WO2025262176A1

WO2025262176A1 - Microflow sensor

Info

Publication number: WO2025262176A1
Application number: PCT/EP2025/067186
Authority: WO
Inventors: Amar Mahendra KAMAT; Felix Christopher WOOD; Natanael Magno GOMES; Thom VAN DER HONING; Ajay Giri Prakash KOTTAPALLI
Original assignee: Sencilia BV; Rijksuniversiteit Groningen
Current assignee: Sencilia BV; Rijksuniversiteit Groningen
Priority date: 2024-06-18
Filing date: 2025-06-18
Publication date: 2025-12-26
Anticipated expiration: 2026-12-18
Also published as: NL2037975B1

Abstract

Systems and methods for sensing flow through a tube are disclosed The flow sensor comprises one or more heaters formed by one or more first electrically conductive thin-film traces and one or more temperature sensors formed by one or more second electrically conductive thin-film traces. The one or more heaters and the one or more temperature sensors may be provided on a flexible polymer substrate, and the flow sensor may be configured to be connectable to an outer surface of the tube such that the flexible polymer substrate conforms to the outer surface of the tube. At least one of the heaters and/or at least one of the temperature sensos may be arranged to cover a substantial part of a circumference of the medical infusion tube, e.g., at least 10 %, at least 25 %, at least 50 %, or at least 90 % of the circumference of the tube.

Description

Microflow sensor

Technical field

This disclosure relates to a flow sensor for measuring microflows, such as in an intravenous infusion system, and in particular, though not exclusively, to methods and systems for measuring microflow, and to a computer program product enabling a computer system to perform such methods.

Background

Intravenous (IV) infusions are the primary mode of drug delivery in neonatal patients. Unfortunately, up to 60% of IV infusions are known to show errors in their flow rates, which could be due to a variety of factors such as in-line occlusions, vertical displacement of infusion pump or patient, siphonage or ‘free flow’, multi infusion flow dynamics, user errors, and so on. Due to the low flow rates used in the neonatal intensive care unit (NICU), the current infusion systems are either too late (by up to an hour) or simply incapable of sounding an alarm to warn the clinician of the flow rate inaccuracy. As an example, it can take the current infusions pumps more than one hour to alarm the nurse of an in-line occlusion, when the infusion flow rate is below 1 ml/hr. Such a long time-to-alarm is dangerous in the administration of time-critical drugs such as vasopressors and inotropes that typically have a short half-life of around 2-3 minutes. It is thus important to monitor the actual flow rate of the IV fluid (drug, medication, and nutrients) into the neonatal patient, since this flow often deviates from the desired set flow rate on the pump, and the resulting flow discrepancy can lead to over/under dosage that is detected too late, resulting in serious clinical consequences for the neonatal patient.

Shimohira, C. et al., ‘Development of micromachined flow sensor for drip infusion system,’ Microsystem Technologies 26 (2020) pages 3677-3683, describes a MEMS flow sensor for application in a drip infusion system. The sensor is in direct contact (via a passivating thin film coating of Parylene-C) with the infusion liquid. However, the polymer substrate is designed as a membrane, with a cavity for insulation purposes on the opposite side (i.e., the side not in contact with the infusion liquid). This design leads to leakage risks due to the polymeric membrane (especially at higher pressures), contamination risks, sterilisation risks (in particular for reusable sensors), et cetera. Additionally, the sensing threshold is relatively high (flow rates are presented on a scale of grams per minute, rather than grams per hour), making the sensor unsuitable for microflow detection and monitoring in the range of single-digit grams per hour or even less. The accuracy of the sensor can be improved by increasing the driving temperature of the sensor, but such high temperatures are clinically not acceptable as they may negatively affect the drugs being administered. Moreover, the sensor requires a fixed and known temperature of the infusion liquid, which is not typically feasible in a clinical setting, where the temperature may vary, e.g., during the day.

Lee, D. et al., ‘Sensitive and reliable thermal micro-flow sensor for a drug infusion system,’ Sens Actuators A Phys 309 (2020), describes a thermal micro-flow sensor for a drug infusion system that is attached to the outside of an infusion tube. The sensor has a low accuracy for flow rates above about 3 ml/h. Moreover, contact between the tube and the sensor is in generally uneven and inconsistent. Increasing the pressure the flow sensor exerts on the tube in order to ensure decent contact, leads to deformation of the tube, which in turn affects the flow resistance. Additionally, the lay-out of the heater and thermistors makes the flow senor sensitive to positioning.

There is therefore a need in the art for a device and method that can detect a microflow rate in an intravenous infusion tube in a non-contact manner with sufficient accuracy over a large range of flow rates.

It is an aim of embodiments in this disclosure to provide a system and method for detecting flow, particularly microflow, that avoids, or at least reduces the drawbacks of the prior art.

In a first aspect, this disclosure relates to a flow sensor for sensing flow through a tube, in particular a medical infusion tube. The flow sensor comprises one or more heaters formed by one or more first electrically conductive thin-film traces and one or more temperature sensors formed by one or more second electrically conductive thin-film traces. The tube can be, e.g., a polymer tube for use in medical applications. The tube may have an essentially circular cross section.

A thin-film pattern may be defined as a two-dimensional pattern (typically formed by one or more metals) with a thickness of less than about 20 pm or less than about 1 pm, e.g., about 0.1-0.5 pm. The resistor may be made from various materials and in various forms and dimensions. The thin-film pattern may be made from a metal, including but not limited to gold (Au), nickel (Ni), nickel-chromium (NiCr), aluminium (Al), or platinum (Pt). A metal or alloy may be used that has a high thermal coefficient of resistance (TCR), i.e. , that has a relatively high change in resistance more for a given change in temperature, a TCR greater than 0.0031 °C. Such thin-film patterns are inherently flexible, and can therefore conform also to surfaces with a relatively small bending radius (e.g., about 1 mm).

In an embodiment, the one or more heaters and the one or more temperature sensors are provided on a flexible substrate, e.g., a flexible polymer substrate. The flow sensor may be configured to be connectable to an outer surface of the tube such that the flexible substrate conforms to the outer surface of the tube.

At least one of the one or more heaters may be arranged to cover a substantial part of a circumference of the medical infusion tube, e.g., at least 10 %, at least 25 %, at least 35 %, at least 50 %, at least 65 %, at least 75 %, or at least 90 % of the circumference of the tube. Similarly, at least one of the one or more temperature sensors is arranged to cover a substantial part of a circumference of the medical infusion tube, e.g., at least 10 %, at least 25 %, at least 35 %, or at least 50 %, at least 65 %, at least 75 %, or at least 90 % of the circumference of the tube. Using a (flexible) thin-film pattern on a flexible substrate allows the heater(s) and/or temperature sensor(s) to conform to a curved surface, such as the outer surface of the tube, maintaining good thermal contact without deforming the tube. Such flexibility is especially relevant for small tubes, such as neo-natal infusion tubes and insulin delivery tubes. By using a heater that covers a substantial part of the circumference of the tube, the provided heat can be distributed over a larger area, leading to a comparable signal strength with a lower maximum temperature. Lower maximum temperatures lead to less degradation of heat-sensitive tubes, and have less risk of adversely affecting the fluid; this is especially relevant in medical applications. Temperature sensors that cover s substantial part of the circumference of the tube lead to a higher sensitivity, especially when the heat is distributed over a relatively large region (e.g., by using a large heater).

Alternatively, the flexible substrate with the one or more heaters and one or more temperature sensors may be embedded inside the tube wall, similarly requiring the substrate to conform with the tube shape. One or more of the thin-film traces may be provided as a serpentine, meandering or ring-like metallic pattern on a single side of a substrate. Polymer substrates, such as a liquid crystal polymer (LCP) or a polyimide (e.g., Kapton), are flexible (allowing conformability to an essentially circular tube), relatively easy to process, have a low thermal conductivity (preventing direct crosstalk between heater and temperature sensor), and have a low electric conductivity.

By providing the heaters and sensors on a flexible substrate that is configurable to conform to the outer surface of the tube, contact between the heaters and temperature sensors on the one hand and the tube on the other hand can be improved (both by increasing the contact area and by improving the contact on the contact area) compared to a flow sensor provided on a rigid substrate, e.g., a resin (PCB) or a semiconductor substrate. Hence, measurement accuracy can be improved. Moreover, this can be achieved without deforming the tube, so that changes in flow due to the measurement can be minimised.

The temperature sensor may be any type of suitable thin-film temperature sensor, such as a thermistor, thermocouple, thermopile, et cetera.

In an embodiment, the flexible polymer substrate has a thermal conductivity of less than 5 W/(m K), e.g., less than 1 W/(m K) or less than 0.5 W/(m K). Having a low thermal conductivity, the substrate effectively acts as a thermal insulator that prevents or at least limits direct thermal conductivity from the one or more heaters to the one or more temperature sensors. This improves the signal to noise ratio. This also allows for a more efficient heater, allowing a higher (or equal) driving temperature at the same (or lower) power dissipation. This is especially relevant in applications where fluid temperature is critical, such as in many medical applications. In general, a higher difference between heater temperature and fluid temperature increases the sensitivity of the flow sensor.

In an embodiment, the flexible polymer substrate has a thickness of less than 500 pm, e.g., between 5-200 pm, between 10-100 pm, or between 25-50 pm. In general, the flow sensor can be mounted in two ways: with the electrically conductive thin-film traces directly in contact with the tube wall (and the substrate ‘on top’, i.e. , the electrically conductive thin-film traces are in between the tube wall and the substrate), or with the substrate making contact with the wall. In the latter case, the electrically conductive thin-film traces are protected by the substrate, which may reduce damage to the electrically conductive thin-film traces by mounting (and potentially removing) the flow sensor; this can increase the reliability and the reusability of the flow sensor. In such a configuration, a thinner substrate leads to a lower thermal resistance between the traces and the tube wall, and hence to a higher accuracy of the flow sensor.

