PASSIVE NASAL PEEP DEVICES

Abstract

Described herein are passive nasal respiratory devices, in particular, passive nasal respiratory devices configured to achieve positive end-expiratory pressure (PEEP) in a subject wearing the device. PEEP devices may have a threshold pressure for opening during expiration. These devices may include a flap valve that opens on inhalation nested with a spring valve that opens when exhalation pressure exceeds a predetermined threshold. The device may be configured to be comfortably worn by a sleeping subject.

Claims

1. A nasal respiratory device for inducing positive end-expiratory pressure that is configured to be worn in communication with a subject's nose, the device comprising: an inspiratory valve including a flap configured to open during inhalation through the device; and an expiratory valve configured to open during exhalation through the device, the expiratory valve arranged such that the inspiratory valve component is nested in the expiratory valve, the expiratory valve including a biasing element preventing opening of the expiratory valve when a pressure across the expiratory valve is below a threshold pressure, wherein the device is configured to be worn one or both of a subject's nostrils without covering the subject's mouth.

2. The device of claim 1, wherein the expiratory valve includes a piston configured to be displaced by expiratory pressure above the threshold pressure.

3. The device of claim 2, wherein the device includes a body, a piston and a biasing element, wherein the piston is positioned between at least a portion of the cap and the body.

4. The device of claim 3, wherein the piston includes a hole configured to contain the biasing element.

5. The device of claim 3, wherein the biasing element includes a spring.

6. The device of claim 1, wherein the threshold pressure is between about 1 cm water and about 20 cm water.

7. The device of claim 1, further comprising a holdfast configured to secure the device to the subject's nose.

8. The device of claim 7, wherein the holdfast includes an adhesive.

9. The device of claim 1, wherein at least a portion of the device includes a hydrophobic surface.

10. The device of claim 1, wherein the inspiratory valve includes multiple flaps.

11. The device of claim 1, wherein the device is configured to be worn in communication with one of the subject's nostrils.

12. A positive end-expiratory pressure device configured to be worn by a subject during sleep, the device comprising: a cone-shaped body having an opening; an inspiratory valve in communication with the opening and including a flap configured to open during inhalation through the device; an expiratory valve configured to open during exhalation through the device, the expiratory valve biased to prevent opening of the expiratory valve when a pressure across the expiratory valve is below a threshold pressure; and a holdfast configured to adhesively secure the device to the subject's nose such that the cone-shaped body is at least slightly within the subject's nostril.

13. The device of claim 12, wherein the inspiratory valve component is nested in the expiratory valve.

14. The device of claim 12, wherein the inspiratory valve includes multiple flaps.

15. The device of claim 12, wherein the expiratory valve includes a piston configured to be displaced by expiratory pressure above the threshold pressure.

16. The device of claim 15, wherein the piston includes a hole configured to contain a spring.

17. The device of claim 16, wherein the expiratory valve includes a cap having a spring post that holds the spring within the hole to provide a preloaded resistance.

18. The device of claim 15, wherein the piston includes the flap of the inspiratory valve.

19. The device of claim 15, wherein the piston is displaced within at least a portion of the cone-shaped body.

20. The device of claim 12, wherein the holdfast includes a compliant material with an adhesive.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0034] The novel features of the invention are set forth with particularity in the claims that follow. A better understanding of the features and advantages of the present invention will be obtained by reference to the following detailed description that sets forth illustrative embodiments, in which the principles of the invention are utilized, and the accompanying drawings of which:

[0035] FIG. 1A and 1B shows one variations of a pair of passive nasal PEEP devices from a top and side perspective view, respectively. The device maintains substantially constant pressure throughout range of expiratory flow, while remaining comfortable. The device used by a particular patient may be chosen to correspond to a patient's titrated CPAP level, as discussed below.

[0036] FIG. 2 is a graph illustrating the pressure/flow profile for a variation of a passive nasal PEEP device similar to that shown in FIGS. 1A and 1B.

[0037] FIG. 3 shows a side view of the cap end region of a device similar to the variation shown in FIGS. 1A and 1B.

[0038] FIG. 4 shows a bottom perspective view of the cap end region of a device similar to the variation shown in FIGS. 1A and 1B.

[0039] FIG. 5 shows a top perspective view of the piston region of a device similar the device shown in FIGS. 1A and 1B.

