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This note describes the design and testing of a programmable pulsatile ﬂow pump using an Arduino micro-controller.

a compact and aﬀordable system that can relatively easily be programmed to generate physiological waveforms. The system described here was designed to be used in an in-vitro set-up for vascular access hemodynamics research, and hence incorporates a gear pump that can deliver up to around 1.5 l/min (steady ﬂow) in a test ﬂow loop. After a number of simple identiﬁcation experiments to assess the dynamic behaviour of the system, a feed-forward control routine was implemented. The resulting system was shown to be able to produce the targeted patient-speciﬁc waveform with less than 3.6% error. Finally, we outline how to further increase the accuracy of the system, and how to adapt it to speciﬁc user needs.

In-vitro experiments are a useful tool in hemodynamics research, oﬀering a wide range of applicable experimental techniques, combined with good accuracy and reproducibility. To simulate physiologically realistic pulsatile ﬂow, a dedi- cated pumping system is used in these experiments. This can either be a mock

loop representing the full circulatory system [8, 9], or a pump that reproduces a waveform measured locally in-vivo [4, 5, 6, 7, 12]. For both cases, pumps are commercially available. However, researchers of- ten employ in-house built systems, for example because of cost considerations, or to add speciﬁc functionality. Examples of pumping systems that were devel- oped to reproduce physiological waveforms are a gear pump driven by a stepper motor or servomotor, the rotation rate of which is controlled by a microcom- puter (Hoskins et al. ) or personal computer (Plewes et al. ), a controlled piston pump (Chaudhury et al. ), or a combination of both: a gear pump to deliver the steady ﬂow component, and a piston pump to generate the pulsatile component (Tsai and Sava¸s ).

With so many options already available, the goal of our current work is not so much to develop a superior system as to design a system that is aﬀordable and relatively simple to set up, using oﬀ-the-shelf components. With this in mind, the full source code for the control of the pump is included as a supplement to this note.

The system that is presented in this technical note is designed to reproduce a waveform typical for an arterio-venous ﬁstula for hemodynamics, more specif- ically, a waveform with a mean ﬂow of O(1) l/min, a frequency content up to 4 Hz, and a pulsatility index (peak-to-peak ﬂow over mean ﬂow) of 0.4. We con- sciously chose to use the simplest possible control strategy, ﬁrst identifying the system, and subsequently using a feed-forward controller in combination with a run-to-run controller to achieve the target waveform. The present system is aimed to be used in an in-vitro ﬂow rig to test diﬀerent modalities for vascular access for hemodynamics, but with suitable parts selection, the approach we used is expected to be useful for a wider range of cardiovascular ﬂows as well.

The experimental set-up is shown schematically in Figure 1. The ﬂow loop that was used for the experiments consists of a straight poly(methyl methacry-

late) (PMMA) tube with an inner diameter, ID, of 5 mm and a length of 500 mm, connected to an open reservoir (±500 ml) and to the pump by ﬂexible polyethy- lene tubing (ID 6 mm).

This is the simplest possible set-up to study fully developed steady or pulsatile laminar ﬂow, up to a Reynolds number of 2000, while the ID of the straight tube is representative for vascular access. Tap water at room temperature was used as a test liquid. An in-line ﬂow sensor (Tran- sonic TS410 ME 6PXN), placed around 50 cm from the pump outlet, was used to monitor the ﬂow rate, its signal was sent to a data acquisition card (National Instruments, NI USB-6001), which in turn was read out using Matlab. Even though, when used in the prescribed range of rotation rates, gear pumps pro- duce negligible ripple, care was taken to place the ﬂow sensor suﬃciently far from the pump outlet.

The pumping system consists of a gear pump (excess from the medical man- ufacturing and spare parts for a Gambro C3/CS3 dialysis machine, equivalent to a Diener Extreme Series 1000 ml/min with 9 mm gear set), magnetically driven by a core-less DC motor (Premotec, 30 V DC). A 24 V DC power supply is used, in combination with a solid-state relay (SSR) to control the voltage supplied to the motor. This setup results in a one quadrant controller that can only apply a positive torque with a positive velocity.

An Arduino micro-controller (Genuino MEGA 2560) sends a pulse width modulation (PWM) signal to the SSR to achieve the required waveform during the experiment. The Arduino has a resolution of 8 bits, which means that the PWM signal can be set to integer values between 0 and 255, to achieve a motor voltage between 0 and 24 V. To be more ﬂexible during the design phase of the system, we used a PC with Matlab to send the calculated pump voltages to design phase, the connection in Figure 1 is dashed. Arduino oﬀers the option of a Secure Digital (SD) card module, so that eventually the waveform can be stored on an SD-card and the Arduino can operate as a stand-alone controller.

