groups or patientpopulations quantitatively. Patients with gastrointestinal dymo-stility, for example, may benefit from the forces calculated based

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Fig. 4. (A) Frequency histogram of the magnitude of force experienced bypills in the stomachs of fasted and fed rats (N ¼ 2 each). Feed state does notsignificantly affect the time fraction of force distribution. Frequency histo-gram of the magnitude of torque experienced by pills in the stomachs offasted and fed rats (N ¼ 2 each) plotted in gray. No difference in torquedistribution is observed between the fasted and fed states. (B) Meangastric-emptying force in rats is two orders of magnitude smaller than inhumans and three orders of magnitude smaller than in dogs. However, pillsdosed to rats are significantly smaller than those dosed to dogs and humansdue to the relatively small size of rats. Trends toward increased gastric-emptying force and torque in the fed state are pronounced, but not statis-tically significant due to intersubject variability.

Table 1. Gastric-emptying forces and torques are directly comparable between canine and human studies because thepills used were identical

Feed state andsubject type

Area-normalized gastric-emptyingforce, dynes∕sq cm SEM

Area-normalized gastric-emptyingtorque, dynes∕cm SEM

Fasted humans 606.0 283.8 3,700.9 8.0Fed humans 962.4 123.7 3,783.4 38.9Fasted dogs 3,857.7 115.3 3,824.4 60.5Fed dogs 3,638.9 236.7 3,689.9 18.7Fasted rats 48.2 5.4 6.1 5.6Fed rats 355.7 213.1 13.0 1.3

Pills administered to rats are significantly smaller than those administered to dogs and humans. Therefore, gastric-emptying forcesand torques were normalized by the cross-sectional area of a sphere with the same volume as the pill in the units of mechanical stress. Incomparing the area-normalized gastric-emptying force (or stress) between rats and humans, although the dosage forms administeredto rats are substantially smaller and have significantly lower mass, fed rats exhibit similar area-normalized forces to fasted humans.

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on noninvasive high-resolution pill tracking to help pinpointexactly where a loss of motility has occurred yielding atypicallylow forces in a particular region. GI net force calculations canalso be used to assess the physiology of aging patients to inves-tigate any correlation between age and the strength of gastric-emptying force, which could be of use to physiologists, physicians,and pharmaceutical scientists designing pills for diseases thatafflict patient populations of a particular age group.

ConclusionsThe net forces and torques, experienced by model pills in thestomach, can be calculated from position as a function of timedata acquired by any modality. Forces and torques derived fromthe Motilis Magnet Tracking System data provide tremendous in-sight into the motive forces experienced by standard oral dosageforms. Analysis of the calculated forces yields a measure of gas-tric-emptying force experienced by pills that provides researchersandclinicians in the fieldsof gastric retentionandgastroenterologya quantitative framework for designing gastroretentive pills andunderstanding their behavior in preclinical and clinical trials.From a clinical perspective, force and torque vectors calculatedfrom high-resolution pill-tracking data provide directional datathat relate to physiology or a suspected pathophysiology usefulin diagnosing gastric dysmotility disorders and diseases. In thehealthy fasted human subjects studied, the direction of the forceswith the greatest magnitude all originate in the distal greatercurvature of the antrum toward the pyloric sphincter, implicatingprimarily circumferential muscle fibers in gastric emptying. Froma pharmaceutical research perspective, the gastric-emptyingforce and torque data can be used to estimate what bioadhesiveor buoyancy force would be necessary to retain a dose withinthe stomach. Additionally, from a clinical perspective, forceand torque monitoring provides magnitude and directional datathat serve as a baseline for comparing with pathophysiologaldigestive states.

MethodsMagnet Tracking System. The tracking system consists of a pill containing apermanent magnet, a detection matrix (4 · 4 magnetic field sensors) anddedicated software implanted in a laptop computer (MTS-1, Motilis) (18).The tracking algorithm calculates the position and the orientation of the pillat 10 Hz, except the rotation around themagnetization axis (i.e., five degreesof freedom, three translations, and two rotations). The trajectory of the mag-net was monitored and stored. Force data were calculated from position as afunction of time data and the temporal distribution of force was analyzed.

Patients. The size of the pills can be adapted to the size of the subject, whichallows using the same approach for human, large animals, and rodents(17, 18). Pills containing magnets were either taken voluntarily by humansand dogs or by oral gavage for rats. The size and mass of the pills wereΦ6.0 ×16 mm (740 mg, density of 1.75 g cm−3), Φ5.3 × 15 mm (530 mg, 1.8 g cm−3),and Φ0.85 × 1.1 mm (4.5 mg, 7.0 g cm−3), for human, dogs, and rats,respectively. The coating of the pill was Palaseal® for human and dogsand gold for rats. Experiments in fasted and fed states were carried out.Rat and canine subjects were confined to limit movement and pill trackingwas performed without anesthesia. Human test subjects were seated in asemireclining position.

Three fed and three fasted human subjects ingested model nonerodible,rigid pills containing magnets per os. Four fed and four fasted Beagle dogsubjects ingested the same model nonerodible, rigid pills as the humansubjects. Additionally, two fed and two fasted Hooded Long Evans ratsubjects were administered small cylindrical magnets that served as modeloral dosages. For all subjects, the position of the magnet was monitoredby the Motilis Magnet Tracking System. Force data were calculated fromposition as a function of time data and the temporal distribution of forcewas analyzed. All testing was performed in accordance with institutionalanimal care and use committee and institutional review board guidelines.

We report maximum forces and torques and analyzed as measures ofthe forces experienced during the peristaltic contractions that led to gastricemptying of a typical oral dosage form, termed gastric-emptying force andtorque.

Statistical Analysis. Comparisons betweenmean values of forces, torques, andstresses between feed states and amongst animals were analyzed byone-way ANOVA.

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8206 ∣ www.pnas.org/cgi/doi/10.1073/pnas.1002292107 Laulicht et al.