In an embodiment, the flexible polymer substrate has a bending radius of less than or equal to 2 mm and/or a Young’s modulus of less than 3 GPa, 4 GPa, or 5 GPa. This ensures that good contact can be obtained, even on small tubes; for example, typical IV tubes have an outer diameter of about 4-4.5 mm (with an inner diameter of about 3 mm), and infusion tubes for neonatal care may be even smaller, typically about a 2 mm outer diameter (with a 1 mm inner diameter).

In an embodiment, the flexible polymer substrate is a wall of the tube. In such an embodiment, the electrically conductive thin-film traces may be provided (e.g., printed) directly on the tube wall, or they may be provided inside the tube wall during or after production of the tube. Providing the electrically conductive thin-film traces directly on the tube wall ensures optimal contact between the traces and the tube wall. In such an embodiment, each of the electrically conductive thin-film traces may be electrically connected to a pair of connectors on either end of the trace, to allow a drive and read-out circuit to be connected. Typically, a trace and the connecters are formed as a single thin-film pattern.

In an embodiment, the flow sensor is configured to use the one or more heaters and the one or more temperature sensors to perform a first flow measurement based on a first flow measurement technique and a second flow measurement based on a second flow measurement technique, different from the first flow measurement technique. The flow sensor may be further configured to determine an output signal based on the first and/or second flow measurements.

For example, the first flow measurement technique may be more accurate than the second flow measurement technique and/or the second flow measurement technique may have a faster response time than the first flow measurement technique. This way, a flow sensor that is both fast and accurate may be obtained. In many applications where an essentially stationary flow is expected, large and rapid changes in flow require less accuracy than a long-term measurement. Typically, rapid changes are used to detect large sudden errors (or to detect or confirm a change in settings), and the long-term measurements are used to determine a cumulative dose or to detect small but persistent errors.

Additionally or alternatively, the first flow measurement technique may be more suitable for a first flow regime, e.g., flow with a Peclet number lower than 1 , while the second flow measurement technique may be more suitable for a second flow regime (different from the first flow regime), e.g., flow with a Peclet number higher than 1. As different measurement techniques use different physical principles, they may have different accuracies in different flow regimes (e.g., diffusion-dominated flow or advection-dominated flow). The Peclet number is a dimensionless number defined as the ratio of the characteristic time constant associated with conduction (i.e. , due to molecular diffusion) to the characteristic time constant associated with advection (i.e., due to bulk movement of the liquid), and is therefore a useful measure to distinguish between flow regimes for flow measurement techniques that are based on heat.

The output signal can be representative of a determined flow rate, or, if a reference flow rate has been set, of a difference between the determined flow rate and the reference flow rate being smaller or larger than a threshold value. Of course, a combination is also possible.

In an embodiment, the first flow measurement technique is a time-varying flow measurement technique and/or the second flow measurement technique is a steady-state flow measurement technique.

Different heat-based flow measurement techniques are known in the art, such as calorimetry, hot-film (or hot-wire) anemometry, and time-of-flight. In brief, calorimetry generally uses a heater and two sensors arranged symmetrically around the heater (along the direction of the flow), and the flow is computed based on a temperature difference between the two sensors. Anemometry generally uses a temperature sensor upstream of a heater to measure the fluid temperature, and the flow is computed based on a measured resistance of the heater. Time-of-flight measurements generally use a heater and a sensor downstream of the heater, and compute the flow based on the time of flight of a heat signal to travel from the heater to the sensor.

Generally speaking, calorimetric methods are relatively accurate in low-flow regimes (e.g., with a Peclet number < 1), while time-of-flight methods are relatively accurate in high- flow regimes (e.g., with a Peclet number > 1). Anemometric methods tend to be less accurate (due to their relative high sensitivity to environmental effects) than calorimetric and time-of-flight measurements, but are relatively fast.

In an embodiment, the flow sensor comprises a first heater upstream from one or more first temperature sensors and a second heater downstream from the one or more first temperature sensors. In such an embodiment, the first heater and at least one of the one or more first temperature sensors may be configured for use in the first flow measurement technique and at least one of the one or more first temperature sensors and the second heater may be configured for use in the second flow measurement technique.

For example, the flow sensor can have a heater-sensor-heater configuration. In such a configuration, the first heater and the sensor may be used for a time-of-flight measurement, while the sensor and the second heater may be used for an anemometric measurement.

In an embodiment, the flow sensor further comprises a second temperature sensor downstream of the second heater. In such an embodiment, the first heater and a first temperature sensor of the one or more first temperature sensors may be configured for use in the first flow measurement technique and a second temperature sensor of the one or more first temperature sensors, the second heater, and the second temperature sensor may be configured for use in the second flow measurement technique.

For example, the flow sensor can have a heater-sensor configuration and a (nonoverlapping) sensor-heater-sensor configuration. In such a configuration, the heater-sensor pair can be used for a time-of-flight measurement and the sensor-heater-sensor triplet can be used for a calorimetric measurement. Additionally, one of the heaters, e.g., the second heater, can be used for a hot-film anemometric measurement.

In an embodiment, when in use, a part (e.g., a centre) of at least one of the one or more temperature sensors is separated from a centre of at least one of the one or more heaters by at least 90°, e.g., at least 120°, at least 150°, at least 160° or about 180°, along a circumference of the tube. In some embodiments, the part of the at least one temperature sensor is separated from the centre of the at least one heater by approximately 90°, approximately 120°, approximately 150°, approximately 160° or approximately 180°. In this context, approximately may refer to, e.g., ±5°, ±2°, or ±1°. By positioning the temperature sensor at some (circumferential) distance from the heater, heat transfer from the heater to the temperature sensor through the tube wall is reduced relative to heat transfer through the fluid flowing through the tube. Such a configuration may also be used to determine the orientation of the fluid sensor, which may affect the sensitivity and/or calibration parameters of the flow sensor.

In an embodiment, the one or more heaters are arranged to cover, when in use, at least 50% of a circumference of the tube, preferably at least 75% of the circumference of the tube, more preferably at least 90% of the circumference of the tube, most preferably at least 95% of the circumference of the tube. This provides a more even heating, and hence clearer signal, and causes the flow sensor to be less sensitive to the positioning relative to the gravitational field.

In an embodiment, the one or more temperature sensors comprise a plurality of temperature sensors circumferentially arranged around the tube. In an embodiment, at least one of the one or more temperature sensors is arranged to cover at least 50% of a circumference of the tube, e.g., at least 75%, at least 90%, or even at least 95% of the circumference of the tube.

In general, a larger surface area of the heaters and/or sensors improves the signal to noise ratio by improving heat transfer through the tube wall to and from the fluid. A smaller longitudinal extent (i.e., in the direction of the fluid flow) results in a sharper signal, especially for time-of-flight based measurements, and hence to a higher signal to noise ratio. If traces of a single material and single width are used (e.g., to simplify the production process), heaters are typically smaller than temperature sensors, as they tend to have a lower electrical resistance; hence, a circular array of heaters may be combined with a single (mostly) circular temperature sensor, for example. In other embodiments, a single relatively large heater may be used to achieve maximally homogeneous heating. In some embodiments, a circumferential array of two or more heaters may be used, in order to obtain information on the heat distribution. Systems with several heaters and/or temperature sensors may be more resilient to failure of one of the heating or temperature sensing elements.

In an embodiment, a distance between each of the one or more heaters and each of the one or more temperature sensors is at least 0.1 mm, e.g., at least 0.2 mm, at least 0.5 mm, at least 0.75 mm or at least 1.0 mm, along a longitudinal direction of the tube. The distance between the heaters and the sensors must be sufficiently large that the effect of thermal flow through the tube wall (and, where applicable, the substrate) does not negatively affect the measurements. Thus, the distance between the heaters and the sensors may depend of a thickness of the tube wall. For example, for certain sensor configurations (for example, configurations wherein the heater(s) and/or sensor(s) substantially encircle the tube), the distance may be at least twice the thickness of the tube wall.

As used herein, the distance is defined either as the edge-to-edge distance (i.e. , the smallest distance between points of two objects) or as a heart-to-heart distance.. It is noted that a typical width of the heaters and temperature sensors can be of the same order of magnitude, e.g., between about 0.5-1 mm.

In an embodiment, the flow sensor comprises a first sensor group comprising a first heater and a first temperature sensor and a second sensor group comprising a second heater and a second sensor.

The first sensor group may be configured for measuring flow velocities with a Peclet number smaller than 1. In such an embodiment, a first distance between the first heater and the first temperature sensor may be in the range 1-2 mm, e.g., about 1.5 mm.

The second sensor group may configured for measuring flow velocities with a Peclet number larger than 1. In such an embodiment, a second distance between the second heater and the second temperature sensor may be in a range 2-15 mm, e.g., in a range 4-10 mm, in a range 6-8 mm, or about 7 mm.

The (expected) Peclet number depends on the (expected) flow velocity. Similarly, optimal and suitable design parameters such as resistances of the electrically conductive thin-film traces, used voltages and currents, et cetera, may depend on the (expected) range of flow velocities. In an embodiment, the flow sensor is configured for measuring a flow velocity is less than 40 mm/s, e.g., less than 10 mm/s, less than 5 mm/s, less than 2 mm/s, or even less than 1.5 mm/s.

In an embodiment, the flow sensor is configured to measure a flow rates of less than 50 mL/h, preferably less than 30 mL/h, more preferably less than 10 mL/h, even more preferably less than 5 mL/h, most preferably less than 1 mL/h.

In an embodiment, the one or more heaters have a resistance of at least 20 Q, e.g., in a range of 30-300 Q, 40-200 Q or 50-100 Q.

In an embodiment, the one or more temperature sensors have a resistance of at least 100 Q, e.g., in a range 100-1000 Q.

