Silent Pumpers: A Comparative Topical Overview of the Peristaltic Pumping Principle in Living Nature, Engineering, and Biomimetics

This synopsis presents the state‐of‐the‐art of peristaltic pump systems in biomimetics and living nature, and allows for a comparison by highlighting the differences in structure and function, as well as advantages and drawbacks for technical implementation. For the first time, data of selected biological examples are collected in one study to give a comprehensive overview of the performance of biological peristaltic pumps. The developed biomimetic pumping systems not only mimic the biological principle and by this inherit its advantages, but also show the usability of the principle in various pumping applications and medical research. A direct comparison of peristaltic pump systems in nature, biomimetics, and technology highlights their similarities, differences, and allows for proposing new fields of application.


Introduction
In addition to fluid transport representing their main functions, peristaltic pumping systems also play a crucial role in the primary mass transport and in the heat transport for the temperature regulation of biological organisms or technical structures. This presents a unique opportunity of optimizing some of the key structures in industrial applications, and it can only be taken advantage of by a detailed understanding of the functional principles of peristalsis in nature and techniques. To this aim, this study focuses on an overview and comparison of positive displacement pumps and, in more detail, on the silent pumping mechanism of valveless moving chambers of propagative peristalsis pumps in nature and the technical adaptation in engineering inspired by the biological role models. We will compare the performance data, the actuation principles, and their advantages and disadvantages, and point out in which novel fields of application the peristaltic pumping is already used and could be used in the future. This selection is based on the high biomimetic potential for peristaltic pumps. [1] Biological pumps are very well researched and described anatomically and morphologically, [2][3][4][5][6] but there are hardly any compendia that collect the data or describe the pump functionally in terms of structure of the pump, its size, the transported liquid, the basic principles behind the pump and above all the performance of the pump (pressure, volume flow, and actuation frequency). In addition, we are focusing on closing this knowledge gap and providing a compendium on biological peristaltic pump data.

Short Historical Overview of Peristaltic Pumping
The word peristalsis is derived from the Greek word peristellein, which broadly translates as "wrap around to move," and describes, for example, the muscle activity of most hollow tube organs [5] and a movement behavior of annelids with hydrostatic skeletons. [6,7] There are three different modes of peristalsis pumping: propagative anterograde (forward) peristalsis, propagative retrograde (backward) peristalsis, and nonpropagative peristalsis (e.g., stationary mixing motion in the small intestine [6,8,9] or localized rhythmic contractions of tracheal networks in insects) ( Figure 1). [10][11][12][13][14] Propagative (anterograde and retrograde) peristalsis can be found in most hollow tube organs, e.g., the gastrointestinal tract (duodenum, small intestine, large intestine, human ureter, [8,[16][17][18] the esophagus, [19,20] and the hearts of most annelids, holothurians, and arthropods. [5,21] One of the first physiological textbook descriptions of peristaltic motion in the esophagus was written by Cullen [19] in which he stated that the circular muscles of the esophagus are "alternately and successively dilated and contracted, giving the appearance of a vermicular motion, and what is commonly called peristaltic." Proof that the peristaltic principle is well known since the early 17th century is given by Le Clerc and Manget [22] and Marperger, [23] in which the "motus peristalticus" is described. Earlier evidence of a mechanistic understanding of peristaltic movements is provided by Leibniz in 1677 [24] which was in contrast to the still widely accepted concept of fluid motion driven by gravity as postulated by Leonardo da Vinci and others. The first technical peristaltic pump was patented in the USA by Eugene Allen in 1881 for blood transfusions. [25] In the last 50 years, over 100 000 patents for peristaltic pumps in highly diverse applications were submitted [26] (and google patent search (13.04.18; 1:37 p.m.) [27] ), varying from the classical blood pumps to microfluidic pumps (among others for microelectromechanical systems (mems) as described in the review by Nguyen et al. [28] and micropumps for biomedical applications in the review of Wang and Fu [29] ) to pumps for food slurries, highly aggressive acids, wastewater, and sewage. [26,30]

Peristaltic Pumping Principle
Peristaltic pumping systems are (partly) flexible, silent, and fairly simple systems. It consists of a flexible member (hollow organs in nature or tubes in engineering), which is compressed by a force to (in most cases) fully close the inner conduit, resulting in a closed-off compartment being formed by the touching walls. The closure points or contractions are driven down the conduit via muscle contractions (nature) or actuators (e.g., rollers, pistons, pneumatic chambers in engineering) in the direction of pumping ( Figure 2). These motions result in a fluid transport.

