ASSISTIVE MESH

CROSS-REFERENCE TO RELATED APPLICATIONS The present application claims the priority benefit of U.S. Provisional Patent Application

Serial No. 62/237, 185, filed October 5, 2015, entitled "System and Method for Implantable Electroactive Polymer Heart Assistive Mesh," incorporated by reference in its entirety herein.

BACKGROUND OF THE INVENTION

Field of the Invention

The present invention relates to a cardiac assist device. More particularly, the present invention relates to use of electroactive polymers and a metallic mesh to assist in ventricular contraction. Description of Related Art

Cardiovascular disease affects more than 1 million people each year in the United States, and represents the leading global cause of death, killing more than 17 million people worldwide annually. Ventricular assist devices (VADs) are commonly used to prevent heart failure caused by cardiovascular disease. VADs are mechanical circulatory support devices used to assist a failing heart perform cardiac functions, including left ventricular assist devices (LVADs), right ventricular assist devices (RVADs), and biventricular assist devices (BiVADs). These devices use pumps placed inside a patient's chest and employ a pneumatic or external fluid-flow pumps to continuously circulate blood collected from the weakened ventricle(s) to either the pulmonary artery or aorta. However, VADs can have adverse effects on a patient, including subjecting the patient to an increased risk of stroke, infection, internal bleeding, and failure by the non-treated ventricle because, among other reasons, VADs can't accurately mimic the heart's natural pumping mechanics. Moreover, VADs are prone to early failure, thus contributing to a high mortality rate for patients receiving VAD treatment.

Alternative procedures include cardiomyoplasty such as grafting healthy skeletal muscle taken elsewhere from the body to the heart, or using gene therapy to reverse cardiac muscle damage and restore ventricular function. However, native skeletal muscle grafts lacks long-term fatigue resistance, and cardiac gene therapy, although promising in theory, has had limited success in practice.

In extreme cases, a patient may require a complete heart transplant. However, such a transplant is often delayed until a donor heart becomes available, making heart transplantation nonviable for many patients.

Recently, "artificial muscle" electroactive polymers (EAPs) have emerged for use in biomedical devices due to their compliancy, built-in sensing and actuation capabilities, and similarities to biological muscles. EAPs are polymers whose shape is changed under electric stimuli, such as voltage or current. Because EAPs exhibit a high energy density similar to that of human muscles, EAPs have emerged as good candidates for actuators in biomedical devices. Moreover, the strain-dependent impedance of EAPs also makes them good candidates for use as sensors in biomedical devices.

However, EAPs have limitations when used in cardiac assist applications. First, dielectric elastomer (DE) type EAPs require high activation voltages— sometimes up to 4 kV or even higher. And because known DE-type EAPs aren't properly insulated, use of such EAPs in biomedical devices— including use in cardiac applications— presents a risk of electric shock to the patient. Also, known DE-type EAPs don't exhibit contraction and relaxation frequencies approximating a person's heartbeat. These EAPs accordingly can't achieve a sufficient beating frequency necessary for use in cardiac applications. Finally, cardiac assist devices employing EAPs don't mimic the heart's natural pumping mechanics including the natural "wringing" or "twisting" of the heart used to ensure blood flows upwards toward the aortic and pulmonary valves.

Thus, there remains a need for an EAP that is well-insulated from its surroundings and which exhibits contraction/relaxation frequencies and/or pumping mechanics that closely approximate a person's typical heartbeat for use in cardiac applications.

SUMMARY OF THE INVENTION

The present invention is broadly concerned with an EAP actuator useful for biomedical applications, and, more particularly, with a cardiac assist device employing such an EAP actuator used to assist with ventricular contraction. For example, aspects of the invention are directed to an EAP actuator for use in biomedical applications that includes a dielectric elastomer film with a metallic mesh embedded therein. The EAP actuator also includes a plurality of electrodes, each coating a respective major surface of the dielectric elastomer film. The EAP actuator is electrically insulated from its surroundings and thus useful in biomedical applications.

Other aspects of the invention are directed to a cardiac assist device employing such an EAP actuator. The cardiac assist device includes a power source and a sleeve configured to substantially surround a heart that is electrically connected to the power source. The sleeve is electrically insulated from its surroundings and thus useful in biomedical applications and, more particularly, in cardiac applications.