In an embodiment, a resistance of (each of) the one or more temperature sensors is at least a factor 5, e.g., at least a factor 10 or at least a factor 50, higher than a resistance of the one or more heaters. This allows a similar bias voltage for the heater and the temperature sensor, simplifying the electronics. In general, the heater(s) should dissipate a sufficient amount of heat to obtain a clear signal, without however heating the fluid too much. The resistance of the temperature sensors should be sufficient to allow a large dynamic range. In an embodiment, a power dissipation of (each of) the one or more temperature sensors is substantially higher than a power dissipation of (each of) the one or more heaters, e.g., at least a factor 10, at least a factor 20, at least a factor 40, at least a factor 100 , at least a factor 1000, or even at least a factor 10000 higher than the power dissipation of (each of) the one or more heaters.

The flow sensor may further comprise, e.g., electronic circuitry to drive the one or more heaters and the one or more temperature sensors, a power source or a connector for connecting to a power source, and a communication interface. The flow sensor may also comprise a data processing unit configured to determine an output signal based on a flow parameter, e.g., a flow volume or flow velocity, based on the measurements. The measurements typically comprise one or more voltages over and/or one or more currents through the one or more heaters and/or the one or more temperature sensors.

In an embodiment, the tube is a tube of an infusion system, e.g., an intravenous infusion system, a subcutaneous infusion system, or an epidural infusion system.

In an embodiment, the tube is a respiratory tube, e.g., a neonatal respiratory tube.

In an embodiment, the flow sensor is configured to regulate the flow through the tube, e.g., in response to a determined flow value. For example, the flow sensor may be configured to send a control signal to the infusion system through the communication interface, the control signal configuring the infusion system to regulate the flow. As a further example, the flow sensor may comprise a flow valve or be physically and/or communicatively connected to a flow valve, and the flow sensor may be configured to control, e.g., actuate, the flow valve.

In an embodiment, the one or more heaters and the one or more temperature sensors are provided inside a wall of the tube. In an embodiment, the one or more heaters and the one or more temperature sensors are provided on an outer surface of the tube.

In a further aspect, this disclosure relates to a housing comprising a flow sensor comprising a flexible polymer substrate as described above, wherein the housing is configured to connect the flow sensor to the tube such that the substrate conforms to an outer surface of the tube.

Such a housing ensures proper connection of the flow sensor to the tube containing the fluid whose flow is to be measured. The housing may be removably connectable to the tube, so that the housing comprising the flow sensor may be reused.

In a further aspect, this disclosure relates to housing comprising an electric circuit and, optionally, a power source, the housing being configured to be connectable to a tube, the tube comprising one or more heater elements and one or more sensor elements. The one or more heater elements and one or more sensor elements may be provided inside a wall of the tube or on an outer surface of the tube. The electric circuit is arranged, when connected to the tube, to drive the one or more heater elements and the one or more sensor elements to obtain a flow sensor as described above.

In an aspect, this disclosure relates to a tube, e.g., an IV-tube of an (intravenous) infusion system or a respiratory tube, comprising one or more heater elements and one or more sensor elements, the tube being configured to be connectable, preferably removably connectable, to a housing as described above.

When connected, the tube and the housing form a flow sensor as described above. By including the heaters and sensors in (or on) the tube, good contact is ensured. A removable housing, which typically comprises the more expensive parts of the flow sensor, may be reused with multiple tubes.

In a further aspect, this disclosure relates to a method for determining a flow rate through a tube. The method comprises: receiving a first signal representative of a calorimetric flow measurement; receiving a second signal representative of a time-of-f light flow measurement; determining an approximate flow rate; and determining the flow rate based on the first signal if the approximate flow rate is lower than a predetermined threshold value and determining the flow rate based on the second signal if the approximate flow rate is higher than a predetermined threshold value.

In an embodiment, the method further comprises receiving a third signal representative of an anemometric flow measurement. Determining the approximate flow rate may then be based on the third signal.

The embodiments will be further illustrated with reference to the attached drawings, which schematically will show embodiments according to the invention. It will be understood that the invention is not in any way restricted to these specific embodiments. Identical reference signs refer to identical, or at least similar elements.

Brief description of the drawings

Fig. 1A and 1B schematically depict flow sensors according to embodiments;

Fig. 2A and 2B schematically depict flow sensors comprising a rigid substrate and Fig. 2C and 2D schematically depict flow sensors comprising a flexible substrate;

Fig. 3A-E schematically illustrate several thermal flow sensors;

Fig. 4A-D schematically depict flow sensors according to various embodiments;

Fig. 5 is a flow chart of a method according to an embodiment;

Fig. 6 is a flow chart of a method according to an embodiment;

Fig. 7A-C are graphs of measurements using flow sensors according to various embodiments and Fig. 7D schematically illustrates a configuration of the used flow sensor; and Fig. 8 is a graph of a relation between power dissipation and fluid temperature for a flow sensor according to an embodiment.

Detailed description

The embodiments in this disclosure generally relate to flow sensors for measuring flow through a tube. Such measurements are typically given as a mass flow (e.g., in grams per hour, g/h) or a volume flow (e.g., in millilitres per hour, mL/h). In practice, many measurement techniques determine a quantity that is related to the flow velocity (e.g., in millimetres per second, mm/s), and the flow velocity is subsequently converted to a mass flow or volume flow by multiplying with a cross section of the tube, or via a calibration procedure. Several measurement techniques are discussed in more detail below with reference to Fig. 3.

It is an aim of these embodiments to accurately and reliably measure the flow rate, specifically for low flow rates. For example, so-called “micro” infusions (with a flow rate in a range of 0.1 - 5 mL/h) are known to be the riskiest in NICU/PICU/ICUs due to problems with flow continuity. The measurement should ideally be made with low error (< 5% of full scale) and low uncertainty (e.g., about ± 0.1 mL/h).

The flow sensors described herein comprise one or more heaters formed by one or more first electrically conductive thin-film traces and one or more temperature sensors formed by one or more second electrically conductive thin-film traces. For simplicity, the electrically conductive thin-film traces may also be referred to herein as just traces. Unless otherwise specified, the term ‘sensor’ refers to a temperature sensor. Due to their thinness, such sensors are generally inherently flexible.

The tube can be a polymer tube for use in medical applications, e.g. an infusion tube for intravenous or subcutaneous infusion, or a respiration tube. The tube may be a round tube. i.e. , a tube with a circular cross section. The fluid can be a liquid or a gas.

Fig. 1A schematically depicts a flow sensor according to a first embodiment. The flow sensor 100 comprises a first electrically conductive thin-film trace 102 acting as a heater and a second electrically conductive thin-film trace 104 acting as a temperature sensor. In this example, only a single heater and a single temperature sensor are shown, but other embodiments may have multiple heaters and/or multiple temperature sensors.

In principle, there is no inherent (physical) difference between a heater and a temperature sensor, the difference is determined primarily by their use. In general, the power dissipated by a heater is at least 5-10 times as high as that dissipated by a temperature sensor, but in other embodiments these differences may be even larger, e.g., 20, 50, 100, 1000, or even 10000 times as high. For example, identical traces could be used for the heater and the temperature sensor, the distinction being obtained by applying different voltages.

However, it is often more practical to use similar voltages for heater and sensor. Therefore, a resistance of the one or more temperature sensors may at least a factor 5 to 10 or more, e.g. about a factor 50-100, higher than a resistance of the one or more heaters. A lower resistance leads to a higher current (at the same voltage), and hence to a higher power dissipation. For example, the one or more heaters may have a resistance of at least 20 Q, e.g., in the range 50-100 Q. The one or more temperature sensors may have a resistance of at least 100 Q, e.g., in the range 100-1000 Q. Differences in resistance may be achieved by e.g., using different materials, different trace widths, different trace thicknesses, or, most commonly, different trace lengths.

It will be discussed below with reference to Fig. 3 how a heater and a temperature sensor can be used as a flow sensor.

The traces 102,104 are provided on a substrate 106. The substrate 106 can be a flexible substrate, e.g., a flexible polymer substrate. The substrate is electrically and thermally insulating, to reduce crosstalk between the different traces. Several methods to provide electrically conductive thin-film traces on a flexible substrate are known in the art.

For example, the flexible polymer substrate can have a thermal conductivity of less than 5 W/(m K) e.g., less than 1 W/(m K) or less than 0.5 W/(m K). The substrate may have a thickness of less than 500 pm, e.g., between 10-200 pm or between 25-100 pm. The substrate may have a bending radius of less than or equal to 2 mm and/or a Young’s modulus of less than about 4 GPa.

As an example, the thin-film patterns may be sputter-deposited and patterned on the sheet through a lift-off process. For instance, an LCP polymer may be cut into the shape of a silicon wafer and may be attached to the silicon wafer using an intermediate photoresist layer. This allows a standard MEMS batch fabrication of devices on the LCP sheet. To conduct the lift-off process, a photoresist may be spun-coated on top of the LCP layer followed by standard resist curing, lithographic UV exposure using the mask containing the resistor patterns and resist developing process. An adhesion layer (e.g., chromium or titanium) is sputter deposited on the patterned resist layer to enhance the adhesion of a ‘main’ material (e.g., gold) on the polymer substrate. This can be followed by sputter deposition of the main conductive material layer. The whole wafer may then be dipped into a suitable solvent, e.g., acetone, to lift-off the photoresist creating an electrically conductive pattern on the polymer substrate, which may be diced and individually packaged as sensors

The polymer thickness, metal pattern thickness, polymer material, and metal can be chosen based on the desired functionality. The traces 102,104 may also be provided directly on the tube (which may then be considered the substrate).

In the depicted example, the heater 102 is electrically connected to two connectors 108I,2 on either end of the heater trace, and similarly, the temperature sensor 104 is electrically connected to two connectors 110i,2 on either end of the sensor trace. Such connectors are well-known in the art and are typically part of the same thin-film pattern as the traces. They can be used to electrically connect the traces to electronic circuitry to drive and read-out the traces.