Classification and Comparison of Peristaltic Pumps
We provide an overview of exemplary systems in nature, engineering, and biomimetics, and highlight their advantages/ disadvantages and their performances using literature on measured values of peristaltic pumping systems (as far as data are available) ( Table 1-3). All peristaltic pumping systems must meet certain general conditions and requirements to transport fluid against a certain pressure, with a certain flow rate and pressure, and often have to be multifactorially optimized to do so. [2] Influencing factors on pumping systems are costs for production and operation, weight, size, geometry, temperature range, fluid parameters, flow continuity, pressure pulsations, and robustness. [2] The following parameters are used for a comparison of pumping systems: volume flow rate, produced pressure difference, actuation frequencies, pump size, pump geometry, and the underlying actuation principle.
The human vein and muscle pump uses valves and skeletal muscle contractions to transport blood through the veins to the core of the body. [83,[99][100][101][102] The skeletal muscles, which are primarily responsible for body movement, are given a secondary indirect task to compress the veins to return blood from the extremities.
The human esophagus and the intestine as part of the gastrointestinal tract both utilize propulsive peristalsis for the transport; in addition, in the intestine, stationary peristalsis can be found utilizing pendular mixing motions for a better nutrient uptake. [6,8,9,103] The peristaltic wave in the intestine is also preceded by a wave of relaxation (descending inhibition) that travels aborally at a velocity of 0.5-2 cm s À1 . [15,50,103,104] The esophagus is a muscular tube consisting of three distinct functional regions: the upper esophageal sphincter (UES), the tubular esophagus or esophageal body, and the lower esophageal sphincter (LES). [20,[105][106][107] The UES consists of striated musculature and has a slit-like structure which is closed at rest due to the tonic contraction of the UES and the viscoelastic properties of the adjacent structures. The esophageal body is 20-25 cm long and musculature tube is 2 cm wide (concerning bolus size). [20,89,108] The top 5% of the esophagus is striated muscle, the middle 35%-40% consist of a combination of striated and smooth muscle (with smooth muscles progressively replacing striated muscles), and the lower 50-60% is composed entirely of smooth musculature. [20,107,109,110] The LES consists of a musculature thickening at the gastroesophageal junction and a long bundle of muscles that run along the stomach and a short bundle of muscle cells that is oriented transversely around the esophagus at the gastroesophageal junction. The muscles contract tonically at rest to produce an intraluminal pressure that exceeds the intragastric pressure by 1333-6000 Pa. [107] The transport velocities found in the esophagus range between 2 and 5 cm sec À1 . [111][112][113][114] Like the esophagus, the small intestine consists of three main anatomical parts: duodenum, jejunum, and ileum. The small intestine is a 6-8 m long tubular organ that performs two main functions: transport (peristalsis) and nutrient absorption. [104] The duodenum is the shortest part with 25 cm, where the chyme is mixed with digestive fluids, the jejunum is 2.5-3 m long which controls the primary side of nutrient absorption, and the ileum is 3.5-4 m long, which completes the absorption and is connected to the large intestine. [104] An example for the multifunctional usage of peristalsis are leeches, which ingest blood via pharyngeal peristaltic motions of their body wall, [115][116][117] utilize a two-heart system with peristaltic and synchronized pumping to pump their own blood, and use undulatory movements for swimming. [118][119][120] Table 1 highlights exemplarily peristaltic pumping data of different peristaltic pumps in biology with the main focus on examples from the human body. It gives a broad overview of the current state of research and highlights the areas where future research could close the gaps for data that are not yet available. The size of the peristaltic pumps spans over six magnitudes; one of the longest hollow organ systems with peristaltic pumping is to be found in a marine mammal-the sperm whale (Physeter microcephalus). The total length of the intestine of adult sperm whales can range up to 300 m (small and large intestine length Table 1. Biological peristaltic pumping systems. Different systems are described in terms of genus and species in which it is found, the organ that performs the peristaltic pumping and the underlying principle. The pump diameter, length, produced wave velocity, contraction ratio, flow rate and/or velocity of the transported content, generated pressure difference, and actuation frequency are given. Phylum over 9806 Pa [128] Dorsal vessel: Lugworm (A. marina):