[0040] FIG. 6 shows a side view of the piston region of a device similar to that shown in FIGS. 1A and 1B.

[0041] FIG. 7 shows a bottom perspective view of the piston region of a device similar the device shown in FIGS. 1A and 1B.

[0042] FIG. 8A shows a side perspective view of a cut-away section of a body region of a passive nasal PEEP device as illustrated in FIGS. 1A and 1B. FIG. 8B is a section through the body region of the passive nasal PEEP device.

[0043] FIG. 9A shows a top perspective view of another variation of a passive nasal PEEP device configured to be placed over both of a subject's nostrils (a whole nose configuration).

[0044] FIG. 9B shows an exploded view of the various components of the device shown in FIG. 9A.

[0045] FIG. 10 illustrates a variation of a device included on (or in some variations integral with) a nasal mask.

DETAILED DESCRIPTION

[0046] The passive nasal PEEP devices described herein may be used to create positive end expiratory pressure during respiration (PEEP) effect in a subject wearing the device are described. These respiratory devices are referred to as passive nasal PEEP devices or simply as devices. The devices and methods described herein may be useful to treat a variety of medical disease states, and may also be useful for non-therapeutic purposes. The devices and methods described herein are not limited to the particular embodiments described. It is also to be understood that the examples and particular embodiments described are not intended to be limiting.

[0047] As used in this specification, the singular forms a, an, and the include plural reference unless the context clearly dictates otherwise. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art.

[0048] As used herein a passive nasal device is one that does not require the addition of a pressurized source of respiratory gas to operate as described (e.g., to apply PEEP and limit exhalation more than inhalation).

[0049] FIGS. 1A and 1B illustrate one variation of a pair of passive nasal PEEP devices 101 that may be placed over (and slightly into) a subject's nostrils in order to inhibit exhalation more than inhalation and create PEEP within the subject. The device shown in FIG. 1A and 1B includes an adhesive holdfast 105, a cone or body region 105 that is capped with the outer cap 107 (having a spiral pattern) that prevents the valves (both the inhalation flap valve that is nested within the exhalation spring or post valve) from leaving the cone or body region. The holdfast extends from body in a direction that is perpendicular to the path air takes through the body. As is apparent in FIG. 1B, the body region 103 or cone extends past the holdfast, and may extend into the nostril(s) of the wearer. The overall thickness of the body region is limited to less than a cm (e.g., less than 0.8 cm, less than 0.7 cm, less than 0.6 cm, less than 0.5 cm, etc.), but the thickness is sufficient for the expiratory valve of the airflow resistor to be displaced if the expiratory pressure exceeds the threshold value, and for the inspiratory valve to open during inhalation without interference (e.g., from nose hairs, nasal tissue, etc.). FIG. 2 illustrates the resistance through exemplary devices as described herein during exhalation. The first line 203 (Flap Valve) shows a device that is not configured as a PEEP valve having a single passive nasal airflow resistor (in this example, having flap valves). The device opens immediately, and the flow increases with pressure towards a linear slope (with flow increasing as pressure increases). In contrast the Eagle 8 201 and Eagle 13 202 devices are passive nasal PEEP devices that have opening thresholds of 8 and 13 cm H.sub.2O, respectively. As pressure increases in these devices, flow is zero until the threshold, then flow increases dramatically (exponentially) as pressure increases.

[0050] Any of the valves described herein can also be placed on a mask that fits on the nose or on a mask that fits on the nose and mouth. Such a mask may be held onto the head by adhesive or alternatively with straps or the like. Such a mask may be reusable or disposable by the patient. For example, FIG. 10 illustrates a mask-type nasal device 1000 including a passive nasal PEEP airflow resistor 1011 as described herein. In some variations the valve 1011 is integral to the mask1012 . In some variations the valve includes an adhesive holdfast that could be applied directly to a subject's nose, but is instead secured over a reusable nasal mask having one or more opening(s) to position the nasal device over the subject's nostril(s).

[0051] FIGS. 3 through 8B illustrate various component parts of a nasal PEEP device such as the one shown in FIG. 1A. Any of the devices described herein may include some or all of these component parts. FIGS. 3 to 8B illustrate the cap region, piston, and body which form the PEEP-type (a passive PEEP valve) that can be adhesively secured to the nose. The PEEP valve may include a spring (not visible in the figures) that can couple to the post and provide the preloaded resistance that is overcome by expiratory resistance above a predetermined level; above this threshold, the cap allows the passage expiratory airflow by displacing all or a portion of the cap. An internal flap valve may be included and arranged so that it can be opened by inhalation (allow easy inhalation) but closed during exhalation; above a threshold expiratory pressure the flap valve may remain closed while the cap or other regions of the body open to allow expiratory airflow. Below the threshold expiration may be limited.