Fig. 1B schematically depicts a flow sensor according to a further embodiment. The flow sensor 120 comprises a sensing unit 100 as depicted in Fig. 1A. The flow sensor further comprises electronic circuitry 118, electrically connected to the one or more first electrically conductive thin-film trace acting as the one or more heaters and to the one or more second electrically conductive thin-film trace acting as the one or more temperature sensors. The electronic circuitry is configured to drive the one or more heaters and the one or more temperature sensors. The electronic circuitry is communicatively connected to a processor 112. The processor 112 is communicatively connected to a memory 114 and to a communication interface 116, in this example a wireless communication interface. The processor 112 may be configured to determine a flow parameter, e.g., a flow volume or flow velocity, based on the measurements and, optionally data stored in the memory (e.g., conversion values, calibration data, or the like). The measurements typically comprise one or more voltages over and/or one or more currents through the one or more heaters and/or the one or more temperature sensors.

The flow sensor 120 further comprises a power source 122 for powering the components 112-118, and a housing 124 arranged for connecting the flow sensor to the tube. The depicted example may operate completely wirelessly. A wireless flow sensor avoids the need for connection wires, which makes the flow sensor more versatile.

Other embodiments may include further or different components. For example, the flow sensor may be implemented as a wired flow sensor, using, e.g., a USB connection or other suitable connection to connect the flow sensor to a further apparatus, e.g., a monitoring device, or an infusion pump. In that case, there may be no need for a power source inside the flow sensor. Additionally, the communication interface may be a wired communication interface. Instead of or in addition to a communication interface, the flow sensor may comprise a display or other output mechanism for outputting (e.g., displaying) a determined flow value. In a wired embodiment, the wire may be integrated in or connected to the tube.

The flow sensor 120 may be configured to regulate the flow through the tube, e.g., in response to the determined flow parameter. For example, the flow sensor may be configured to send a control signal to the infusion system via the communication interface 116. The control signal may in turn configure the infusion system to regulate the flow accordingly. As a further example, the flow sensor may comprise a flow valve (not shown) inside or in line with the tube, or be physically and/or communicatively connected to such flow valve. In that case, the flow sensor may be configured to control, e.g., actuate, the flow valve based on the determined flow parameter.

For example, current in-line sensors (e.g., a pressure sensor) may sense an increase in the pressure (suggesting an occlusion), and trigger the syringe pump to “back off” a little to release the pressure. This is done to ensure that the patient does not get any accidental bolus that can be harmful. A flow sensor according to an embodiment could use the same or a similar communication protocol with the infusion pump to avoid any accidental overdoses when a deviating flow rate is detected. This can be one possible way of sensor-pump communication.

Alternatively, a feedback loop (e.g. PID control) can be implemented to maintain the infusion rate at a fixed value. In this case, the sensor measures the flow downstream and communicates constantly with the infusion system’s pump to ensure that the flow rate at the measured location is maintained constant. This may result in a so-called “self-correcting” pump.

Fig. 2A and 2B schematically depict flow sensors comprising a rigid substrate and Fig. 2C and 2D schematically depict flow sensors comprising a flexible substrate. As shown in Fig. 2A, flow sensors with a rigid substrate 202 do not conform to the typically round circumference of the tube 200. As a consequence, the contact area between the flow sensor and the tube is very small, leading to a low heat transfer, and hence low measurement quality.

In Fig. 2B, a force is exerted on the tube 200, causing the tube to deform. This increases the contact area with the flow sensor (again on a rigid substrate 204). However, this deformation changes (reduces) the cross-sectional area of the tube, which may negatively affect the flow. Moreover, if the deformation is variable, the flow measurements may be less reliable, as the determination of a mass or volume flow rate typically assumes a constant cross-sectional area. Also in this case, the contact area is still limited to less than half of the circumference of the tube, and more typically even less than a quarter.

Despite these drawbacks, many current flow sensors use a rigid substrate, e.g., a semiconductor substrate, because this allows the flow sensor to be produced in a straightforward and cheap manner using standard semiconductor production techniques. The same considerations apply when using rigid (or semi-rigid) sensor elements, e.g., a rigid heater and/or rigid temperature sensor (e.g., sensor elements with a ceramic protective casing), regardless of whether the substrate is rigid or flexible. These issues are less severe if the smaller the sensor element is relative to the circumference of the tube, which is one of the reasons that many current flow sensor tend to minimise the sizes of the sensor elements.

Fig. 2C shows a flow sensor with flexible (thin-film) sensor elements on a flexible substrate 206. The substrate (with the sensor elements) conforms to the outer surface of the tube 200, increasing the contact area and improving heat transfer both from the heater to the tube wall and hence to the fluid inside the tube, and from the fluid to the tube wall and then to the temperature sensor, without deformation of the tube. Such conformation is especially relevant when the sensor elements are large (wide) relative to the circumference of the tube; in other words, when (at least one of) the sensor elements is arranged to cover a substantial part of a circumference of the tube, e.g., at least 10%, at least 15%, at least 20%, at least 25%, at least 30%, at least 35%, at least 40%, at least 45%, or at least 50%. In other embodiments, at least one of the sensor elements, e.g., at least one heater and/or at least one temperature sensor may cover an even larger part of the circumference of the tube, e.g., at least 60%, at least 75%, at least 90%, or even at least 95%.

Thus, by providing the heaters and sensors formed by thin-film traces on a flexible substrate that is configurable to conform to the outer surface of the tube, contact between the heaters and sensors on the one hand and the tube on the other hand can be improved compared to a flow sensor provided on a rigid substrate, e.g., a resin (PCB) or a semiconductor substrate, without deforming the tube. Hence, measurement accuracy can be improved, and changes in flow due to the measurement (e.g., overheating of the tube or fluid, or deformation of the tube) can be minimised.

Fig. 2D shows another flow sensor with a flexible substrate 208. In this case, the substrate is arranged around a significant part of the circumference of the tube, e.g., at least 50% of a circumference of the tube, e.g., at least 75%, at least 90%, or even at least 95% of the circumference of the tube. This allows for various arrangements of heaters and temperature sensors on a single substrate, e.g., a sensor opposite a heater, one or more heaters arranged circumferentially around the tube, or one or more heaters arranged circumferentially around the tube. Using the entire circumference, or a significant part thereof, increases the sensitivity of the flow sensor by increasing the surface area and hence heat transfer to and from the fluid, and reduces the sensitivity to the positioning of the flow sensor, which may be affected by gravitational effects, and/or may allow to detect the orientation of the flow sensor and possibly correct for any orientation-depended effects. Additionally, more uniform heating (as may be obtained by heating around the entire circumference or a significant part thereof) may reduce the risk of local overheating, thus reducing the risk of undesired changes to the fluid whose flow is being measured. Obtaining uniform heating may include, e.g., using several heating positioned circumferentially around the tube and/or heaters specifically designed to provide homogeneous heating taking into the heat generation and heat distribution over the heater.

Fig. 3A-E schematically illustrate several thermal flow sensors. In these figures, depicting a longitudinal cross section, the fluid whose flow is measured, is located above the tube wall 300 (inside the tube), whereas the heaters and temperature sensors are located below the tube wall (outside the tube). The (expected) flow direction is from left to right.

In general, there are two heat transport mechanisms present in a (flowing) fluid: diffusion (or conduction) and advection. Diffusion depends on the physical properties of the fluid, in particular on the thermal conductivity of the fluid, and is generally independent of the flow. Advection is (heat) transport through (bulk) movement of the fluid, and is hence dependent on the flow and mostly independent of the type of fluid. The ratio between the associated time scales is the (dimensionless) Peclet number Pe = L v/a, wherein a is the thermal diffusivity of the fluid, v is the magnitude of the flow velocity, and L is a characteristic length (typically the distance between heater and sensor). The (thermal) Peclet number may also be defined as the product of the Reynolds number and the Prandtl number: Pe = Re • Pr. The transition of heat transfer mechanism from conduction-dominated to advection- dominated occurs at a Peclet number of around 1 in a flowing fluid. Below Pe~l, the heat transfer is conduction-dominated, while above Pe~l, the heat transfer is advection- dominated. Here, the heat transfer refers to the transfer of energy from one or more heaters to one or more temperature sensors defining a measurement unit. For normal saline (0.9% NaCI in water), a « 0.14 mm²/s, so for a tube with a 1 mm inner diameter, Pe « 2.5 — — — , mm ml/h where p denotes the flow rate in ml/h. The thermal diffusivity depends on the fluid, and is typically much higher for gases; hence the flow sensor design may be optimised based on the fluid for which the flow rate is to be measured.

It is noted that the described thermal flow sensors tend to be more accurate at higher heater temperatures, as the resulting thermal gradients are larger, leading to a better signal- to-noise ratio (SNR). However, in many applications, there may be limitations to the amount of the heat the fluid can safely absorb. For instance, many drugs are temperature sensitive, and hence, maximum fluid temperature must typically be kept below 40 °C or even below 38 °C. Fig. 8 shows a relation between heater power and fluid temperature for an exemplary embodiment. In this example, keeping the power dissipation below about 55 mW would ensure the fluid temperature remains below 40 °C, while limiting the power dissipation to 42 mW would result in a fluid temperature of < 37 °C. Additionally, especially for wireless implementations, the power dissipation may be limited by the capacity of the power supply and the desired minimal operation time. Fig. 3A-C illustrate a calorimetric flow sensor comprising a heater 302 and two temperature sensors 304I,2 arranged symmetrically around the heater in the direction of the flow, i.e., the first temperature sensor 304i is located a certain distance upstream from the heater and the second temperature sensor 3042 is located the same distance downstream from the heater. The calorimetric flow sensor works by heating the fluid using the heater and determining the temperature difference between the two temperature sensors. These temperature sensors can be thermistors or other suitable temperature sensors such as thermocouples, thermopiles, and so on. Thermistors use the temperature dependence of the resistance of the thermistor to determine the temperature. Thermocouples and thermopiles are based on a voltage generated at an electrical junction between two materials with a temperature difference between their ends.