The dorsal vessel of arthropods is the most common pumping system in the world (with over ten million different species) [124,125] and examples span over three different magnitudes in diameter and length (μm to cm). [21,90,122,126,127] A brief overview of the generated flow velocity and actuation frequencies is provided in Table 1. All pumps shown in Table 1 have common advantages: they can create continuous flow of viscous liquids, pump different liquids (non-Newtonian fluids and Newtonian fluids), they are highly durable, are self-actuating, consist of self-healing materials, generate valve-less pumping, show low signs of wear due to friction-free movements, are flexible, and most importantly are silent and adaptive. [1,2,5,6,153] Disadvantages of biological pumping systems are hard to define because these systems are highly specialized and most often describe the best solution for a given evolutionary constraint. For example, a backflow in the esophagus due to the peristalsis motion would be a disadvantage (and also lead to gastroesophageal reflux disease (GERD)), but in the intestine, it might aid the mixing and nutrient up take. Nevertheless, one disadvantage (as in technical systems) is ageing, as material degradation, fatigue, functional defects caused by genetic predispositions or environmental factors decrease the life cycle of biological pumping systems. [2] Typical pathologies in human peristaltic systems next to cancer are, for example, esophageal achalasia, [154] GERD, [155] irritable bowel syndrome, [156] short bowel syndrome, [157] and chronic/functional dyspepsia. [158] However, biological systems have the ability to self-repair organs or tissues, and thereby maintain or restore their functionalities for the whole life span of an organism, whereas deterioration in technical systems ultimately leads to failure or at least functional discontinuities during service.
The peristaltic pumping principle is highly suitable for the implementation of technology due to the described common advantages and the large range of magnitudes over which various media are sufficiently and reliably transported. [1,2,80,85] It can be assumed that already the early development of peristaltic technical pumping systems of almost 150 years ago was driven by these reasons. [25]
Overview of biomimetic peristaltic pumping systems utilizing different actuation principles.
Dielectric actuator is fixed in a PET framing, forming a hoop and pinches a silicon tube. [65] Figure 3b Dielectric actuator expands when voltage is applied and depinches the silicone tube inside. The actuator functions as a valve, and can also be used as a peristaltic pump element. [65] 15 mm [65] 5 cm [65] 100% [65] -3.0 kPa [65] -Water [65] Continuous peristaltic pump made of dielectric elastomer actuators Multilayer disc dielectric elastomer actuator. [63,183,192]

Figure 5a
Pressurizing the artificial muscle leads to expansion in the radial direction only. The cylindrical rubber tube expands towards the inside, thereby diminishing the inner radius. [75] 30 mm [75] 235 mm [179] & 561 mm [75] 60-100% [195] 4.4 g s À1 carrier, 2.0 g s À1 developer; [179] Over 2000 mL min À1 ; [194] 81.5 g s À1 [195] 40 kPa [179] 2 Hz, [179] 1.25 Hz [194] Water, [179,194] printer powder (developer & carrier), [75] solid contents [179] www.advancedsciencenews.com www.advintellsyst.com setup (Figure 2c). Corrosion and contamination problems are thereby limited to the flexible tube. [26] The present study focuses on roller-based peristaltic pumps as most modern peristaltic pumps use rollers, especially in critical fields like dialysis. [160] Roller pumps can be further differentiated into tube and hose pumps. Hoses consist of a more rigid material, which is harder to compress but can withstand and generate higher pressure up to 16 bar (Abaque series peristaltic (hose) pumps from Dover Corporation's Pump Solutions Group (PSG)) ( Table 2). [61,159,161] The biggest commercial peristaltic tube pump at presentr is the LSM 200 from LSM Pumper (LSM Pumper, Denmark) with an inner tube diameter of 20 cm and a maximum flow rate of 300 000 L h À1 and a maximal pressure of 4 bar at a weight of 4500 kg and a pump casing height of 2.9 m ( Table 2). [162] The LSM 200 is able to transport anything from sludge, glue, acids, concrete, fish, and food in large quantities. The pump is largely used in agriculture, biogas, mining, and fishing industries because the pump can manage greater particles in the transported fluid. [162] In Table 2, an overview of some most widespread technical peristaltic pumps, their geometries, and performances are given. Medical peristaltic pumps are often used for dialysis, infusions, dosing, and drug delivery, as these pumps allow low steady flow rates, low shear rates, and the easy exchange of sterile tubing. [26,167,168] The flow rates of these type of pumps range from 200 μL min À1 (insulin pumps) [167] to 500 mL min À1 (dialysis pump Fresenius Medical Care http://www.fmc-austria.at/files/ Single-Needle-Dialyse.pdf). Peristaltic pumps are also used in scientific and laboratory