[0052] Thus, in FIGS. 3 and 4, a cap portion is shown in side and side perspective views, respectively. The cap may mate with the body region (shown in FIGS. 8A-8B), over a piston region (shown in FIGS. 5-7). The cap may have a thickness, e.g. of around 1 mm (e.g., between 0.8 mm and 1.5 mm, e.g., 1.2 mm) which may provide a relatively stiff support. The cap may include rib notches 402 for mating with ribs (e.g. on the piston). The corners 407 forming the notches may act as bearing surfaces for displacement of the cap during operation (above the cracking threshold of expiratory pressure). A spring post 406 is included which may hold the spring within the assembly including the body and the cap region. The spiral shapes 409 may be configured so inhalation (inspiration) through the assembly may be only minimally impeded during operation. For example, the spiral shapes shown add only about 0.05 cm H.sub.2O to the inspiratory resistance at 300 mL/s flow. This may be contrasted with the somewhat larger resistance when using one or more straight crossbars. In operation, this cap member may be displaced to allow expiration through the device above the threshold expiratory pressure.

[0053] FIGS. 5-7 illustrate the piston member that may be held between the cap and the body. As illustrated in FIG. 5, the piston may include a spring hole 503, and surrounding male bearing surfaces 507 (which may mate with the cap bearing surfaces 407. The ribs 505 may extend from the spring hole and support the edge region, and may also form a support for the internal flap valve (not shown). The flap valve may overlap enough so as not to blow through (e.g., by removed from) the device during exhalation; the surface of the piston may provide sufficient contact with the flap so that it can seal against the surface during exhalation, and there is sufficient clearance so that the flap valve can open upon inhalation.

[0054] For example, in FIG. 6, the piston includes a flap valve (flapper) seat 605. This seat may be curved. Curving the seat may enhance the seal and may reduce undesirable vibration during operation. The piston may also include a piston valve seat region 609, and a spring cylinder (which may house a spring, not shown, providing the biasing force).

[0055] FIG. 7 shows a bottom view of the piston. As shown, two of the ribs 702 may be made as thin as possible (e.g. 0.4 or 0.5 mm), while the horizontal ribs 704 may be thicker; in some variations the flap valve may bend along the horizontal ribs. The surface 709 may form part of the piston valve seat.

[0056] FIG. 8A shows a partially cut-away side view of the body portion of the assembly, which may form a passage to be placed in communication with a nostril. In this example, the body includes a cannula attachment region 808; the cannula may be used to sample the pressure within the device during operation (and/or the pressure within the nostril). The body may be connected to the adhesive holdfast (not shown), e.g., on a shelf around the body 809. The cone shape may include a journal region 805 to increase stiffness of the cone region. In FIG. 5, flap valve folding guides 801, 803 are also shown to help guide folding/bending of the internal flap valve.

[0057] FIG. 8B shows a side cross-section through the assembly, including the body 811, the piston, 813, and the cap 812. A spring or other biasing member (not shown) may be positioned in the assembly in the biasing region 815. A flap valve (not shown) may also be positioned within the assembly 819 so that it can open during inhalation and close during exhalation.

[0058] Finally FIGS. 9A and 9B illustrate a whole-nostril variation. In FIGS. 9A (closed during exhalation at low pressure) and 9B (showing an exploded view), the device is adapted with a central release region that is biased to open during exhalation above the threshold. The release region includes a housing 901 with a bias (spring) 903. The housing may be reusable, e.g., by replacing the adhesive holdfast and flap regions 905.

[0059] In the exploded view of FIG. 9B, the housing includes a cover (polymeric region 911), a bias 903 (e.g., spring), a pressure plate 914, and an upper cover base 916 and a lower cover base 918. The whole-nose (e.g., both nostrils) apparatus may also include a holdfast 920 that includes an adhesive and may also include an adhesive backing (e.g., foam, etc.), a flap layer 922 (e.g., polyethylene) with one or more cut-out flaps, and a flap restricting layer or limiting layer 924 that prevents the flaps from opening during exhalation. The entire device may be configured so that exhalation pressure from either or both nostrils may be sufficient to open the release valve above a threshold pressure. In any of the whole-nose variations the nested valve (including the bias within the housing) may be centrally located between, or otherwise in communication with, both nostrils. In some variations multiple nested valves may be used, e.g., each positioned over a nostril region.