If there is no flow, as depicted in Fig. 3A, the heat distribution 306 is symmetric around the heater, and the temperature difference between the temperature sensors is zero. In this case the heat distribution is only caused by diffusion. In case of flow, the heat distribution is skewed due to advection, as shown in Fig. 3B. As a result, the upstream temperature sensor becomes cooler and the downstream temperature sensor becomes warmer, leading to a temperature difference that depends on the flow velocity. If the flow velocity becomes too large, as shown in Fig. 3C, the amount of heat reaching the upstream sensor via the fluid becomes negligible, and the sensitivity of the sensor sharply drops. Consequently, the optimal distance between the heater 302 and the temperature sensors 304I,2 depends on, inter alia, the thermal diffusivity of the fluid, the operating temperature of the heater, and the (expected) fluid velocity, with a larger distance being suitable for measuring larger flow velocities and vice versa. The minimum distance can be limited by heat transfer through the tube wall and the environment. The maximum distance can be limited by thermal diffusion through the fluid and thermal losses to the environment, as well as the desired Peclet number regime.

Fig. 3D illustrates a time-of-f light flow sensor comprising a heater 312 and a temperature sensor 314 positioned downstream of the heater. In its simplest form, the heater heats the fluid for a relatively short period of time, creating a heat pulse, which is some time later measured by the temperature sensor. The time difference between the emitting and receiving the heat pulse provides a measurement of the flow velocity, taking into account the time needed by the signal to traverse the tube wall (twice). The distance between the heater and the temperature sensor should be sufficiently large that the heat transport is dominated by the fluid flow (and not by thermal conduction through the tube wall). Due to thermal diffusion in the fluid, the amplitude of the heat signal emitted by the heater decreases over time, while the pulse width increases. As a result, the larger the distance between the heater and the temperature sensor, and the lower the fluid velocity, the lower the signal-to-noise ratio becomes. Hence, the optimal distance between heater and sensor depends on the physical properties of the fluid and of the tube wall, as well as on the (expected) flow velocity.

Instead of individual pulses, the heater can also emit a periodic signal, e.g., a sine wave. The travel time (and hence flow velocity) is then correlated with a phase difference between the emitted and received signals. The amplitude (or amplitude difference) may be used to resolve phase multiplicity, and/or to assure the measurement is of sufficient quality.

Fig. 3E illustrates a hot-film (or hot-wire) anemometric flow sensor comprising a heater 322 and an optional temperature sensor 324 typically positioned upstream of the heater. In this application, the “anemometric flow sensor” refers to a hot-film (or hot-wire) anemometric flow sensor unless otherwise specified. The working principle of such sensors is based on the dependence of the heat transfer from the heater to the fluid on the fluid velocity, and on the temperature dependence of the resistance of the heater. In general, several operating principles may be distinguished: either the voltage or the current may be kept constant, while the current respectively voltage varies. The varying current or voltage may be measured ‘passively’, allowing to derive a variable resistance (and hence variable heater/sensor temperature), or the current or voltage may be actively controlled in order to keep a constant resistance (or constant heater/sensor temperature) versus variable resistance (or variable temperature). In both cases, the resistance R may be determined using Ohm’s law V = I R, where V denotes the voltage and I denotes the current.

As the heat transfer from the heater to the fluid depends not only on the flow velocity but also on the fluid temperature, a temperature sensor 324 is typically provided to calibrate the hot-film anemometric flow sensor, especially if a high accuracy is required and the fluid temperature is not exactly known or can be variable. For example, for an infusion system, the fluid temperature may be dependent on the environmental temperature, which may change over the course of a day, or on the infusate temperature (e.g., when it is taken out of the refrigerator and placed into the IV syringe). Such a temperature sensor is typically positioned sufficiently far that the temperature sensor 324 is not affected by the heater 322. If the temperature changes only slowly, the heater may also be used as a temperature sensor (so that only one electrically conductive trace is needed, acting both as a heater and a temperature sensor at different moment in time), by driving the heater/sensor at a much lower voltage than when the heater/sensor is used as a heater.

Several of these measurement techniques may be combined using the same heaters and temperature sensors. For example, the heater 302 of a calorimetric flow sensor may be kept at a constant temperature, and the corresponding changes in current and/or voltage may be used to estimate a flow velocity using a hot-film anemometric flow sensing technique. As a further example, the temperature sensor 314 of a time-of-flight flow sensor may be used as the ‘calibrating’ temperature sensor 324 of a hot-film anemometric flow sensor, especially when a pulsed time-of-flight measurement technique is used (so that the temperature in between the pulses may be used to calibrate the anemometric heater 324). An ‘inverted’ pulse (i.e., a heater that is most of the time on and periodically switched off) can similarly combine a hot-film anemometric techniques with a time-of-flight technique. As yet a further example, the heater 302 of a calorimetric flow sensor may be driven with a periodic signal, using an amplitude difference between the two temperature sensors 304I,2 for a calorimetric measurement technique and a phase difference between the heater 302 and the downstream temperature sensor 3042 for a time-of-flight measurement technique. Other examples and combinations may be readily apparent to the skilled person.

Different measurement techniques have different advantages and disadvantages. As noted above, calorimetric measurements tend to be more accurate for lower flow regimes but may saturate at higher flow rates; whereas time-of-flight measurements tend to be more accurate for higher flow regimes. Both calorimetric and time-of-flight measurements may be considered inherently temperature-compensated methods, as they do not depend on the fluid temperature (or only negligibly so). Time-of-flight measurements generally have a relatively low temporal resolution, whereas hot-film anemometric measurements have a much higher temporal resolution, with calorimetric measurements typically having only a slightly lower time resolution than anemometric measurements. Using a set-up as described below with reference to Fig. 7, the response time of the hot-film anemometric measurement is about 3-5 s, the response time of the calorimetric measurement is about 5-8 s, and the response time of the time-of-flight measurement is about 50-60 s of stable flow (in this context defined as deviations of less than 0.2 ml/h within a 50 s window). It is noted that although these response times may depend on the actual flow rate and the details of the setup (e.g., tube diameter, tube wall thickness, heater-sensor distance, et cetera), the relative magnitude of response times is representative of a wide array of configurations and settings.

Thus, in an embodiment, multiple (different) measurement techniques may be combined. Depending on the implementation, the different measurement techniques may share none, some or all of the heaters and/or temperature sensors. For example, the flow sensor may use a calorimetric technique and a time-of-flight technique and use a weighted combination to determine the flow; typically, the weight for the calorimetric result will be higher for lower flow rates and the weight for the time-of-flight result will be higher for higher flow rates. These weights may be zero for certain flow rates.

As a further example, a time-of flight technique may be used for a high-accuracy result with a low temporal resolution, while a hot-film anemometric technique is used for a low- accuracy result with a high temporal resolution. In many applications, long-term accuracy is more important than short-term accuracy, e.g., to ensure a patient receives a correct dosage of a drug over an hour or a day. For such measurements, a high accuracy is more important than a high temporal resolution. However, incidents (e.g., occlusion stopping substantially all flow, siphonage or “free flow” leading to a greatly increased flow, or vertical movement of the pump and/or patient causing a sharp rise or drop in the flow rate) must typically be detected quickly, and in such cases, accuracy is less relevant. Here, temporal resolution refers to the time needed to determine a change in flow rate, which may be different from the sample frequency.

Table 1 provides a comparison of the time-to-alarm for a commercially available infusion pump (in this case, a B. Braun Perfusor® Space pump) using two different alarm settings, with the time to alarm of a flow sensor according to an embodiment. The time-to- alarm is determined from the time an artificial occlusion was created in an IV line, for different pre-occlusion flow rates. Especially for flow rates of 1 ml/h or below, the time-to-alarm of the infusion pump becomes extremely long, orders of magnitude longer than the half-life (~ 2-3 minutes) of many crucial drugs such as vasopressors and inotropes.

Table 1. Time-to-alarm for different pre-occlusion flow rates for a prior art system and for a flow sensor according to an embodiment. pre-occlusion flow infusion pump infusion pump flow sensor

(ml/h) time-to-alarm time-to-alarm (embodiment)

(75 mmHg) (384 mmHg) time-to-alarm

0.3 — 2h 54m 15s 13s

0.4 — 1h 46m 44s 12s

0.5 24m 24s 1h 24m 13s 13s

0.7 — 57m 33s 13s

1 9m 55s 40m 28s 13s

2 3m 34s 23m 15s 11s

3 — 12m 40s 16s

5 1m 26s 6m 5s 14s

10 57s 5m 1s 18s

Fig. 4A and 4B schematically depict a flow sensor according to an embodiment. The flow sensor comprises a heater 402 and a temperature sensor 404 provided on a substrate 406. The substrate can be a flexible substrate. The flow sensor is applied to a tube wall 400 of a tube through which a fluid is flowing the flow of which is to be measured by the flow sensor. Although the flow sensor is shown only on the ‘top’ side of the tube, the flow sensor may wrap around the tube. The heater and the sensor can be positioned on a surface of the substrate that is in direct contact with the outer surface of the tube wall, or they can be on the opposite surface of the substrate, such that the substrate is provided between the tube wall on the one hand and the heater and the temperature sensor on the other hand.

