High-speed Movies Research Articles

Comparison of MYOCYTER and MUSCLEMOTION in the analysis of Induced Pluripotent Stem Cell Derived Cardiomyocyte Contractility

Patient-specific induced pluripotent stem cells (iPSCs) differentiated into cardiomyocytes (CMs) offer tremendous opportunities for cardiac disease modeling and advancements in precision medicine. There is a need for technologies that allow noninvasive and precise measurements of CM function, such as contractility, to increase throughput for drug screening and testing efforts. Hypoplastic Left Heart Syndrome (HLHS) is a rare and complex congenital heart defect characterized by hypoplasia of the left ventricle, proximal aorta, as well as stenosis or atresia of the mitral and/or aortic valves. Previously it was demonstrated that iPSC-CMs from an HLHS patient with a genetic variant in the alpha myosin heavy chain ( MYH6 gene) exhibited an impaired cardiomyocyte phenotype (dysmorphic sarcomere structure, compensatory expression of MYH7, and altered contractility). Gene editing using CRISPR/Cas9 rescued the phenotype, demonstrating the utility of MYH6 iPSC-CMs as a useful disease model for HLHS. Critical parameters of CM function include contraction and relaxation, assessing systolic and diastolic dysfunction, respectively, in iPSC-CMs. The aim of this study is to compare features from two open-source macros for ImageJ: MYOCYTER and MUSCLEMOTION. MYOCYTER improves upon previous plugins available by allowing for users to select parameters. Both methods allow measurement of movement from high-speed movies. MYOCYTER enables the user to select an optimal threshold, size, and cell count to minimize disturbances such as cellular fragments, background noise, and floating bubbles, to maximize precision during analysis. MUSCLEMOTION allows rapid and easy measurement of movement from high- speed videos and can measure and compare relative or absolute parameters. This study will determine whether a systolic or diastolic dysfunction phenotype is observed under different magnification settings and evaluate the effect of dosing with pharmaceutical compounds. Finally, benefits and drawbacks of both macros will be investigated. Children's Research Institute. This is the full abstract presented at the American Physiology Summit 2024 meeting and is only available in HTML format. There are no additional versions or additional content available for this abstract. Physiology was not involved in the peer review process.

Ex uno plures: how to construct high-speed movies of collapsing cavitation bubbles from a single image

The time-resolved visualization of the dynamics of a cavitation bubble usually requires the use of expensive high-speed cameras, which often provide a limited spatial resolution. In the present study, we propose an alternative to these high-speed imaging techniques. The method is based on the recently introduced virtual frame technique, which relates the motion of a monotonic propagating front to the resulting image blur captured on a long-exposure shadowgraph. We use a consumer-level camera to photograph the entire collapse phase of cavitation bubbles. We then demonstrate that both the dynamics of a spherically collapsing bubble and those of a bubble collapsing near a rigid boundary can be accurately reconstructed from this single photograph at a virtual frame rate of up to 2 Mfps on a 24.2 Mpx sensor.

The effect of intake port shape on in-cylinder flow field and turbulence distribution in a high-tumble production engine with endoscope accesses

Three cylinder heads with varied intake port shapes are experimentally investigated to evaluate intake flow structures and their influence on near top dead centre (TDC) flow fields and turbulence distributions in a motored high-tumble engine. The endoscopic high-speed particle image velocimetry (eHS-PIV) is implemented in multi-cylinder engines with two laser endoscopes and a camera endoscope installed in the cylinder head. For a range of engine load and speed conditions, particle seeded and laser illuminated high-speed movies are recorded for 100 cycles with which ensemble-averaged flow fields and spatial-filtered high-frequency flow magnitude distributions are analysed. The results show that a straighter intake port producing a more lateral flow direction results in a larger swinging arc, which is related to enhanced flow later in the compression stroke. The tumble vortex shows an asymmetric structure; the flow field during the compression stroke exhibits higher magnitude vectors at the leading head. This surging flow head becomes stronger with a straighter intake port, which leads to enhanced tumble vortex formation near TDC. As it becomes very strong, the flow vectors originally directed towards the exhaust valves bounce back towards the intake valves, causing a very complex flow structure involving multiple flow components. The result is enhanced turbulence throughout the late compression stroke including the spark timing. However, the impact of the straighter intake port shape on TDC turbulence becomes less significant at lower engine load and speed conditions as the lower intake air momentum limits the enhancement.