[0060] As mentioned above, in any of these variations the device may be used with a mask, rather than directly attaching to the nostril. For example, FIGS. 3 and 4 show components that may be used to form a cap region of some variations of the device. In some variations the device includes a cap region.

Threshold Pressure

[0061] In some embodiments, a pre-loaded spring (forming part of the expiratory valve of the airflow resistor) selectively restricts the opening of the expiratory valve. Expiratory flow is possible only when the pressure of the patient's airstream exceeds the cracking pressure of the valve. Selection of a spring that has a large preload distance relative to maximum valve displacement ensures that the expiratory pressure provided to the patient stays close to constant as airflow increases, instead of the pressure increasing significantly with increasing pressure. A ratio of preload distance to maximum valve displacement between 2:1 to 8:1 has been found to be effective for this purpose. The spring may be a compression spring, extension spring, or torsion spring. Other embodiments utilize magnets, rather than springs, to provide an expiratory threshold valve.

Inspiratory Resistance

[0062] In some embodiments, the inspiratory and expiratory valves are nested, rather than acting in parallel. Nesting both the inspiratory and expiratory valves increases the cross-sectional area available to each valve. (If the valves are acting in parallel, an increase in the cross-section area occupied by one valve reduces the area available for the other valve). Increasing the cross-sectional areas for the inspiratory valve is important because higher cross-sectional area enables lower inspiratory resistance. Minimizing inspiratory resistance of the inspiratory valve is important, as this can be the major contributor to inspiratory resistance of the entire device. Minimizing inspiratory resistance of the device is critical, as this minimizes the pressure drop across the device during inspiration, thereby causing a sleep apnea patient's airway pressure to be less negative, and therefore less likely to collapse. Also, increasing the cross-sectional area available for the expiratory valve is important because it increases the force of spring that can be used to achieve a given threshold pressure. This enables use of a stiffer, easier to manufacture spring.

[0063] Moisture frequently condenses on the inner surfaces of PEEP valve devices. This moisture can be present between the inspiratory valve flapper and the valve seat of the piston, and it can increase the pressure required to open the inspiratory valve. In some embodiments, the side of the flapper facing the valve seat of the piston, and the valve seat of the flapper, have a hydrophobic surface. These hydrophobic surfaces may be attained by high surface roughness, by a low surface energy coating, or other means.

Device Thickness

[0064] Minimizing the distance that the device protrudes out of the nostrils may be important for several reasons: minimizing the visual presence of the device, in order to make it less obtrusive and more acceptable for users; reducing the likelihood that the device will rub against other objects such as a pillow during sleep; and reduce the likelihood that the device would contact a male patient's facial hair.

[0065] In some embodiments, the housing for the compression spring in the piston extends beyond the plane of the valve seat, and protrudes into the nose cone of the body. Positioning the spring in this way, instead of placing the spring so its full length extended above the piston's valve seat, and did not protrude into the nose cone of the body, enables the overall device height to be reduced.

[0066] In some embodiments, the piston, body, and endcap components are made from a high stiffness plastic. High stiffness plastics that could be selected for these parts include Vectra liquid crystal polymer, polyether ether ketone, carbon filled nylon, and glass filled nylon. In other embodiments, the piston, body, and endcap components are made from a metal. Aluminum or stainless steel alloys could be selected for these parts.

Seal at Low Expiratory Flow

[0067] To maintain positive pressure in the airway, during end-expiratory pause, it is desirable for the device to maintain a therapeutic level of pressure at low expiratory flow rates.

[0068] In some embodiments, the inspiratory valve flapper is an elastomer. A highly compliant elastomer that is capable of significant strain before plastic deformation occurs, is well suited for this application. Such a material helps insure that the inspiratory valve flapper will not be deformed (for example, during assembly), which could cause a leak path between the flapper and the valve seat of the piston, and thus prevent adequate pressure from being maintained at low expiratory flow rates.