The heater 402 has a width w_H and the temperature sensor 404 has a width w_s, both as measured along the longitudinal direction of the tube (in the direction of the flow). In the depicted example, the flow is assumed to be in one direction only, so that the temperature sensor is positioned downstream from the heater. The substrate has a thickness d_s and the tube wall has a thickness d_w. For a typical infusion tube, d_w is about 0.5 - 0.6 mm. The tube has an inner diameter and an outer diameter D_o. The tube wall has a thermal diffusivity a_w. The fluid flowing through the tube is characterized by a thermal diffusivity a_f and flows with a flow velocity v.

As shown in Fig. 4B, there are essentially three routes along which heat flows from the heater 402 to the temperature sensor 404: through the substrate 406, through the tube wall 400, and through the fluid. It is assumed that the flow sensor is well insulated, so that heat flow through the environment is negligible. Each route is associated with a respective thermal resistance R _-3. In general, to obtain a good signal-to-noise ratio, it is desirable that the heat flow is dominated by the route through the fluid. However, due to the non-contact nature of the measurement, the heater and the fluid are separated by the wall thickness of the tube, and the fluid and the temperature sensor are likewise separated by the wall thickness of the tube. Therefore, in general, the distance L between the heater and the temperature sensor may be selected to be larger than twice the wall thickness, i.e., L > 2d_w, in particular in configurations wherein the heater(s) and/or temperature sensor(s) are arranged circumferentially around the tube. In other arrangements, the distance L may depend differently on the thickness of the tube wall and the effective cross section of the heat transfer path through the tube wall.

The different routes are also associated with different characteristic time constants.

The time constant associated with the transfer of heat through the thickness of the tube wall d can be approximately calculated as —² which, in the case of a typical infusion tube (wall thickness = 0.5 mm, thermal diffusivity of PVC = 0.08 mm²/s), amounts to around 6 seconds (3 seconds from heater to fluid and 3 seconds from fluid to temperature sensor). The flow velocity may be of the order of magnitude of about 1 mm/s, and may add several seconds more to the travel time of a heat signal from the heater to the temperature sensor. This puts certain limitations on the time-of-flight measurement, for instance, placing an upper limit on the frequency (~ 1/6s = 0.16 Hz neglecting the contribution of the travel time through the fluid) of the time-varying signal used for the heater in the time-of-flight method. This in turn implies that the time-of-flight method, used in a non-contact configuration, will not be capable of detecting certain high-frequency events such as a sudden flow variability event (e.g. accidental bolus or underdose).

It is noted that these considerations do not play a significant role in configurations in which the flow sensor is in direct contact with the fluid.

Another consequence of performing a non-contact measurement (as opposed to a measurement where the heater/sensor are in contact with the fluid, or separated from the fluid only by the substrate) is the careful consideration of the heater/sensor configuration, especially their spacing. As noted above, there are three main routes of heat transfer between the heater 402 and the sensor 404 (in parallel): i) conduction via the substrate; ii) conduction via the tube wall (and, optionally, the substrate thickness); and iii) heat transfer via the liquid which further comprises the following three routes (in series): conduction via the tube wall (and, optionally, the substrate) from heater to fluid, conduction/advection via the fluid, and finally conduction via the tube wall (and, optionally, the substrate) from the fluid to sensor. Each of these heat transfer pathways is associated with a resistance to heat flow. Assuming a simplified 2D wall model, the resistances R_{l t} R₂ and /?₃ can be approximated as follows: for a configuration wherein the heater and sensor are in direct contact with the wall tube, or for a configuration wherein the substrate is in between the heater/sensor and the tube wall. The full equivalent resistance may then be obtained using:

1 _ 1 1 1

Req R1 R2 R3

Since these heat transfer resistances are in parallel, heat transfer through each route will occur in inverse proportion to the resistance — in other words, most heat will tend to flow via the least resistive path. In the above formulae, it must be noted that all the terms barring RS,L are geometry and material-dependent, and are constant for a given configuration. Only RS,L is dependent on the fluid flow velocity, and is expected to reduce as the flow velocity v increases. Thus, the sensitivity of the flow sensor increases with the ratio of /?₃ (in particular R_{3 L}) to the equivalent resistance R_eq, and can be optimised by maximizing the values of /?! and Z?₂ while minimizing the value of R_{3 L}, as this makes heat transfer via the fluid route the most dominant pathway. From the formulae above, this implies high values for the separation of the heater and sensor L and for the heater area w_H and the temperature sensor area w_s, and small values for the substrate thickness d_s. If the heater and temperature sensors are embedded in the tube wall, the effective tube wall thickness between the heater/sensor and the fluid may also be minimized.

Translating the insights from the simplified 2D model to the actual 3D case, it can be concluded that:

- The heater 402 and the temperature sensor 404 have to be spaced apart (unlike the in-line ‘contact’ configuration where the H-S distance is typically maintained as low as possible). A close distance will result in unintended heater-sensor interference (via heat transfer from the polymer sheet and the IV tubing) that will decrease the sensitivity of the system to changes in fluid flow velocity. However, if the sensors are spaced too far apart, the heater signal will attenuate before reaching the temperature sensor’s sensing threshold. Thus, there exists a trade-off, and the ideal H-S distance L is usually around 1-10 mm in an infusion set-up. For a time-varying heater signal, the H-S distance L should be longer (in the longitudinal direction) to increase the Peclet number and ensure advection-dominated heat transfer. For calorimetry, the H-S distance should be shorter to maintain the Peclet number lower than 1.

- The area of the heater w_H (or array of heaters) and temperature sensor w_s should be maximized, preferably along the circumferential dimension and not along the longitudinal dimension. The larger area enhances the heat transfer pathway via the fluid, thus increasing the sensitivity of the device. Using a flexible (polymeric) substrate 406 for the heater/sensor allows to wrap the heater/sensor around the tube, thus increasing the surface area.

- A lower thickness of the tube wall d_w enhances the heat transfer pathway via the fluid (route #3) and reduces the heat transfer via the tube wall (route #2). This can be achieved, for instance, by reducing the tube thickness where the sensor is located, e.g., using a specifically designed tube.

- In order to maintain a large value for the H-S distance L, another possible configuration is one where the heater and sensors are on the opposite sides of the tube, as shown in Fig. 4C. In this example, the resistances of the heat transfer via routes #1 and #2 are increased, while the heat transfer route via route #3 is roughly the same as before. These configurations are readily achievable using a flexible substrate - as an example, a single flexible substrate can be wrapped around the tube to achieve the configuration.

Fig. 4D schematically depict a flow sensor according to an embodiment. The flow sensor comprises a first measurement group 412 comprising a first heater 402i and a first temperature sensor 404i positioned downstream of the first heater, and a second measurement group 414 comprising a second heater 4022, a second temperature sensor 4042 and a third temperature sensor 404s, the second and third temperature sensors being positioned symmetrically around the second heater. The first measurement group is configured to act as time-of-flight flow sensor, while the second measurement group is configured to act as a calorimetric flow sensor. Additionally, the second heater is configured to act as a hot-film anemometric flow sensor. In this example, the second measurement group is positioned downstream from the first measurement group. Such a flow sensor may be used, for example, to perform the method described with reference to Fig. 6.

More sensors can be added to improve the accuracy as needed. E.g., an upstream sensor for the first heater 402i can help identify backflow with more accuracy; more sensors upstream and downstream of the second heater 4022 can enable flexibility in the measurement of higher flow rates, as desired.

Fig. 5 is a flow chart of a method according to an embodiment. The method may determine a flow rate based on sensor output provided by a sensor as described above. The method may be performed, for example, by a processor included in the flow sensor (e.g., processor 112 in Fig. 1), or by an external data processing system (e.g., a personal computer, smart phone, monitoring device, or wearable device communicatively connected to the flow sensor).

A first step 502 comprises receiving a first signal representative of a flow measurement obtained using a first measurement technique, e.g., a calorimetric flow measurement. A step 504 comprises receiving a second signal representative of a flow measurement obtained using a second measurement technique, different from the first measurement technique, e.g., a time-of-flight flow measurement. The first and second signals are obtained using different measurement techniques, and may therefore have accuracies that depend in different ways on the flow rate. For example, calorimetric measurements are typically more accurate in low-flow regimes, e.g., for flows with Peclet number Pe_Cal < 1. Similarly, time-of- flight measurements are typically more accurate in high-flow regimes, e.g., for flows with Peclet number Pe_ToF > 1. It is noted that the Peclet number depends, inter alia, on the detector geometry, in particular the distance between the heater and the sensor(s). Hence, the flow sensor may be designed such that the calorimetric low-flow regime partially overlaps with the time-of-flight high-flow regime, i.e. , such that 0 < v(Pe_ToF = 1) < v(Pe_Cal = 1). This can be assured by using a smaller distance between heater and sensor(s) for the calorimetric measurement unit than for the time-of-flight measurement unit.

An optional step 506 comprises receiving a third signal representative of a flow measurement obtained using a second measurement technique, different from the first and second measurement techniques, e.g., a hot-film anemometric flow measurement. In other embodiments, even more measurement techniques may be used. A step 508 comprises determining (estimating) an approximate flow rate. In embodiments including the third signal, the approximate flow rate may be determined based on the third signal. Additionally, or alternatively, the approximate flow rate may be determined based on the first and/or second signals.

A step 510 comprises determining weights for the first and second signals, and optionally for the third signal, based on the approximate flow rate. These weights may be binary, multivalued discrete, or continuous. Binary weights only use weights valued 0 or 1; an example of is determining the flow rate based on (only) the first signal if the approximate flow rate is below a reference flow rate and based on (only) the second signal if the approximate flow rate is above the reference flow rate. Multivalued discrete weights use more than two different weights, e.g., 0, 1 , and 1. For example, only the first signal is used when the approximate flow rate is lower than a first threshold value (e.g., corresponding to = v(Pe_ToF = 1)), only the second signal is used when the approximate flow rate is higher than a second threshold value (e.g., corresponding to v₂ = v(Pe_Cai = 1)). and in between, both signals are used. A continuous weight may use, for example, a continuous transition between two threshold values. The weight may be based, for instance, on the uncertainty of the measurements, which may have been determined in a calibration setup.