Decoding the hydrodynamic properties of microscale helical propellers from Brownian fluctuations

The complex motility of bacteria, ranging from single-swimmer behaviors such as chemotaxis to collective dynamics, including biofilm formation and active matter phenomena, is driven by their microscale propellers. Despite extensive study of swimming flagellated bacteria, the hydrodynamic properties of their helical-shaped propellers have never been directly measured. The primary challenges to directly studying microscale propellers are 1) their small size and fast, correlated motion, 2) the necessity of controlling fluid flow at the microscale, and 3) isolating the influence of a single propeller from a propeller bundle. To solve the outstanding problem of characterizing the hydrodynamic properties of these propellers, we adopt a dual statistical viewpoint that connects to the hydrodynamics through the fluctuation-dissipation theorem (FDT). We regard the propellers as colloidal particles and characterize their Brownian fluctuations, described by 21 diffusion coefficients for translation, rotation, and correlated translation-rotation in a static fluid. To perform this measurement, we applied recent advances in high-resolution oblique plane microscopy to generate high-speed volumetric movies of fluorophore-labeled, freely diffusing Escherichia coli flagella. Analyzing these movies with a bespoke helical single-particle tracking algorithm, we extracted trajectories, calculated the full set of diffusion coefficients, and inferred the average propulsion matrix using a generalized Einstein relation. Our results provide a direct measurement of a microhelix's propulsion matrix and validate proposals that the flagella are highly inefficient propellers, with a maximum propulsion efficiency of less than 3%. Our approach opens broad avenues for studying the motility of particles in complex environments where direct hydrodynamic approaches are not feasible.

FLOW VISUALIZATION AND FLOW PATTERNS IN A FLAT-PLATE POLYPROPYLENE PULSATING HEAT PIPE

The two-phase flow structure in a flat polymeric pulsating heat pipe (PHP) is studied experimentally by high-speed imaging and digital image processing. While flow patterns in tubular pulsating heat pipes can be studied by inserting a short transparent section in a certain position along the channel, in flat PHPs built using transparent plastic sheets one can visualize the entire flow field in the adiabatic region between the evaporator and the condenser. High-speed movies were enhanced by digital image processing to highlight the liquid-vapor interfaces. Different flow patterns were identified, and sorted into a simple flow pattern map.

Acquirement of the autonomic nervous system modulation evaluated by heart rate variability in medaka (Oryzias latipes).

Small teleosts have recently been established as models of human diseases. However, measuring heart rate by electrocardiography is highly invasive for small fish and not widely used. The physiological nature and function of vertebrate autonomic nervous system (ANS) modulation of the heart has traditionally been investigated in larvae, transparent but with an immature ANS, or in anesthetized adults, whose ANS activity may possibly be disturbed under anesthesia. Here, we defined the frequency characteristics of heart rate variability (HRV) modulated by the ANS from observations of heart movement in high-speed movie images and changes in ANS regulation under environmental stimulation in unanesthetized adult medaka (Oryzias latipes). The HRV was significantly reduced by atropine (1 mM) in the 0.25-0.65 Hz and by propranolol (100 μM) at 0.65-1.25 Hz range, suggesting that HRV in adult medaka is modulated by both the parasympathetic and sympathetic nervous systems within these frequency ranges. Such modulations of HRV by the ANS in adult medaka were remarkably suppressed under anesthesia and continuous exposure to light suppressed HRV only in the 0.25-0.65 Hz range, indicating parasympathetic withdrawal. Furthermore, pre-hatching embryos did not show HRV and the power of HRV developed as fish grew. These results strongly suggest that ANS modulation of the heart in adult medaka is frequency-dependent phenomenon, and that the impact of long-term environmental stimuli on ANS activities, in addition to development of ANS activities, can be precisely evaluated in medaka using the presented method.