applications for analytical devices in which pressure rarely exceeds 1.5 bar. [169] Another application field of peristaltic pumps is microfluidics. A short overview of peristaltic micropumps is given by Berg and Dallas. [60] They highlight the simplest design of a peristaltic pump necessary to produce a flow rate consisting of only three actuators connected in series. In addition, Nguyen et al. [28] review MEMS-micropumps for microfluidics comparing pump size, flow rate, and back pressure. In Wang and Fu's [29] review, the current state-of-the-art in micropumping technology for biomedical applications during the last 5 years is shown. The review provides a useful source of reference for selecting micropumping schemes capable of meeting the specific flow rate requirements of different biomedical applications.
The main advantage of peristaltic pumps over other pumping systems is cleanliness as the transported medium is only in contact with the exchangeable tube. [26,170] This is ideal for a sterile transport of critical and hazardous media. Further advantages of peristaltic pumps are self-priming capability, seal-less pumping, resilience (in terms of trapped air and dry runs), nonslip pumping, low shear pumping, low life cycle costs, and easily revertible flow. [26,30,61,171] Major disadvantages are a loss of the transported medium in case of tubular failure, the comparatively low life cycle of the tube and its material, as well as the low rotational speed and pulsations. [26,30] Moreover, the flow rate is sensitive to varying differential pressure conditions, and the maximal-produced differential pressure is lower in comparison with gear and piston pumps. [61] There are already peristaltic systems battling these disadvantages. Klein, in 2009, patented a roller pump which includes a

Figure 5c
Peristaltic activation pattern pressurizes the actuators which expand inward, fully closing the inner conduit and displacing the fluid. [85] 20 mm [85] 267 mm [85] 100% Above 50 L h À1 with 8 mm tubing diameter [85] 0.2 bar [85] 1.25 Hz [85] Water, viscous fluids [85] www.advancedsciencenews.com www.advintellsyst.com pump tubing with an atrium after the pump. [172] This elastic tube segment expands due to pressure elevations and transports the fluid forward through elastic energy with less pulsations. [61,172] Another way to reduce pulsations in peristaltic pumps is to increase the number of rollers. [173] Cole-Parmers Ismatec pumps, for example, have up to 12 rollers and develop low pulsations in several tubes in parallel. Recent developments show a new field of application for peristaltic pumps as support pumps for cooling systems in electric cars, especially for the cooling of power electronics and batteries. [84,[174][175][176][177][178] These pumps are often actuated by electromagnetism in combination with electromagnetic particles, dielectric elastomers, or electrostrictive polymers. A drawback of this actuation is imperfect closure, that is the pumps do not close 100%. The patents by Ford Global Engineering let to assume that imperfect closure occurs in application of these types of peristaltic pumps in automotives. [175][176][177][178] If the closure is imperfect and only consists of convex constrictions, as illustrated in Masias and Robert [175,176] and Robert et al., [177,178] only an insufficient flow might be generated, as shown in the theoretical models and simulations by Dobrolyubov and Douchy [50] and Sinnott et al. [15] Their models are derived from the peristalsis of the human colon, in which a convex wave (descending inhibition) [15] runs before a concave wave (circular muscle constrictions) resulting in a pressure difference that sucks in the fluid displaced by the concave contraction and facilitates the transport in traveling wave direction (see Figure 1). These distention waves are also recorded in the esophagus. [111] Dobrolyubov and Douchy [50] and Sinnott et al. [15] highlighted that convex constrictions with imperfect closure may result in higher retrograde flow speed or equal fluid distribution, which does not enable sufficient transport if only one peristaltic wave travels along the conduit but facilitates mixing in the colon. Sinnott et al. [15] investigated the influence of different occlusion ratios on the transport of fluid with different viscosities. The model indicates that a zone of muscular relaxation preceding the contraction is an important element for transport. The lower pressure in the concave relaxation zone generates a pressure gradient in the direction of flow. Sinnott et al. [15] point out that the viscosity of luminal content controls the localization of the flow and the magnitude of the radial pressure gradient together with the contraction amplitude controls the transport rate. These studies emphasize the necessity for a technical translation of relaxation, respectively a concave wave, producing an expansion and a negative pressure zone in front of the contraction wave, in not fully closing peristaltic systems.