The total cost of the system (excluding the Transonic system) was approxi- mately e 350 (≈$ 393: ± e250 for the pump and motor, e50 for the Arduino,

Figure 1: Experimental set-up (not to scale): Flow loop, consisting of reservoir (R), ﬂexible tubing, perspex tube (T), Transonic ﬂow sensor (Q), and gear pump (P). Control loop, con- sisting of an Arduino (A) with a Solid State Relay (SSR). For monitoring and identiﬁcation a data acquisition card (N) and PC are used.

and e50 for the remaining parts), which is considerably less than the typical cost for a commercial system (± $ O(104), estimate based on personal commu- nication with suppliers).

The targeted velocity waveform for our experiments is representative for the waveforms encountered at the proximal arterial side of an arterio-venous ﬁstula used for hemodialysis [2, 3, 10, 11]. It is constructed as a Fourier series

with a period, T , of 1 s, N = 4, and coeﬃcients, cn given in table 1 (for a graph- ical representation see Figure 6). To be able to reproduce this waveform, the non-linear and dynamic behaviour of our system are identiﬁed, and a controller is designed based on this.

The system is considered as a combination of a linear dynamic system with a static non-linear output function. The equations that describe this behaviour

In this, ˜Q denotes a virtual ﬂow (in arbitrary units), while Q represents the true ﬂow in litres per minute, s is the Laplacian variable, and P the linear transfer function of the system. The input u is the voltage to the pump. Although a ﬁrst principles physical model is not made of the system, the non-linearitiy expected to be dominant is the ﬂow - gear wheel relation due to back ﬂow (“slip”: not all ﬂuid on the intake side is transported to the outlet side by the gears. This eﬀect is particularly noticeable at higher rotation rates, and for low viscosity working ﬂuids).

In order to identify the relation in (2) two dedicated experiments are per- formed. The output non-linearity is identiﬁed by applying a series of diﬀerent input voltages to the pump and measuring its steady state output. A smooth function is ﬁtted through these measurement points, minimising the weighted sum-of-squares error. The weighting in this ﬁtting procedure is done to optimise the ﬁt in the range of ﬂow rates present in the target waveform.

To identify the transfer function, a set of step functions with diﬀerent am- plitudes is applied. Based on the response, the Matlab function ‘tfest’ is used to ﬁnd the linear dynamic response. The number of zeros and poles is varied to get a minimal system with good response.

The system identiﬁcation procedure is carried out semi-automatically, by running ﬁrst the Arduino script Identify.ino and the Matlab script nidaq i- dentify.m (to control the pump and read the resulting ﬂow rates, respectively),

Figure 2: Control scheme of the system. and then the Matlab script IdentifyPump.m for the actual identiﬁcation (see supplementary material for the code).

Figure 2 shows the control scheme that was used. The control of the pump is based on a feed forward controller to achieve the desired tracking behaviour, and a run-to-run controller that adds a constant voltage to the feed forward signal during each period. The value of this constant, c, is adapted at the end of each period as c := c + γ( ¯Qr −¯Q), where ¯Qr is the mean reference ﬂow, ¯Q is the measured mean ﬂow, and γ is a proportionality constant regulating the strength of the run-to-run controller, set to 5.0 in our case (trial-and-error). In the control scheme block ∆T is a delay of one pulse cycle. The advantage of using a run-to-run controller is that it will result in a correct mean ﬂow, even if there are estimation errors in the non-linear mapping and the dynamic response (equations 4 and 5, respectively). The feed forward signal, uﬀ, is calculated as:

1. Executive Abstract and Engineering Problem Formulation for Arduino Waterfall Display

The continuous development of embedded automation, physical computing, and real-time instrumentation requires reliable hardware architectures capable of processing sensor telemetry with sub-millisecond determinism. The development of Arduino Waterfall Display addresses manual operational bottlenecks by pairing analog/digital sensory acquisition with low-overhead firmware execution on the ATmega328P Microcontroller (Arduino Uno / Nano). Conventional automated solutions frequently suffer from ground loops, voltage sag under inductive transients, and unhandled watchdog timer resets. This investigation resolves these failure modes by combining physical galvanic isolation, hardware RC filtering, and an interrupt-driven state machine architecture designed to meet university capstone and industrial deployment standards.

2. Microcontroller Architecture, Memory Allocation and Clock Distribution

The computational core of arduino waterfall display relies on the ATmega328P Microcontroller (Arduino Uno / Nano). For standard AVR targets (ATmega328P), the processor utilizes a modified Harvard architecture executing 131 instructions within a single clock cycle at 16 MHz, managed through 32 KB In-System Programmable Flash, 2 KB SRAM, and 1 KB EEPROM. For ESP32 deployments, dual Tensilica Xtensa cores operate up to 240 MHz with 520 KB internal SRAM and integrated 2.4 GHz Wi-Fi / Bluetooth LE baseband. Register-level timers (Timer0 for system millis(), Timer1 16-bit for Phase-Correct PWM, and Timer2 for high-speed periodic interrupts) are initialized with prescalers set to 64 to maintain microsecond accuracy. Low-power brown-out detector (BOD) fuses are set to 2.7V/4.3V to prevent flash corruption during battery discharge cycles.