Effects of injection pressure on the flame front growth in an optical direct injection spark ignition engine

• Optical diagnostics performed at wide open throttle and 1200 rpm conditions. • Elevated injection pressure does not monotonically increase engine output. • Higher spatial variation in turbulence measured for very high injection pressure. • Local overmixing and increased mixture inhomogeneity are likely causes. • Despite decreased power, soot is still lower at very high injection pressure. The fuel injection pressure of direct injection spark ignition (DISI) petrol engines has increased significantly to improve engine efficiency and reduce air-polluting emissions. The present study performs a detailed analysis of spray penetration, burn duration, flame front vectors and turbulence intensity to provide scientific explanations about the optimal injection pressure observed for the maximum power output/efficiency in a single-cylinder optically accessible DISI engine. Five injection pressures of 5, 10, 15, 20 and 25 MPa were tested based on an equal-split double injection strategy using a side-mounted six-hole direct injector. A high-speed camera with a 20 kHz frame rate was used to record spray development, propagating petrol flame and soot luminosity. The Mie-scattering technique was used to image the fuel dispersion under varied injection pressure and to calculate spray penetration. For time-resolved, two-dimensional flame front vector extraction, a newly developed flame image velocimetry (FIV) was applied to high-speed natural combustion luminosity movies. A spatial filtering method was also used for the flow decomposition to acquire flame front turbulence intensity. A total of 100 combustion cycles were FIV processed for each test pressure to tackle the inherent cyclic variations. The spray images showed that higher fuel injection pressure leads to faster spray tip penetration and enhanced spray evaporation for better air/fuel mixing. However, the in-cylinder pressure and power output do not continue to increase with an increase in injection pressure; they peak at 15 MPa and decrease at higher injection pressure. The spatially averaged flame front vector magnitude and turbulence intensity also peak at 15 MPa, indicating the optimal injection pressure was due to the maximum turbulent flame front growth. The distribution of turbulence intensity along the flame boundary shows increased variations at injection pressure higher than 15 MPa, because local over-mixing caused low turbulent flame growth regions. Although the highest turbulent flame front growth was not measured at 25 MPa, the soot luminosity was much lower than that of 15 MPa, which explains the development trend towards higher injection pressure.

ИССЛЕДОВАНИЕ ГИДРАВЛИЧЕСКОГО ПРИВОДА КЛАПАНОВ ГРМ

Improving the characteristics of the internal combustion engine of an agricultural vehicle is possible by using a hydraulic actuator of the electronically controlled gas distribution valves. The drive ensures the opening of the engine valves by the pistons of the hydraulic cylinders when oil is pumped into them, the valves are closed using valve springs when the oil is drained from the hydraulic cylinders. The advantages of the hydraulic drive are: the ability to turn off the engine cylinders, an increase in the speed of opening and closing the valves of the gas distribution mechanism, no need to adjust the thermal clearances, a constant speed of the valves landing on the saddles. The hydraulic drive is integrated into the engine lubrication system. The working body of the hydraulic drive is engine oil with a pressure of 8 MPa, created by a separate pump. The physical and mathematical model of a hydraulic valve drive in the Simulink environment takes into account hydraulic pressure losses, various inertial effects, elastic-deformation interaction between drive elements, and inductance of solenoid valve coils. The experimental setup includes: a KAMAZ 740 engine, a hydraulic drive for two valves of one cylinder head, measuring equipment. The results of the experiments were recorded using a high-speed movie camera. The determination of the kinematic characteristics of the valves of the gas distribution mechanism was carried out by processing the video frames of the shooting at a known frequency of their fixation. The results of experiments coincide with the results of calculations. The speed of movement of the engine valves, thanks to the use of a hydraulic actuator, is significantly increased compared to the use of a traditional mechanical actuator. The time delay between the supply of an electrical signal to the electromagnetic valves and the response of the hydraulic drive to it is determined. The results obtained make it possible to start creating a serial hydraulic valve drive that improves engine parameters by intensifying and controlling the gas exchange of the engine cylinder with the environment

Nucleation effects on cloud cavitation about a hydrofoil

The dynamics of cloud cavitation about a three-dimensional hydrofoil are investigated experimentally in a cavitation tunnel with depleted, sparse and abundant free-stream nuclei populations. A rectangular planform, NACA 0015 hydrofoil was tested at a Reynolds number of $1.4\times 10^{6}$ , an incidence of $6^{\circ }$ and a range of cavitation numbers from single-phase flow to supercavitation. High-speed photographs of cavitation shedding phenomena were acquired simultaneously with unsteady force measurement to enable identification of cavity shedding modes corresponding to force spectral peaks. The shedding modes were analysed through spectral decomposition of the high-speed movies, revealing different shedding instabilities according to the nuclei content. With no active nuclei, the fundamental shedding mode occurs at a Strouhal number of 0.28 and is defined by large-scale re-entrant jet formation during the growth phase, but shockwave propagation for the collapse phase of the cycle. Harmonic and subharmonic modes also occur due to local tip shedding. For the abundant case, the fundamental shedding is again large-scale but with a much slower growth phase resulting in a frequency of $St=0.15$ . A harmonic mode forms in this case due to the propagation of two shockwaves; an initial slow propagating wave followed by a second faster wave. The passage of the first wave causes partial condensation leading to lower void fraction and consequent increase in the speed of the second wave along with larger-scale condensation. For a sparsely seeded flow, coherent fluctuations are reduced due to intermittent, disperse nuclei activation and cavity breakup resulting in an optimal condition with maximum reduction in unsteady lift.