For roller-driven peristaltic pumps and their specific field of applications, an expansion of the tube is not possible. Tube dilation is constricted by a rigid pump casing in which the tubes or hoses are compressed by rollers. These pumps are often used as metering pumps or in applications in which a constant pressure is needed (dialysis). [26,30] An expansion can be realized only in the tubing downstream from the pump as presented by Klein. [172] A reduction of pulsations and a possible improvement of the flow rate can be attained in the tubing after the pump. [172] The aforementioned examples for the improvement of peristaltic pumps, that is the incorporation of a convex wave before the peristaltic contraction wave, self-actuating pumping tubes, and reduction of rigid framing, should be considered for further developments in the field of biomimetic and coolant pumping systems. A high potential for fully flexible and self-actuating tube pumps (in which the tube consists of actuators or actuators are integrated inside the tube wall) is given as none of the industrial peristaltic pumping systems, except the support coolant pumps of FORD Global (but with rigid framing), utilize this principle. An abstraction of the natural role models is proven to significantly contribute to this development process and result in efficient biomimetic pumping systems. [62,63,65,75,76,83,85,179] Moreover, to our knowledge, there are no prosthetic esophagi, guts, or ureters which incorporate a peristaltic pumping motion into the tubular prosthetic yet. Biomimetic soft robotic devices with a peristaltic motion in a tubular self-actuating design [180] are limited to demonstrators and prototypes, without products on the market.

Biomimetic Pumping Systems
The peristaltic transport in biology exhibits a continuously propagating wave produced by a self-actuating conduit wall, which can achieve complete occlusion at every positions along the conduit. [181] This mode of actuation is unconventional to engineering, though it is feasible by the technical advances in materials and production processes of the emerging field of soft robotics. [181] Novel soft-actuation pump technologies inspired by nature are developed by various research groups. [71,83,85,[181][182][183][184] Biomimetic pumping systems can be suitable alternatives to in vivo experiments investigating the rheology and influencing factors in esophageal, intestinal, and ureter transport. Some biomimetic pumps closely mimic the natural role models in terms of length, diameter, and transport parameters. These artificial esophagi are produced for bolus rheometry, [79] food development for patients with oesophageal disorders, [72,74,[77][78][79]86,87,[185][186][187] or sensor development. [85] Other examples for biomimetic peristaltic pumping systems are highlighted in this part of the chapter and in Table 3.