Still other aspects of the invention are directed to a method of contracting a heart using such a cardiac assist device. In some aspects, the EAP actuator is electrically connected to the power source in such a way that a first portion of the cardiac assist device is contracted separate from a second portion of the cardiac assist device. In this regard, the different portions can be contracted sequentially and at a frequency that mimics the pumping function of a human heart.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention are described in detail below with reference to the attached figures, wherein:

Figure (Fig.) 1A is a general DE-type actuator, and Fig. IB is the DE-type actuator of Fig. 1 A in an activated, or contracted, state;

Fig. 2 is a novel EAP actuator according to one embodiment of the invention;

Fig. 3 is the EAP actuator shown in Fig. 2 in an activated, or contracted, state;

Fig. 4 is a cardiac assist device employing the EAP actuator shown in Figs. 2 and 3;

Fig. 5 is a bottom view of the cardiac assist device shown in Fig. 4;

Fig. 6 is another embodiment of a cardiac assist device employing the EAP actuator shown in Figs. 2 and 3;

Fig. 7 is a bottom view of the cardiac assist device shown in Fig. 6;

Fig. 8 is another embodiment of a cardiac assist device employing the EAP actuator shown in Figs. 2 and 3;

Fig. 9 is a bottom view of the cardiac assist device shown in Fig. 8; and

Fig. 10 is another embodiment of a cardiac assist device employing the EAP actuator shown in Figs. 2 and 3. DETAILED DESCRIPTION

The present invention is concerned with a non-invasive, cardiac assist device configured to surround a person's heart and mimic natural cardiac muscle contraction. The cardiac assist device takes the natural form of the heart's geometry and prevents or reduces further enlargement of a failing heart. The cardiac assist device also has a novel insulating electric shield, making it ideal for implantation within a patient.

Figs. 1A and IB depict a DE-type actuator 100 as one example of a known EAP. The DE-type actuator 100 includes a dielectric elastomer film 106, which is a soft elastomer material such as silicone. The dielectric elastomer film 106 is coated on both sides with compliant electrodes 102 and 104. The electrodes 102 and 104 are connected to a circuit (not shown). When a DC voltage is applied to the electrodes 102 and 104— i.e., when a voltage is applied to one of the two electrodes 102 and 104 and the other electrode is grounded— the dielectric elastomer film 106 contracts in the thickness direction, as depicted by arrows 108 and 110, and, accordingly, expands in the film-plane direction, i.e., a direction transverse to the direction of contraction, as depicted by arrows 112, 114, 116, and 118. However, because at least one of the electrodes 102 and 104 is electrically charged, the DE-type actuator 100 is ill-suited for biomedical applications because it presents a high risk of electric shock to the patient.

Fig. 2 is a cross-sectional view of a novel EAP actuator 200 that overcomes the limitations of the known DE-type actuator 100. The EAP actuator 200 includes a dielectric elastomer film 206 coated on both sides with electrodes 202 and 204. The dielectric elastomer film 206 comprises first major surface 206a and an opposing second major surface 206b. The dielectric elastomer film 206 can be any suitable electroactive polymer. For example, dielectric elastomer film 206 may be a polymer exhibiting a modulus of about 10 psi. In some embodiments, the dielectric elastomer film 206 is Polydimethylsiloxane (PDMS), an acrylic elastomer such as VHB™ available from 3M™, Silicone-rubber, or Ecoflex 00-30. A compliant electrode is coated onto the film 206 adjacent to the first major surface 206a and second major surface 206b, respectively, such that the EAP actuator 200 comprises a first electrode 202 and a second electrode 204. The first and second electrodes 202 and 204 can be any suitable conductor. For example, the electrodes 202 and 204 may be a conductive metal having a resistivity range of 2.50* 10 ^~6 to 5.00* 10 ^~6 p (Ω-m). In some embodiments, the electrodes 202 and 204 are carbon fiber, carbon black, graphite, gold leaf, or carbon grease. Moreover, the electrodes 202 and 204 can be formed using any suitable coating technology including sputtering, direct thin film coating, spraying, or casting.

The EAP actuator 200 includes a metallic mesh 208 embedded within the dielectric elastomer film 206. As shown in Figs. 2 and 3, in some embodiments the metallic mesh 208 is disposed substantially at a center of the dielectric polymer in the thickness direction; i.e., the mesh 208 is disposed at a portion of the dielectric elastomer film 206 equidistant from each of the first and second major surfaces 206a and 206b. Although not shown, in other embodiments the metallic mesh 208 may be disposed in the dielectric elastomer film 206 such that it is located nearer to one of the two major surfaces 206a and 206b than the other. The metallic mesh 208 can be any suitable conducting material. For example, in some embodiments the metallic mesh 208 is composed of a shape-memory alloy displaying a large strain rate (i.e., superelasticity) such as nickel -titanium alloy (NiTi). More particularly, in some embodiments the metallic mesh 208 is constructed of NiTi that is 50-500 μπι thick, and composes 55-60% Ni by weight. In other embodiments, the metallic mesh 208 may comprise, e.g., a metallic mesh fabric (a composite of a metallic substance and nylon), Terfenol-D, a copper-aluminum-nickel alloy, a copper-zinc- aluminum alloy, an iron-manganese-silicon alloy, or Nitinol.