A step 512 comprises determining the flow rate based on the weights and at least the first and second signals. In some embodiments, the flow rate may also be based on the third and possibly further signals.

The steps may be performed explicitly or implicitly. For example, the first, second, and optional further signals may be provided to a trained machine learning algorithm, which has been trained to determine a flow rate based on the first, second, and optional further signals. In machine learning implementations, it is typically desirable to use all available signals. Suitable machine learning methods are well-known in the art. The training data may comprise a wide variety of (calibrated) flow rates, fluid temperatures, and ambient temperatures.

Fig. 6 is a flow chart of a method according to an embodiment. A first step 602 comprises the flow sensor being activated. An optional waiting step 604 may help the system reach an equilibrium. For example, the heat emitted by the heaters needs some time to be transmitted through the tube wall, through (and by) the fluid, and back through the tube wall to the temperature sensors. This may take several seconds, e.g., up to about 30-60 s for a typical infusion tube. If a periodic time-of-flight signal is used, the system may require at least a full period in order to determine a phase difference between the emitted and received signals.

The flow sensor then performs one or more flow measurements, possibly using several different measurement techniques. In the depicted example, a calorimetric flow measurement 606, a hot-film anemometric flow measurement 608, and a time-of-f light flow measurement 610 are performed. Of these, the anemometric flow measurement has the highest temporal resolution, and is therefore used, in a step 612, to determine whether the flow is stable (e.g., the changes in flow rate over time are below a predetermined threshold), or whether an incident has occurred. Examples of incidents are (partial) occlusions, resulting in a sudden drop in the flow rate; backflow, especially during multi-infusions; a (sharp) rise or drop in flow rate due to vertical movement of either the pump or the patient; siphonage or 'free flow' of infusate due to improper placement of syringe inside the pump; or gas bubbles in a liquid, leading to a quick variation in detected flow rate due to the difference in thermal conductivity and heat capacity between the gas bubble and the liquid. In case a non-stable flow is detected, an error may be output 614. This can be a visual and/or auditory warning, e.g., a flashing red light, a beeping noise, et cetera, and/or a signal that is sent to an external device, e.g., a beeper, monitoring device, et cetera. It is noted that not all flow errors are accompanied by a non-stable flow. In other embodiments, the determination of whether the flow is stable may only (or additionally) be used to indicate the reliability of the time-of-flight flow. In lower flow regimes, even relatively fast changes in flow rate may be detected as erroneous using e.g. the calorimetric flow measurement.

A step 616 comprises estimating the flow rate. In the current example, the flow rate is estimated based on the hot-film anemometric flow rate, but in other embodiments, the flow rate may (additionally or alternatively) be estimated based on the calorimetric flow rate and/or the time-of-flight flow rate. A step 618 comprises determining whether the estimated flow rate is below a predefined threshold value, e.g., 1 ml/h. The predefined threshold may be adjustable based on, e.g., the type of fluid flowing through the tube. For example, the predefined threshold may be based on the Peclet number of the fluid flowing through the tube. If the estimated flow rate is below the threshold, the flow rate is determined 620 based on the calorimetric flow rate 606 and, optionally, the hot-film anemometric flow rate 608. If the estimated flow rate is above the threshold, the flow rate is determined 622 based on the calorimetric flow rate 610 and, optionally, the hot-film anemometric flow rate 608.

A step 624 comprises outputting the determined flow rate, e.g., on a display on the flow sensor, and/or by sending a signal to an external device (as also described above for step 614). In some embodiments, this step may comprising comparing the determined flow rate to a set flow rate, and outputting an error if the determined flow rate deviates more than a given amount, e.g., 5% or 10%, from the set flow rate. The flow sensor may output a binary signal (‘good’ or ‘bad’) based on a comparison between the determined flow rate and the set flow rate. In some embodiments, also a temporal average of the flow rate may be determined and output and/or compared to a set flow rate, for example, the instantaneous flow rate and the average flow rate over the past 5 minutes, past 15 minutes, or past hour, or some other suitable time interval. If a comparison with a set flow rate is made, the instantaneous flow rate may be allowed a larger deviation than the time-averaged flow rate. In many settings, a binary output that can be easily perceived (e.g., seen and/or heard) is very useful so that a user can instantly see whether or not intervention has to take place.

Steps 606-624 may be repeated, e.g. continuously or on fixed intervals.

In other embodiments, the steps may be performed in a different order, e.g., the check 612 whether the flow rate is stable can be performed after the flow estimation 616 or after the determination 620,622. Additional steps may be included, or certain steps may be omitted. For example, a first measurement technique (typically the hot-film anemometric measurement) may be used only to detect sudden changes in flow rate (i.e. , unstable flow), while a single second measurement technique (e.g., the calorimetric measurement or the time-of-f light measurement) may be used to determine the flow rate. In that case, there is no need to first determine an initial estimate of the flow rate. In another embodiment, the flow rate may be determined 624 based on the calorimetric, hot-film anemometric, and time-of- flight measurements, using (non-binary) weights based on the estimated flow rate. In that case, a step comprising determining weights based on the estimated flow rate may replace the step 618 of determining whether the estimated flow rate is below a predefined threshold. Fig. 7A-C are graphs of measurements using flow sensors according to various embodiments. The graphs show results of an experiment in which a pressurised water tank maintained at 0.5 bar, filled with deionised water, is connected to a Codan extension IV line, with a 2 mm outer diameter and a 1 mm inner diameter. This IV line is, in turn, connected to a Bronkhorst mini CORI-FLOW™ M12V14I Low Flow Coriolis Mass Flow Controller, which acts as a reference flow controller. A flow sensor according to an embodiment is attached to the IV line, at a point close the reference flow controller, and is placed within a Binder KT53 incubator which regulates the ambient temperature. A National Instruments USB-6289 data acquisition system powers the flow sensor, and records the resistances of the heater and temperature sensors. The reference flow controller regulates flows ranging from 0.1-10 ml/h as well as 0 ml/h, and the incubator regulates ambient temperatures between 15-40 °C. For each test, 5-10 different flows are selected in a cycle, and each flow is sustained for a minimum of 30 minutes.

Fig. 7D schematically shows the flow sensor used in this experiment. The flow sensor consisted of a single heater flanked by 2 pairs of temperature sensors arranged symmetrically around the heater 702. The first pair of temperature sensors 704I,2 are located 1.5 mm up- and downstream of the heater, and the second pair of temperature sensors 7043,4 are located 4 mm up- and downstream of the heater, referred to as U2, U1, H, D1, and D2, respectively. Temperature sensors U1 and D1 from the first pair and temperature sensors U2 and D2 form the second pair of sensors. All traces are around 100 Q in resistance.

In all tests, the temperature sensors were driven at 0.1 V and the resistance was derived by measuring the current. For the calorimetric measurement (show in Fig. 7A) and for the hot-film anemometric (shown in Fig. 7C), the heater was biased at a constant 2 V. Thus, these results use a constant voltage biasing for the steady-state heater. This approach differs from the constant-temperature biasing that is more commonly used but which requires a strict tolerance on the sensor resistances during manufacturing. The constant voltage biasing approach used here poses less strict requirements on the manufacturing tolerances of the heaters and sensors. For the time-of-flight phase shift measurements (shown in Fig. 7B), the heater was biased with a sinewave pattern with limits of 0.1 V and 2 V with a time period of 25s, thus again using a controlled voltage (instead of, e.g., a controlled time-varying current).

In particular, Fig. 7A shows measurements using a calorimetric measurement technique. As explained in more detail with reference to Fig. 3A-C, calorimetry relies upon the change in symmetry of the heat plume due to fluid flow. This method is inherently compensated with respect to the ambient temperature. At zero flow, a symmetric plume exists above the heater (assuming a configuration as shown in Fig. 3A-C), and the temperatures measured by the sensors upstream and downstream are similar. At non-zero fluid velocities, this plume becomes skewed towards the downstream sensor, introducing asymmetry in the readings of the upstream and downstream sensors that can be calibrated against the flow rate. One way to measure asymmetry is to record the difference in the resistance of equidistant upstream and downstream sensors (Di - Ui) and calibrate them against flow rate. However, it must be noted that the difference (Di - Ui) vs flow rate curve shows a peak - this peak occurs at the flow rate where the heat plume is located directly below Di. The ‘usable’ portion of the calibration curve is thus till this inversion point, and for the experimental conditions described above (which reflect typical clinical conditions), this inversion point is around 1 mL/h for a H-Di distance of 1.5 mm. These experimental data show that the calorimetry method is highly accurate (error ~ ±2% of full scale, where the scale is till 5 mL/h) till the inversion point (in Fig. 7A, till about 1 mL/h). In general, the inversion point can be adjusted by adjusting the distance between H and D the greater the H-Di distance, the higher the flow rate at the ‘inversion’ point of the curve, and vice versa. However, the H-Di distance cannot be arbitrarily long, and the maximum value is given by the limit of Peclet number < ~1 , beyond which Di will not be able to reliably sense the heat plume generated by the heater H.

Fig. 7B shows measurements using a time-of-flight measurement technique. Time-of- flight generally works best in the advective regime (Pe > 1). An advantageous way to implement this method is to have a time-varying signal on the heater (e.g., a sinusoidal bias voltage) and measure the phase shift of this sinusoidal wave received by the downstream sensor. Since the method works best in the advection-dominated regime with high Peclet numbers, the H-S distance L in the time-of-flight method is ideally longer than in the calorimetry method (in the results shown below in Fig. 7A, the H-S distance was 7 mm). However, more variability is observed in the conduction-dominated low Peclet number regime. Some of the main advantages of the time-of-flight method are that it is inherently temperature compensated, is independent of the fluid and geometry (in advection-dominated flows), and finally injects lesser heat into the fluid compared to the steady state methods. This last point is especially important for, e.g., certain drugs that may degrade at higher temperatures. The results shown in Fig. 7B show high accuracy with errors on the order of ±1% of full scale (full scale ~ 0-5 mL/hr) for flows above about 1 ml/h. However, the measurement frequency is limited by the long time constants which makes it difficult to measure high-frequency flow instability events.