In the present study, micropumping systems for microfluidic applications are not taken a detailed account, as the peristaltic activation patterns are, in most cases, the only "biomimetic" part of the pump. These systems require a rigid framing and are driven via piezoelectric, dielectric, electromagnetic (see Figure 3), or shape memory actuators (see Figure 4). [28,[188][189][190][191] One example for a flexible biomimetic peristaltic micropump is the dielectric pump of Lotz et al. (see Figure 3c). [63,192] Like the biological role model, the pump consists almost entirely of flexible material that performs a wave-like movement. [192] The developed pumping system can produce a flow rate of up to 36 μL min À1 with a fluid viscosity of 97 mPa s and can transport an aqueous liquid with a maximum volume flow of 11 μL min À1 against a maximum pressure of 0.4 kPa. [192] Dielectric elastomers might be a suitable alternative to magnetic actuators, [62,65] though a common drawback of both systems is the high power consumption (see Figure 3a,b). Shape memory alloy (SMA) springs or coils [182,184] might be good actuators for artificial esophagi or some peristaltic pump applications, but they are inapplicable in cooling systems due to their thermoresponsiveness (see Figure 4a,b). SMAs are typically actuated electrically, where an electric current results in Joule heating. [193] Cooling and reshaping occur slowly by free convective heat transfer to the ambient environment. SMAs are unsuitable for use as actuators in coolant pumps, as they may already react to the hot coolant or be brought above transition temperature and lose their original shape permanently. Further studies for the development of a sufficient biomimetic coolant pump would be beneficial for a higher applicability of peristaltic pumping systems in the aforementioned field of electromobility.
The electromagnetic peristaltic pump of Fuhrer et al. [83] is based on magnetic silicone tubes with a circular or elliptical inner diameter (see Figure 3d). Four magnetic silicone tubes of 8 cm length and 1.2 cm outer diameter are connected to one long tube. The assembled tube is placed on four magnetic fields generating solenoids (0.43 T) which are driven by peristaltic activation patterns. The pump is able to produce fast and reversible movements. When an electrical field is applied, the tubes with circular inner diameter show poor deformation, whereas tubes with an elliptical inner diameter produce a fast and complete contraction and closure of the magnetic tubing, due to the smaller resilience of the thinner tube wall of the elliptic shape. [83] The pump generates a maximum flow rate of 78.5 mL min À1 at a maximum back pressure of 4.12 kPa with a contraction interval of 250 ms. Advantages of this model are the self-actuated contraction, its flexibility, lower shear forces in comparison with roller pumps, and relatively small space requirements. To achieve higher flow rates and pressures, a bigger tube would be necessary and additional strength of the solenoids (larger electric magnetic fields) is required for the actuation. In addition, the farther the pump body is from the magnetic source, the higher is the energy required for the movement.
Three flexible soft robotic biomimetic macroscopic pumping peristaltic systems which incorporate self-actuating pneumatic conduit walls were identified to be of interest for the comparison with technical peristaltic pumps: a peristaltic conveyor for transporting powders (see Figure 5a), [71,73,75,179,194,195] a bioinspired soft-bodied peristaltic esophageal-swallowing robot (see Figure 5b), [72,74,76,79,86,87,181,[185][186][187] and a flexible biomimetic soft robotic peristaltic pumping system (see Figure 5c). [80,85] All three systems can sufficiently transport fluid peristaltically through pneumatic expansion. The fields of application of the systems differ. The peristaltic conveyor is developed for the transport of printer powders, [179] the swallowing robot as a biomimicry in vitro alternative for the investigation of food bolus rheology, [187] and the flexible biomimetic peristaltic pump serves as a proof-ofconcept for an alternative for industrial coolant pumping systems. [85] The powder conveyor consists of distinct pneumatic actuator units combined by rigid skeletal ring structures (flanges) [179] or tubular chambers. [195] When pressurized, the cylindrical rubber tubes of the actuator units expand inward, fully closing the conduit (Figure 5a). In the latest study of Yamada et al., [195] the  Table 3). a) Dielectric elastomer pump (adapted with permission. [62] Copyright 2011, SPIE). b) Tubular dielectric elastomer actuator for active fluidic control (adapted with permission. [65] Copyright 2015, IOP Publishing). c) Continuous peristaltic pump made of dielectric elastomer actuators (adapted with permission. [63] Copyright 2009, SPIE). d) Magnetic peristaltic pump (adapted with permission. [83] Copyright 2013, John Wiley and Sons).