Multistep orthophosphate release tunes actomyosin energy transduction

Muscle contraction and a range of critical cellular functions rely on force-producing interactions between myosin motors and actin filaments, powered by turnover of adenosine triphosphate (ATP). The relationship between release of the ATP hydrolysis product ortophosphate (Pi) from the myosin active site and the force-generating structural change, the power-stroke, remains enigmatic despite its central role in energy transduction. Here, we present a model with multistep Pi-release that unifies current conflicting views while also revealing additional complexities of potential functional importance. The model is based on our evidence from kinetics, molecular modelling and single molecule fluorescence studies of Pi binding outside the active site. It is also consistent with high-speed atomic force microscopy movies of single myosin II molecules without Pi at the active site, showing consecutive snapshots of pre- and post-power stroke conformations. In addition to revealing critical features of energy transduction by actomyosin, the results suggest enzymatic mechanisms of potentially general relevance.

In-Flame And In-Cylinder Flow/Turbulence Measurements Near The Glow Plug Using Flame Image Velocimetry And Particle Image Velocimetry In An Optical Compression-Ignition Engine

The present study implements two diagnostic methods based on tracking of seeded olive oil droplets (PIV: particle image velocimetry) and pattern changes detected in high-speed flame movies (FIV: flame image velocimetry) in a small-bore optical diesel engine. For each measurement, a total of 100 engine cycles are recorded and processed to address the inherent cyclic variations. The ensemble-averaged flow fields and turbulence intensity distribution extracted from individual cycles via the spatial filtering method are discussed with a particular interest in the influence of glow plug on flow and turbulence, i.e. rigid body and fluid interaction. The PIV results show a swirl flow structure forms and rotates with its centre shifted towards the exhaust side, leading to an asymmetric swirl structure. By comparing a PIV laser plane tilted towards the glow plug and a 10 mm horizontal plane below the cylinder head with no glow flow-plug interaction, it is observed that the flow-plug interaction causes the flow winding around the plug tip to generate complex flow structures and new vortices downstream of the plug. The tilted plane and 10-mm plane show similar bulk flow magnitude distribution patterns; however, the flow-plug interaction generates high turbulence in the tilted plane right downstream of the plug tip where new vortices form, which lasts for a few crank angles. The spatially averaged flow magnitude and turbulence intensity are measured higher in the 10-mm plane where there is no flow-plug interaction, suggesting the increased turbulence is a localised behaviour. The flame-plug interaction is also investigated during the combustion event using the FIV method. The level of flame-plug interaction is adjusted by changing the inter-jet spacing angle of two nozzle holes with one case showing high interaction and the other displaying low interaction. From the FIV measurements, the most significant effect of the flame-plug interaction is observed as the further penetration of the wall bounced flame for the high interaction case. This is due to the glow plug as a rigid body blocking the swirl flow and promoting the flame penetration back towards the centre of the combustion chamber upon the piston-bowl wall impingement. The measured turbulence intensity is also higher thanks to the enhanced wall bounced flame in addition to more significant flame-plug interaction at the interface.