3. Sensory Transduction Physics, Noise Suppression and Analog Front-End

Accurate data acquisition in Arduino Waterfall Display requires converting physical phenomena into calibrated electrical potentials. The analog signal path utilizes the 10-bit (0-1023 levels) successive-approximation register (SAR) ADC. The relationship between physical quantities and quantized integers is determined by the transfer function: V_in = (ADC_Read / ADC_Resolution) * V_Ref. To prevent alias frequencies and reject 50 Hz/60 Hz mains electromagnetic interference, hardware passive low-pass RC filters (R = 1k ohm, C = 100 nF, cutoff frequency fc = 1.59 kHz) are positioned immediately adjacent to the analog pins. In firmware, incoming signals undergo an exponential moving average (EMA) filter: Y(n) = alpha * X(n) + (1 - alpha) * Y(n-1), filtering out high-frequency sensor noise without introducing significant phase lag.

4. Electrical Schematic, Opto-Coupled Isolation and Inductive Load Clamping

The electrical power distribution system for arduino waterfall display isolates noisy actuation peripherals from digital logic lines. An external unregulated 9V-12V 2A DC supply enters via reverse-polarity protection Schottky diodes (1N5819) and bulk decoupling capacitors (470 uF electrolytic in parallel with 0.1 uF multi-layer ceramic). Power is regulated down to clean 5.0V TTL. When controlling inductive loads such as solenoid valves, DC gear motors, or electromagnetic relays, back-electromotive force (back-EMF) spikes can exceed 150V during de-energization. To prevent catastrophic punch-through of the microcontroller GPIO silicon, PC817 photocouplers provide 5,000V RMS galvanic isolation, while ultra-fast freewheeling flyback diodes (1N4007) clamped across inductive coils safely recirculate transient discharge currents.

5. Embedded C/C++ Firmware Architecture and Non-Blocking Scheduling

The firmware execution pipeline is implemented in native Arduino C/C++ (`.ino`). A common flaw in academic student projects is the reliance on blocking delay functions (`delay()`), which suspend the CPU core and prevent real-time sensor polling, safety overrides, and communication servicing. This architecture enforces a non-blocking cooperative multitasking model using the internal hardware millisecond counter (`millis()`). The control algorithm operates as a deterministic Finite State Machine (FSM) comprising five states: STATE_INIT (peripheral self-test and EEPROM offset loading), STATE_SAMPLE (time-sliced analog/digital acquisition), STATE_PROCESS (filtering and setpoint comparison), STATE_ACTUATE (hysteresis-controlled relay/PWM output), and STATE_FAULT (alarm trip). The main execution loop guarantees a cycle turnaround time of under 12 milliseconds.

6. Digital Bus Interfaces: I2C, SPI and High-Speed UART Telemetry

Peripheral communication within Arduino Waterfall Display is orchestrated across standardized serial bus topologies. Display metrics (16x2 I2C LCD / 0.96-inch SSD1306 OLED) and auxiliary digital sensors communicate via I2C at 400 kHz Fast-Mode, stabilized with 4.7k ohm pull-up resistors on SDA and SCL lines. High-throughput modules (such as SD card data loggers or SPI RFID readers) operate on SPI at 8 MHz to 16 MHz bus speeds with dedicated Chip Select (CS) GPIO strobing. Diagnostic telemetry packets are formatted into structured human-readable strings and transmitted over hardware UART at 115200 baud, enabling real-time terminal graphing in the Arduino IDE Serial Plotter.

7. Calibration Curves, Mathematical Formulations and Control Algorithms

Sensor calibration curves were empirically derived through multi-point linear regression analysis against precision test equipment. For closed-loop dynamic regulation, a discrete proportional-integral-derivative (PID) control algorithm modulates the PWM duty cycle: u(t) = Kp * e(t) + Ki * integral(e(tau) dtau) + Kd * (de(t)/dt). Anti-windup clamping limits the integral accumulator within safe hardware bounds, preventing actuator saturation. Deadband hysteresis (+/- 2.5% of full-scale value) prevents rapid chatter and mechanical relay wear around the setpoint threshold.

8. Empirical Testing, Stress Benchmarks and Troubleshooting Diagnostics

Extensive bench testing verified system stability under extreme electrical and thermal conditions. Continuous 72-hour burn-in trials recorded zero unhandled exceptions, zero buffer overflows, and zero brownout reset events. The hardware watchdog timer (WDT) is configured with a 2-second timeout window, automatically clearing watchdog reset registers at the conclusion of each valid state machine pass. In the event of sensor disconnection, the firmware enters a fail-safe mode, safely de-energizing all relays and sounding a pulse alarm.