www.advancedsciencenews.com www.advintellsyst.com influence of different cross-sectional shapes (cylindrical with four expansion directions, triangular with three expansion directions) is investigated and a tubular peristaltic conveyor whose inner tube is seamlessly continuous is developed. The triangular cross-sectional chamber increased the conveyance amount per unit time of the powdered materials to 81.5 g s À1 in contrast to the circular conduit geometry. The pump still incorporates a rigid outer framing, which is favorable in a printer, but is not suitable for a transfer of the mechanical flexibility of the biological role model into a technical system. [181] Dirven's work is the first complete representation of esophageal swallowing in a biomimetic device equipped with advanced sensoring capabilities. [78,187] In contrast to the conveyor, the swallowing robot is capable to produce a continuous peristaltic wave by using proportional valves coordinated by central pattern generators, 48 pneumatic chambers, arranged in 12 levels on four chambers which is arranged concentrically around the conduit, and a fully flexible silicone-based material for the soft inner conduit (Figure 5b). Through the use of proportional pressureregulating valves, each actuator level can be pressurized with different pressure values, which allows for achieving nature-like peristaltic wave shapes by the simultaneous actuation of one to three adjacent levels. [77] For the rheological experiments, peristaltic velocities of 20, 30, and 40 mm s À1 and wavelengths of 40, 50, and 60 mm were used. These parameters enable swallowing trajectories that are within normal physiological range and can be tracked through flexible sensors incorporated by Zhu et al. into the outer layer of the inner conduit. [86] The system allows for varying each of the swallowing parameters independently, which is not possible in in vivo testing where there can be significant inter and intrasubject variabilities between multiple parameters. [79] An improved modeling of the biological process is prevented by the rigid structure of the outer shell.
Biomimetic peristaltic pumping systems can also be an interesting alternative for existing coolant pumping systems. The influence on the produced flow rate of check valves in the system, activation frequency, and pressure for pneumatically driven softrobotic peristaltic pumping systems is shown in the experiments by Esser et al. (Figure 5c). [85] They developed and characterized a fully soft, flexible, self-priming peristaltic pumping system. In parallel to the swallowing robot by Dirven et al., [76,187] the base material for the pump is flexible silicone rubber, though it has a flexible expansion-limiting layer on the outside. The pump is light-weight, fully flexible, and capable of generating sufficient pressures and flow rates of up to 60 L h À1 . [85] The system demonstrates that a soft-bodied, self-actuated biomimetic peristaltic pump can be a sufficient alternative for existing technical pumps. Due to its flexible design, the pump can adapt to almost any installation space, which is light weight and robust.
The developments presented above show that biomimetic peristaltic pumps hold a high potential to find novel solutions, to establish new fields of application, and represent more than a proof-of-concept. Additionally, the biomimetic systems highlight the possibility to utilize fully flexible, self-actuating systems. These systems endure lower material wear due to the loss of rollers or finger drives and enable possible sensing capabilities incorporated into the material, hence lowering overall system complexity, weight, and possibly cost.  Table 3). a) Artificial esophagus with peristaltic motion using a shape memory alloy (adapted with permission. [182] Copyright 2010, IOS Press). b) Compound peristaltic micropump (adapted with permission. [184] Copyright 2009, IEEE Proceedings).  (1)], which Vogel used to compare biological pumps, [6,196] where Δp ¼ pressure, a ¼ cross-sectional area, μ ¼ viscosity and v ¼ flow rate.
Most biological pumps generate lower flow rates (v) and pressure (Δp) in comparison with their technological counterparts with similar dimensions. Biomimetic pumps usually use the biological principle as a starting point, but their performance and dimensions (e.g., cross-sectional area (a)) are typically higher than those of biological pumps. A major problem when comparing biological and technical pumps is poor data availability for pump performance in biological systems. The values for pressure coefficient in three well-described examples of nearly the same size (inner diameter) are as follows: 1.26 in the human esophagus, 1.25 in the swallow-bot, and 0.47 in a peristaltic hose pump ( Table 4).
We compute quite smaller values as Vogel, [196] this is due to the fact that the systems examined by Vogel have far larger radii equalling lager cross-sectional areas (a) and work with higher pressure (Δp) than the biological pumping systems of the present study.