In some embodiments, the EAP actuator 200 further includes first and second insulating layers 210 and 212, adjacent to first and second electrodes 202 and 204, respectively. Insulating layers 210 and 212 may be a Polytetrafluoroethylene (commonly known as Teflon™) dielectric coating. In other embodiments, insulating layers 210 and 212 may be any suitable dielectric coating such as, e.g., PDMS, VHB™, Silicone-rubber, or Ecoflex 00-30.

As best understood with reference to Fig. 3, during use the metallic mesh 208 is connected to a power source 306 (e.g., a 4 kV, direct current power source) and the electrodes 202 and 204 are each connected to ground 308. The power source 306 necessary to provide the appropriate contraction forces for biomedical applications is a relatively high voltage (e.g., approximately 4 kV) but low power source (e.g., approximately 88 mW) power source. Thus, the EAP actuator 200 is relatively efficient as compared to known biomedical actuators such as ionic EAP actuators. Moreover, because both of the electrodes 202 and 204 are connected to ground 308— unlike the DE-type actuator 100, where one of the electrodes 102 and 104 is connected to a voltage source— the EAP actuator 200 is electrically shielded from its surroundings. The EAP actuator 200 is thus poised for use in biomedical devices, particularly for use in cardiac applications, because the electric shielding reduces the risk of electric shock to a patient's surrounding tissue as compared to known DE-type actuators 100. And in embodiments coated with, e.g., Teflon™, the additional insulating layers 210 and 212 provide a second protection layer against electric shock, further poising the EAP actuator 200 for use in biomedical applications.

The voltage applied to the metallic mesh 208, together with the grounded electrodes 202 and 204, creates respective electric fields between the metallic mesh 208 and each electrode 202 and 204. In response, the dielectric elastomer film 206 contracts in the thickness direction, i.e., a direction depicted by arrows 302. Relatedly, the dielectric elastomer film 206 expands its surface area in the film-plane direction, i.e., a direction transverse to the thickness direction, as depicted by arrows 304. In this regard, the EAP actuator 200 is useful as an actuator or sensor in biomedical devices while providing a reduced risk of electric shock. Namely, the contraction and expansion of the EAP actuator 200 can be used to, e.g., contract a heart (described in more detail below). Moreover, because the EAP actuator 200 is electrically shielded from its surroundings, and because in some embodiments the EAP actuator 200 is further insulated by insulating layers 210 and 212, the EAP actuator 200 can be implanted in a patient's body without risking damage to the surrounding tissue.

For example, and turning now to Fig. 4, in some embodiments the EAP actuator 200 is utilized in a cardiac assist device 400. The cardiac assist device 400 includes a sleeve 404 configured to substantially surround a person's heart 402. The sleeve 404 is substantially composed of an EAP similar to the EAP actuator 200 discussed in connection with Figs. 2 and 3. For example, the sleeve 404 may include a dielectric elastomer film 406 and a metallic mesh 408 disposed therein. For ease of illustration, the metallic mesh is shown in Figs. 4-10 as being on top of the dielectric elastomer film so that the pattern of the metallic mesh is visible. In practice, however, the metallic mesh would be embedded within the dielectric elastomer film as described in connection with Figs. 2 and 3.

In some embodiments, the cardiac assist device 400 is constructed using nano-fiber fabrication techniques to fabricate the sleeve 404 coated with multiple layers of insulating Teflon and electric shielding layers. And in some embodiments, the cardiac assist device 400 is constructed using 3D printing and casting methods. For example, using an MRI image of a patient's heart 402, a 3D printer is used to print a model heart. A cast of the model heart is formed, and, using the cast as a mold, the cardiac assist device 400 is fabricated by layering a dielectric elastomer and metallic mesh around the mold. For example, a first layer of the dielectric elastomer is layered on the mold, followed by the metallic mesh 408, and then a second layer of the dielectric elastomer. The first and second layers of the dielectric elastomer together form the dielectric elastomer film 406 with the metallic mesh 408 embedded therein. The dielectric elastomer film 406 is coated on either side with a suitable electrode material and, finally, an insulating material such as Teflon™. The insulating layers may be applied using any suitable process and, in some embodiments, is applied using hot press sealing, solution casting methods, or spraying.