[0069] In some embodiments, the inspiratory valve flapper is adhered to the piston with an adhesive that has a negligible or low shrinkage rate. Shrinkage of the adhesive for this joint could distort the surface of the flapper and cause leakage paths. In other embodiments, the inspiratory valve flapper is retained from translating during inspiration by a retaining feature or part. In these embodiments, no adhesive contacts the inspiratory valve flapper.

[0070] In some embodiments, the inspiratory valve flapper has an interference fit with the piston's spring cylinder. This overlap may impart residual stresses in the flapper that bias it to a closed position. In other embodiments, the inspiratory valve flapper does not have an interference fit with any other parts. The lack of interference fit may reduce distortions to the flapper and reduce leak paths at low flow.

[0071] In some embodiments, the piston's valve seat is not flat. In some embodiments, the valve seat has an arc along the major axis. In this embodiment, the curvature of the piston's valve seat prevents a leak path from being exposed when the ends of inspiratory valve flapper bend due to gravity. In other embodiments, the valve seat has an arc along the minor axis. This curvature reduces the magnitude of bending of the inspiratory valve flapper along the major axis due to gravity, thus reducing the potential leak path.

Nasal Cannula Attachment

[0072] It is desirable for the nasal PEEP valve device to be able to integrate with a nasal cannula, in order to facilitate monitoring of nasal pressure during a sleep study.

[0073] The nasal cannula compatible embodiment of the body contains a housing for connecting to nasal cannula tubing, and a passageway with fluid communication between the housing and the inner surface of the nose cone, which is in constant fluid communication with the patients nasal passage when the device is in use. This enables the measurement of intranasal pressure. Measurement of intranasal pressure provides accurate data on the pressure delivered to the patient during expiration, whereas other potential measurement systems may not output the actual pressure delivered to the patient. Additionally this system provides accurate data on the pressure drop across the device during inspiration which may be helpful for healthcare practitioner to monitor.

[0074] In some embodiments, the tubing housing of the nasal cannula compatible body and the passageway to the inner surface of the nose cone are not concentric. This avoids adding unnecessary height to the body's valve seat, thus enabling the overall height of the device to be minimized.

[0075] It is important for the facial adhesive to be easy to apply for the patient. Even with nasal cannula tubing extending from the nasal PEEP valve device, it must be easy to achieve a good seal with the facial adhesive. In order to accomplish this, in some embodiments the housing for the nasal cannula tubing is angled between the major and minor axes of the device. In other embodiments, the housing for the nasal cannula tubing is angled towards the endcap (and away from the nose cone), in order to provide the patient with more space in which to apply the facial adhesive.

Noise

[0076] It is important for the device to make as little noise as possible during use, in order to avoid disturbing the patient and their bed partner.

[0077] The flapper alignment guides in the nose cone of the body restrict the bending of the inspiratory valve flapper during inspiration. The presence of these guides greatly reduces vibration and noise during inspiration.

Nose Cone Stiffness

[0078] During use, the nose cone of the body sits in the patient's nostrils. It is desirable for the nose cone to have as thin walls as possible, in order to maximize the cross-sectional area of the nose cone. On the other hand, it is desirable for the nose cone to be stiff and for it to be resistant to plastic deformation. To address this, in some embodiments of the nose cone there is a beam across the minor axis connecting the two sides of the cone. This provides a stiff, deformation-resistant cone with thin walls.

Stiction Between Piston and Body

[0079] Moisture frequently condenses on the surface of the piston's valve seat and the body's valve seat. It is possible for such condensation to cause stiction at the beginning of expiration, which causes the patient for experience a popping sensation. It is desirable to minimize or eliminate this effect.

[0080] In some embodiments, the contact surface area of the body's valve seat is minimized. In some embodiments, the contact surface is a rim with a sharp angle, approximating a line contact. In other embodiments, the contact surface is a series of small nubs that protrude above the surface of the rest of the body's valve seat.

[0081] In some embodiments, piston's valve seat and the body's valve seat are constructed to be hydrophobic. This results in less water adhering to the surfaces, as well as weaker water-solid interactions. Two methods that may be used to make these surfaces hydrophobic are application of a rough surface finish and application of a low surface energy coating.

[0082] In some embodiments, a compliant element allows one side of the piston's valve seat to open before the other, reducing the stiction force that must be overcome at a given instant in time.