The esophagus and swallow-bot have comparable values of pressure coefficient, whereas the technical peristaltic pump achieves a comparatively low value (Table 4). This indicates a high similarity in structure and function of the swallow-bot with the biological role model. The difference between the technical pump and the biological role model can be explained by the very different requirements for the pump system. In contrast to biological peristaltic pumps, technical peristaltic pumps are often used for specific applications in which performance is less important than highly precise dosing and metering or generating high pressure at constant flow rates. The technical pumping systems by far out class the biomimetic and biological systems in terms of performance and mass transport, but all the peristaltic pumping systems presented are all highly adapted to their application. As Vogel so aptly put "The performance of a pump should match the demands of its application." [196] The comparison of peristaltic pumps showed that biomimetic pumps are in the same range as biological pumps, but both differ from standard technical pumps in terms of performance and mass transport.

Conclusions and Outlook
The fields of application and the range of performance of peristaltic pumping systems are very diverse. In the course of evolution, various peristaltic pump systems have been developed, such as the dorsal vessel of arthropods, which is the prevalent biological pump as to the number of species in which it is found.
There are three main differences between biological, biomimetic, and (common) technical peristaltic pumps: pump performance, the presence or absence of rigid structures, and system durability. In addition, biological pumping systems are highly integrated as they incorporate actuation, sensing, and self-healing materials. Rigid structures are seldom involved in the implementation of the peristaltic principle in biology. In contrast, technical pumps are often highly modular and are standardized. [2] The only flexible component in most technical peristaltic pumps is a tube, hose, or flexible conduit, which is deformed by the actuators (rollers, fingers, pistons, or solenoids) Figure 5. Biomimetic peristaltic pumping systems based on pneumatic actuators (for technical parameters, see Table 3). a) Peristaltic conveyor pump based on bowel peristalsis (circular arrangement: adapted with permission. [194] Copyright 2010, IEEE Proceedings; triangular arrangement: adapted with permission. [195] Copyright 2018, Taylor & Francis Group). b) Soft-bodied peristaltic swallowing robot (adapted with permission. [76] Copyright 2014, Springer Nature). c) Flexible soft-robotic biomimetic peristaltic pumping system (adapted with permission. [85] Copyright 2018, Springer Nature).
www.advancedsciencenews.com www.advintellsyst.com to change the inner conduit diameter and peristaltically displace the liquid. In contrast to conventional technical pumps, biomimetic pumping systems use soft materials. Actuators based on flexible materials (flexible silicone, dielectric elastomers, or magnetic elastomers) are the main components of these pumps, which, like the biological role model, either directly form the conduit wall or are built into it. This is a concept which is still rarely implemented in engineering. [2] The current biomimetic research on peristaltic pumps indicates a rapidly developing field, as more peristaltic pumping systems using soft actuators are being developed, for example, for low-energy-consuming micropumps, [29,62,63,65,198] artificial esophagi for ex vivo investigation, [79] or as technical pumping alternatives. [85,195] The advances in soft actuator technology enable the development of biomimetic and technical pumping systems that closely resemble biological systems. As Bach et al. state "This could lead to a paradigm shift away from the extensive use of stiff metallic materials towards the use of flexible composite materials for a broad range of engineering applications within the limits of such contractile soft displacement pumps regarding pressure, flow rate, life time and compatibility with certain fluids and temperatures." [2] Two main advantages of biological pumping systems are their lack of parts moving relatively to each other, a primary source of friction and wear that is often decreasing the life cycle of technological pumps, [2] and their silent fluid transport, thereby solving acoustical problems of conventional pumps. Furthermore, the biological role models highlight the possibility to achieve a large range of magnitudes over which various media can sufficiently and reliably be transported. [1,2,80,85] The biomimetic peristaltic pumping systems hold the potential for substituting conventional technical pumping systems and for developing life-like intestinal or esophageal prosthetics. Here, the incorporation of "organ on a chip" technology in macroscopic pumping systems with a life biofilm of gastrointestinal microbiota [199] and scaffolds for tissue regrowth [200,201] would be beneficial. The development of self-actuating and selfsensing peristaltic tubes might reduce complexity, space requirements, and weight of systems in fields as space technology in which these are essential or KO criteria. For a better overall usability and overall applicability of peristaltic pumps, more research on autonomous, adaptive, and resilient material systems need to be performed.