The cardiac assist device 400 is implanted in a patient's body such that it substantially surrounds a person's heart 402. Specifically, an open end 410 of the cardiac assist device 400 receives the right and left ventricles of the heart 402 and the device is moved upward (i.e., moved in a direction extending from the bottom of the heart 402 towards the top of the heart 402 as it is depicted in Fig. 4) until it substantially surrounds the right and left ventricles of the heart 402. Because, as discussed, the cardiac assist device 400 may be constructed using an MRI image of the person's heart 402, when the device is in a fully implanted position as depicted in Fig. 4, the sleeve 404 substantially conforms to the outer contours of the heart 402. During implantation, the cardiac assist device 400— and more particularly, the metallic mesh 408, as will be more fully discussed below— is electrically connected to a power source (not shown). The voltage source may be a battery located outside the patient's body and thus electrically connected to the cardiac assist device 400 using electric leads passing from an outside of the patient's body to the cardiac assist device 400 inside the body near the patient's heart 402. Or, in other embodiments, the power source may be a battery implanted in the patient's body with the cardiac assist device 400. As discussed above, the power source may be a relatively high-voltage, low- power source, such as, e.g., a 4 KV, 1 W source.

During use of the cardiac assist device 400, a voltage is applied to the metallic mesh 408 by the power source, and the electrodes are grounded. As discussed, this results in respective electric fields formed between the metallic mesh 408 and the electrodes, causing the dielectric elastomer film 406 to contract and thus assist with the pumping functions of the person's heart 402. By using, e.g., a step function, the DC voltage is oscillated on and off at a frequency mimicking the person's heartbeat, resulting in a sleeve 404 that contracts and relaxes in conjunction with the beating heart. For example, the cardiac assist device 400 may be activated and relaxed at a frequency matching the patient's heart beat, and typically in the range of 0 Hz to 3 Hz.

Unlike prior-art assist devices, the cardiac assist device 400 is composed of suitable materials to achieve a relatively high contraction/relaxation frequency, similar to the beating frequency of a human heart. Specifically, the achievable actuation frequency will ultimately depend on the stiffness properties of the dielectric elastomer film 406 and metallic mesh 408 composite. In one embodiment, the metallic mesh 408 is made of NiTi, with the dimensions of the NiTi mesh determined using, e.g., physics-based and control-oriented modeling, such that the stiffness of the dielectric elastomer film 406 and metallic mesh 408 composite results in a sufficiently high (e.g., up to 3 Hz) activation/relaxation frequency.

The metallic mesh 408 imbedded in the cardiac assist device 400 also supports the person's heart 402 and helps reduce further enlargement of a failing heart. For example, with reference to Figs. 4 and 5, in some embodiments the metallic mesh 408 is constructed in a cross- hash weave pattern. In this embodiment, the metallic mesh 408 includes a plurality of longitudinal members 502 intersecting with a plurality of latitudinal members 504. Together, the intersecting longitudinal and latitudinal members form a basket-like structure that surrounds the heart 402. Accordingly, in addition to assisting with the pumping function of the heart as discussed above, the sleeve 404 provides support to the weakened heart 402, reducing or eliminating further enlargement of the heart 402.

The invention is not limited to the particular structure of the metallic mesh 408 shown in Figs. 4 and 5. Instead, any suitable arrangement of the metallic mesh 408 may be employed without departing from the scope of this invention. For example, and turning now to Figs. 6 and 7, in some embodiments the metallic mesh 608 may be structured in a spiral configuration. Specifically, and in a similar vein to the cardiac assist device 400 shown in Figs. 4 and 5, Fig. 6 depicts a cardiac assist device 600 that includes a sleeve 604 that surrounds a person's heart 402 and includes a dielectric elastomer film 606 and a metallic mesh 608. However, in this embodiment metallic mesh 608 is a single strip of a metallic material embedded in the dielectric elastomer film 606 in such a way that, when the sleeve 604 is placed around the person's heart 402 as depicted in Figs. 6 and 7, the metallic mesh 608 surrounds the heart 402 in a spiral configuration. As with the metallic mesh 408 in Figs. 4 and 6, the metallic mesh 608 serves as a lead for a voltage source used to activate the cardiac assist device 600 while supporting a failing heart 402.