Binding in Bearing

[0083] In some iterations of the device, binding in the bearing between the piston and the endcap caused an uneven exhalation with the sensation of popping

[0084] In some embodiments, a circular bearing is used (rather than a square bearing, for example), to reduce the chance of bearing binding due to rotation.

[0085] In some embodiments, the male bearing surface of the piston and female bearing surface of the endcap are constructed to have a low coefficient of friction.

[0086] In some embodiments, the male bearing surface of the piston is tapered, providing greater play when less of the bearing surface is engaged.

[0087] In some embodiments, there is a large pathway providing fluid communication between the outside of the device and the inner wall of the body, providing expiratory flow a pathway to directly exit the device after passing through the expiratory valve. This may reduce the proportion of the moist expiratory airflow that passes over the bearing, and thereby reduce the water deposited on the bearing.

Combination Therapy

[0088] In some methods of treatment of sleep disordered breathing patients with nasal PEEP valves, a means to restrain the patients mouth in a closed position, such as a chin strap, is used in conjunction.

Patient Selection

[0089] In some methods of treatment of sleep disordered breathing patients with nasal PEEP valves, patients are selected for this therapy based on nasal resistance screening or upper airway resistance screening.

Oral-Nasal Therapy

[0090] In some embodiments and methods, a threshold valve through which inspiration is less restricted than expiration, is applied to either the nose or mouth, and the other is sealed to prevent air leaks.

[0091] In other embodiments, a threshold valve through which inspiration is less restricted than expiration, is applied to both the nose and mouth.

Auto-Titrating PEEP Valve

[0092] In some embodiments and methods, a threshold valve for treating sleep disordered breathing comprises: a sensor, an actuator, an adjustable expiratory valve, and an inspiratory valve. In these embodiments and methods, the threshold valve would continually adjust the expiratory pressure delivered to the patient, based on the information received by the sensor related to the efficacy of the treatment. Among the advantages of an auto-titrating PEEP valve are:

[0093] The ability for a patient to have customized therapy delivered to treat their sleep disordered breathing. The ability for a patient to receive varying levels of pressure over the course of a night. At any time, the patient would receive no more pressure than necessary, thereby minimizing discomfort.

[0094] Additionally, some embodiments and methods of the auto-titrating PEEP valve have a ramp function, whereby pressure is reduced while the patient is attempting to fall asleep, and subsequently increased once the patient is asleep. In some embodiments, a timer is used to support the implementation of this ability. In other embodiments, a sensor to detect whether the patient is sleeping is used.

Diagnostic Devices

[0095] It may also be desirable to titrate the appropriate pressure to use in treating sleep disordered breathing using a threshold valve.

[0096] In some embodiments and methods, a threshold valve can be adjusted to provide multiple pressure settings.

[0097] In some embodiments and methods, the pressure settings are adjusted manually, by moving part of the device while it is attached to the patient. For example, a sleep technician can rotate a knob on the device, thereby changing the preload of a spring, and adjusting the expiratory threshold pressure. In other embodiments and methods, the pressure settings can be adjusted without physically touching the device, thereby avoiding waking the patient up. For example, the sleep technician can select a pressure from a digital interface, and this pressure is communicated to the device via wires or wirelessly. The device contains a microcontroller and adjusts the expiratory threshold pressure in accordance to the new input signal.

[0098] In some embodiments and methods, the pressure settings are discrete. In others, pressure settings cover a continuous range.

[0099] In some embodiments and methods, a respiratory support device that provides active pressure delivers expiratory positive airway pressure (EPAP) to a patient, in order to titrate the pressure needed for a threshold expiratory valve to treat sleep disordered breathing.

[0100] In some embodiments and methods, an auto-titrating threshold valve is used for titration of sleep disordered breathing patients.

[0101] As used herein in the specification and claims, including as used in the examples and unless otherwise expressly specified, all numbers may be read as if prefaced by the word about or approximately, even if the term does not expressly appear. The phrase about or approximately may be used when describing magnitude and/or position to indicate that the value and/or position described is within a reasonable expected range of values and/or positions. For example, a numeric value may have a value that is +/0.1% of the stated value (or range of values), +/1% of the stated value (or range of values), +/2% of the stated value (or range of values), +/5% of the stated value (or range of values), +/10% of the stated value (or range of values), etc. Any numerical range recited herein is intended to include all sub-ranges subsumed therein.