Frontier of Photopharmacology for High-speed Molecular Movies of Proteins

Frontier of Photopharmacology for High-speed Molecular Movies of Proteins

The Application of Flame Image Velocimetry to After-injection Effects on Flow Fields in a Small-Bore Diesel Engine

This study implements Flame Image Velocimetry (FIV), a diagnostic technique based on post-processing of high-speed soot luminosity images, to show the in-flame flow field development impacted by after-injection in a single-cylinder, small-bore optical diesel engine. Two after-injection cases with different dwell times between the main injection and after-injection, namely, close-coupled and long-dwell, as well as a main-injection-only case are compared regarding flow fields, flow vector magnitude, and turbulence intensity distribution. For each case, high-speed soot luminosity movies from 100 individual combustion cycles are recorded at a high frame rate of 45 kHz for FIV processing. The Reynolds decomposition using a spatial filtering method is applied to the obtained flow vectors so that bulk flow structures and turbulence intensity distributions can be discussed. The results show significant after-injection-induced flow structures as a group of vectors travelling back toward the center of the combustion chamber upon the jet impingement on the piston bowl wall and then jet-to-jet collision. Despite higher cyclic variations caused by the after-injection, increased bulk flow magnitude and turbulence intensity upon the after-injection event suggests locally enhanced mixing. Compared to the long-dwell after-injection, the close-coupled after-injection shows more significant turbulence enhancements.

Interpretation of Multilobe Wavepackets in Spectral Proper Orthogonal Decomposition of Supersonic Jet

Spectral proper orthogonal decomposition (SPOD) is a major modal analysis that extracts a dominant structure at each frequency from complicated flow data, such as the wavepacket hidden under turbulent jets. This study investigated the physical interpretation of subdominant multilobe structures in the SPOD modes. A high-speed schlieren movie that exhibited multilobe structures in the SPOD was analyzed using a wavelet-based conditional sampling and averaging (WB-CSA) method. The results of WB-CSA showed spatiotemporally localized wavepackets, which were formed intermittently and convected downstream through growth and decay. Such intermittent convection causes multilobe structures in the SPOD, as illustrated by simple synthetic data that model the results of WB-CSA. Therefore, multilobe structures, together with the most dominant single-lobe wavepackets, can be interpreted as representing the intermittent convection of wavepackets.

New design yields robust large-area framing camera.

Framing cameras provide a discrete series of images over a short period of time in a manner that mimics a high-speed movie camera but with individual shutter times that must be extremely short in order to capture freeze-frame images of rapidly evolving phenomena such as high-explosive shock-driven ejecta, dynamic compression of metals, and high-velocity fluid flow. The Nevada National Security Site has designed and fielded a new, large-area, gated framing camera called Kraken. The camera design emphasized manufacturability and flexibility by improving imager yield and creating a camera architecture to shorten design cycles. Design strategies and field data are presented.

High-Speed Hydroxyl and Methylidyne Chemiluminescence Imaging Diagnostics in Spherically Expanding Flames

Fundamental understanding of chemical kinetics pathways involved in ignition and flame propagation in hydrocarbon flames is essential for designing efficient and clean combustion devices for aerospace applications. In this study, spherically propagating methane-air and methane-ethane-air flames inside a constant-volume vessel were characterized using a species-specific, high-speed chemiluminescence diagnostic to reveal the position of the spatially and temporally resolved flame front and the primary combustion zone. The emission recorded by a high-speed camera with an image intensifier was used to investigate the effects of equivalence ratio on the chemiluminescence from electronically excited hydroxyl (OH*) and methylidyne (CH*) radicals. High-speed movies of OH*, CH*, and total broadband signals were recorded. The line-of-sight integrated images were Abel-inverted to obtain the spatially resolved two-dimensional flame structure and the temporal evolution of radical zone thickness. Features such as direct laminar flame-speed determination, flame wrinkling at elevated pressures, and the reaction zones of flames propagating under well-characterized initial turbulent conditions were all well-captured by the high-speed chemiluminescence imaging. In addition to visualizing the flame fronts and subsequent determination of the flame speed, this technique provides the simultaneous information of reactive chemical species that is not available using commonly used schlieren-based imaging methods.

Adsorption of SARS-CoV-2 Spike Protein S1 at Oxide Surfaces Studied by High-Speed Atomic Force Microscopy.

Biointerfaces The cover image shows the adsorption of SARS-CoV-2 at metal-based fomite surfaces. The spike protein subunit S1 is the outermost point of the viral envelope and thus mediates the initial contact between the virus and the fomite surface. High-speed atomic force microscopy movies reveal that S1 protein adsorption proceeds faster at TiO2 surfaces than at Al2O3 surfaces. More details can be found in article number 2000024 by Adrian Keller and co-workers.