From the preceding discussion, it follows that a combination of a calorimetric measurement and a time-of-flight measurement provides two independent systems that give the desired performance in two separate flow regimes. However, a method is needed to identify which flow regime applies, so that the appropriate method can be applied. In principle, the time-of-flight measurement might be used to this end, but such a method may be relatively slow to detect the correct flow regime or to detect changes in the flow rate. Faster results may be obtained, for instance, via anemometry, as shown in Fig. 7C. In this case, the electrical resistance value of the steady-state heater of the calorimetric sensor of Fig. 7A is used to infer the approximate flow rate regime (the higher the flow rate, the higher the cooling of the heater and thus lower the electrical resistance of the heater biased at a constant voltage). Anemometry requires temperature compensation via an ambient and/or fluid temperature sensor, and in general has a higher error than each of the two methods mentioned above. However, it is ideally suited to provide a quick estimation of the flow rate regime. Further, it does not need its own independent heater(s) and temperature sensor(s), since the steady-state heater used for calorimetry can also be used for the anemometry calculation. The temperature compensation can be performed using a temperature sensor used to approximate the fluid temperature (e.g., from the time-of-flight system), and, optionally, an ambient temperature sensor. As shown in the Fig. 7C, the resistance of the steady-state heater varies according to the fluid velocity AND the ambient temperature (affecting the fluid temperature), and multi-dimensional relationships between the heater resistance, flow rate and ambient/fluid temperature may be defined a priori using lab tests. Once an appropriate temperature compensation relation is established, it can be used to estimate the fluid flow rate in an approximate manner (error ~ ±6% of full scale) as shown in Fig. 7C.

The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the disclosure. As used herein, the singular forms “a,” “an,” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises” and/or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.

The corresponding structures, materials, acts, and equivalents of all means or step plus function elements in the claims below are intended to include any structure, material, or act for performing the function in combination with other claimed elements as specifically claimed. The description of the present disclosure has been presented for purposes of illustration and description, but is not intended to be exhaustive or limited to the embodiments in the form disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the invention. The embodiments were chosen and described in order to best explain the principles and the practical application, and to enable others of ordinary skill in the art to understand the various embodiments with various modifications as are suited to the particular use contemplated.

Claims

1. A flow sensor for sensing flow through a medical infusion tube, the flow sensor comprising one or more heaters formed by one or more first electrically conductive thin-film traces and one or more temperature sensors formed by one or more second electrically conductive thin-film traces, the one or more heaters and the one or more temperature sensors being provided on a flexible polymer substrate, the flow sensor being configured to be connectable to an outer surface of the medical infusion tube such that the flexible polymer substrate conforms to the outer surface of the medical infusion tube; wherein at least one of the one or more heaters is arranged to cover a substantial part of a circumference of the medical infusion tube, preferably at least 10 %, more preferably at least 25 %, even more preferably at least 50 %, most preferably at least 90 % of the circumference of the medical infusion tube; and/or wherein at least one of the one or more temperature sensors is arranged to cover a substantial part of a circumference of the medical infusion tube, preferably at least 10 %, more preferably at least 25 %, even more preferably at least 50 %, most preferably at least 90 % of the circumference of the medical infusion tube.

2. The flow sensor as claimed in claim 1, wherein the one or more heaters have a resistance of at least 20 Q, preferably 50-200 Q; and/or wherein the one or more temperature sensors have a resistance of at least 100 Q, preferably 100-1000 Q.

3. The flow sensor as claimed in claim 1 or 2, wherein a power dissipation of the one or more temperature sensors is at least a factor 10, preferably at least a factor 20, more preferably at least a factor 40, even more preferably at least a factor 100 higher than a power dissipation of the one or more heaters.

4. The flow sensor as claimed in any one of the preceding claims, wherein the flexible polymer substrate has a thermal conductivity of less than 5 W/(m K), preferably less than 1 W/(m K), more preferably less than 0.5 W/(m K).

5. The flow sensor as claimed in any one of the preceding claims, wherein the flexible polymer substrate has a thickness of less than 500 pm, preferably between 10-200 pm, more preferably between 25-100 pm.

6. The flow sensor as claimed in any one of the preceding claims, wherein the flexible polymer substrate has a bending radius of less than or equal to 2 mm and/or a Young’s modulus of less than 5 GPa.

7. The flow sensor as claimed in any one of the preceding claims, wherein the flexible polymer substrate is a wall of the medical infusion tube.

8. The flow sensor as claimed in any one of the preceding claims, wherein, in use, a part, preferably a centre, of at least one of the one or more temperature sensors is separated from a centre of at least one of the one or more heaters by at least 90°, preferably at least 120°, more preferably at least 150°, even more preferably about 180°, along a circumference of the medical infusion tube.

9. The flow sensor as claimed in any one of the preceding claims, wherein the one or more heaters comprise a plurality of heaters circumferentially arranged around the medical infusion tube.

10. The flow sensor as claimed in any one of the preceding claims, wherein the one or more temperature sensors comprise a plurality of temperature sensors circumferentially arranged around the medical infusion tube.

11. The flow sensor as claimed in any one of the preceding claims, wherein the flow sensor is configured to use the one or more heaters and the one or more temperature sensors to perform a first flow measurement based on a first flow measurement technique and a second flow measurement based on a second flow measurement technique, different from the first flow measurement technique.

12. The flow sensor as claimed in claim 11 , wherein the first flow measurement technique is a time-varying flow measurement technique and/or wherein the second flow measurement technique is a steady-state flow measurement technique.

13. The flow sensor as claimed in claim 11 or 12, wherein the flow sensor comprises a first heater upstream from one or more first temperature sensors and a second heater downstream from the one or more first temperature sensors, wherein the first heater and at least one of the one or more first temperature sensors are configured for use in the first flow measurement technique and wherein at least one of the one or more first temperature sensors and the second heater are configured for use in the second flow measurement technique.

14. The flow sensor as claimed in any one of the preceding claims, further comprising a second temperature sensor downstream of the second heater, and wherein the first heater and a first temperature sensor of the one or more first temperature sensors are configured for use in the first flow measurement technique and wherein a second temperature sensor of the one or more first temperature sensors, the second temperature sensor and the second heater are configured for use in the second flow measurement technique.

15. The flow sensor as claimed in any one of the preceding claims, comprising a first sensor group comprising a first heater and a first temperature sensor and a second sensor group comprising a second heater and a second sensor, wherein the first sensor group is configured for measuring flow velocities with a Peclet number smaller than 1 , preferably a first distance between the first heater and the first temperature sensor being in the range 1-2 mm, preferably about 1.5 mm, and/or wherein the second sensor group is configured for measuring flow velocities with a Peclet number larger than 1 , preferably a second distance between the second heater and the second temperature sensor being in a range 2-15 mm, preferably in a range 4-10 mm, more preferably about 7 mm.

16. The flow sensor as claimed in any one of the preceding claims, wherein the flow sensor is configured to measure a flow rates of less than 50 mL/h, preferably less than 30 mL/h, more preferably less than 10 mL/h, even more preferably less than 5 mL/h, most preferably less than 1 mL/h.

17. The flow sensor as claimed in any one of the preceding claims, wherein the medical infusion tube is a tube of an intravenous infusion system, a subcutaneous infusion system, or an epidural infusion system.

18. The flow sensor as claimed in claim 17, wherein the flow sensor is configured to regulate the flow through the medical infusion tube, preferably the flow sensor being configured to: send a control signal to the infusion system through a communication interface, the control signal configuring the infusion system to regulate the flow; or control a flow valve comprised in or connected to the flow sensor.

19. The flow sensor as claimed in any one of the preceding claims, wherein the one or more heaters and the one or more temperature sensors are provided inside a wall of the medical infusion tube, or wherein the one or more heaters and the one or more temperature sensors are provided on an outer surface of the medical infusion tube.

20. A housing comprising a flow sensor as claimed in any one of the preceding claims, wherein the housing is configured to connect the flow sensor to the medical infusion tube such that the substrate conforms to an outer surface of the medical infusion tube.

21. A housing comprising an electric circuit and, optionally, a power source, the housing being configured to be connectable to a medical infusion tube, the medical infusion tube comprising one or more heater elements and one or more sensor elements, preferably the one or more heater elements and one or more sensor elements being provided inside a wall of the medical infusion tube or on an outer surface of the medical infusion tube, the electric circuit being arranged, when connected to the medical infusion tube, to drive the one or more heater elements and the one or more sensor elements to obtain a flow sensor as claimed in any one of claims 1-16.

22. A medical infusion tube, preferably an IV-tube of an infusion system or a respiratory tube, comprising one or more heater elements and one or more sensor elements, the medical infusion tube being configured to be connectable, preferably removably connectable, to a housing as claimed in claim 21.

23. A method for determining a flow rate through a medical infusion tube, the method comprising: receiving a first signal representative of a calorimetric flow measurement; receiving a second signal representative of a time-of-f light flow measurement; determining an approximate flow rate; and determining the flow rate based on the first signal if the approximate flow rate is lower than a predetermined threshold value and determining the flow rate based on the second signal if the approximate flow rate is higher than a predetermined threshold value.

24. The method as claimed in claim 23, further comprising receiving a third signal representative of an anemometric flow measurement; and wherein determining the approximate flow rate is based on the third signal.

25. A computer program product comprising software code portions configured for, when run by a processor, executing the method steps according to claim 23 or 24.

26. A non-transient storage medium storing a computer program product according to claim 25.