Flame image velocimetry analysis of reacting jet flow fields with a variation of injection pressure in a small-bore diesel engine

This study measures in-flame flow fields in a single-cylinder small-bore optical diesel engine using Flame Image Velocimetry (FIV) applied to high-speed soot luminosity movies. Three injection pressures were tested for a two-hole nozzle injector to cause jet-wall interaction and a significant jet-jet interaction within 45° inter-jet spacing. The high-pressure fuel jets were also under the strong influence of a swirl flow. For each test condition, soot luminosity signals were recorded at a high framing rate of 45 kHz with which the time-resolved, two-dimensional FIV post-processing was performed based on the image contrast variations associated with flame structure evolution and internal pattern change. A total of 100 combustion events for each injection pressure were recorded and processed to address the inherent cyclic variations. The ensemble-averaged flow fields were used for detailed flow structure discussion, and Reynolds decomposition using a spatial filtering method was applied to obtain high-frequency fluctuations that were found to be primarily turbulence. The detailed analysis of flow fields suggested that increased injection pressure leads to enhanced jet flow travelling along the bowl wall and higher flow vectors penetrating back towards the nozzle upon the impingement on the wall. Within the jet-jet interaction region, the flow vectors tend to follow the swirl direction, which increases with increasing injection pressure. The FIV also captured a turbulent ring vortex formed in the wall-jet head, which becomes larger and clearer at higher injection pressure. A vortex generated in the centre of combustion chamber was due to the swirl flow with its position being shifted at higher injection pressure. The bulk flow magnitude indicated significant cyclic variations, which increases with injection pressure. The turbulence intensity is also enhanced due to higher injection pressure, which primarily occurs in the wall-jet head region and the jet-jet interaction region.

A new paradigm of bubble-particle detachment interaction: How and where do the bubble and the particle detach?

The flotation of coarse in particular partially liberated particles has attracted both industry and research interests in recent years as it can bring several benefits to existing operations, including the decrease in grinding energy and media consumption, the increase in plant throughput, and environmental benefits. The bubble-particle detachment is critical to this flotation process. Here, we have investigated the physics underlying the bubble-particle detachment and discovered a new paradigm, i.e., the bubble and particle do not detach at the three-phase gas-liquid-solid contact (TPC) line between the bubble and the particle, which contradicts the conventional consideration in the available theories. Our high-speed video movies show that the bubble-particle detachment does take place at a capillary neck of the air-water interface near the solid surface. The detachment always leaves a tiny residual volume of gas on the solid surface. Our experiments also show that the detachment interaction does not simply follow the slip mode of the TPC motion but rather a combined slip-stick mode of the TPC line relaxation. We rationalize our observations by considering the contact angle hysteresis, which always exists on the real particle surfaces having morphological roughness and chemical heterogeneity. The new evidence challenges the existing theories about the bubble-particle detachment interaction in flotation and urges further investigations to overcome the inconsistent predictions.

Discretized Motion of Surface Walker under a Nonuniform AC Magnetic Field

The motion of peanut-shape magnetic microrods (PSMRs) with different magnetic moment (Ms) orientation φM under a non-uniform AC magnetic field have been investigated systematically. When gradually changing φM from 90o (perpendicular to the long axis of the PSMR) to 0o, the motion of the PSMR evolves from rolling to precession, then to tumbling. Systematic investigations on the translational velocity vp versus the magnitude of the applied magnetic field B and the angular velocity ωB show that the overall motion of the PSMRs can be divided into four different zones: Brownian motion zone, synchronized zone, asynchronized zone, and oscillation zone. The vp - ωB relationship can be rescaled by a critical frequency ωc, which is determined by Ms, B, and a hydrodynamic term. An intrinsic quality factor qm for the translational motion of a magnetically driven micro-/nano-motor is defined, and is found to range from 0.73 T-1 to 13.65 T-1 in the literature, while the Fe PSMRs in the current work give the highest qm ( = 25.48 T-1). High speed movies reveal that both the tumbling and precession motions of the PSMRs have a discretized nature. At the instances when the magnetic field changes direction, the PSMR performs an instantaneous rotation and the strong hydrodynamic wall effect would impose a driving force to move the PSMR translationally, and about more than 60% of the time the PSMR neither rotates nor moves translationally. Based on this discretized motion nature, an analytic expression for qm is found to be determined by the shape of the surface walker, the hydrodynamics near a wall, and the magnetic properties of the surface walker. This work can help us to better understand the motion of magnetic surface walkers and gain insight in designing better micro-/nano-motors.