In still another embodiment as shown in Figs. 8 and 9, the metallic mesh 808 may be arranged in a parallel-ring configuration. More particularly, a cardiac assist device 800 once again includes a sleeve 804 with a dielectric elastomer film 806 and a metallic mesh 808. In this embodiment, however, the metallic mesh 808 includes a plurality of substantially parallel metallic rings, with a ring having the smallest diameter arranged near a bottom of the sleeve 804 and the heart 402 as it is depicted in Fig. 8, and with the diameter of the rings gradually increasing in a direction extending from the bottom of the heart 402 towards the top of the heart 402. Although not shown, in this embodiment one of the rings may be connected to the power source, with each of the remaining rings in turn electrically connected to one another. Or, alternatively, each individual ring may be directly connected to the power source. In any event, as with the other suitable configurations, the parallel ring configuration similarly supports the heart 402 while providing electrical connectivity within the sleeve 804.

Regardless of the pattern of metallic mesh used, in some embodiments of the invention different portions of the cardiac assist device are activated at different times or with different activation forces according to a control strategy aimed at mimicking the pumping function of a human heart 402. More particularly, those skilled in the art will appreciate that a human heart 402 generally contracts by "wringing" the cardiac muscles in a spiral-like pattern, which causes the pumping of the blood throughout the chambers and cardiovascular system. Fig. 10 is a cardiac assist device 1000 including a sleeve 1004, a dielectric elastomer film 1006, and a metallic mesh 1008 as generally described above in connection with Figs. 4-9, which is configured to activate different regions 1010, 1012, and 1014 of the device 1000 at different times and/or with different contraction forces in an effort to mimic the wringing contraction of the heart 402. Specifically, different regions 1010, 1012, and 1014 of the cardiac assist device 1000 are activated at different times and/or with different activation forces and in a synchronized manner to mimic the wringing action of the heart 402.

In some embodiments, this is achieved by electrically insulating different portions of the metallic mesh 1008, and activating those various portions at different times and at a predetermined schedule. For example, a portion of the metallic mesh 1008 located generally in region 1010 may be electrically insulated from a portion located in region 1012, which in turn is electrically insulated from a portion located in region 1014. During use, a voltage is supplied to a lowest region 1010 (i.e., a region of the metallic mesh located nearest to the bottom of the heart 402 as it is depicted in Fig. 10) of the metallic mesh 1008 first, followed sequentially by applying the voltage to different regions of the metallic mesh 1008 in a direction extending from the bottom of the heart 402 towards the top of the heart 402. For example, a voltage is first applied to a portion of the metallic mesh 1008 located generally in region 1010, followed by applying a voltage to a portion generally located in region 1012, and finally followed by applying a voltage to a portion generally located in region 1014. A highest portion of the metallic mesh 1008 (i.e., a portion located nearest to the top of the heart 402 as it is depicted in Fig. 10) is thus activated last, and, accordingly, the cardiac assist device 1000 contracts from its lowest portion upward, simulating the natural contraction of a heart 402.

In other embodiments, a desired control scheme may be achieved by using different voltage magnitudes along the cardiac assist device 1000 in the direction extending from the bottom of the heart 402 towards the top of the heart 402 as it is depicted in Fig. 10. For example, a highest voltage may be applied to a portion of the metallic mesh 1008 located generally in region 1010, a lower voltage may be applied to a portion of the metallic mesh 1008 located generally in region 1012, and a lowest voltage may be applied to a portion of the metallic mesh 1008 located generally in region 1014. Thus, under this control scheme, the cardiac assist device 1000 will contract first and/or more intensely in region 1010, and will contract last and/or less intensely in region 1014, again mimicking the natural contraction of the heart 402.

In still other embodiments, in order to achieve a desired control strategy the material properties of the dielectric elastomer film 1006 and/or the metallic mesh 1008 may be varied in the direction extending from the bottom of the heart 402 towards the top of the heart 402 as it is depicted in Fig. 10. For example, the dielectric elastomer film 1006 may be thickest in the region 1010, and thinnest within the region 1014. Moreover, the cardiac assist device 1000 may have a greater surface area within region 1014 than within regions 1012 or 1010. Accordingly, the bottom of the cardiac assist device 1000— i.e., the portion generally located within region 1010— may charge relatively quickly (due to its reduced surface area) and exhibit a greater contraction force (due to its increased thickness) compared to the top of the cardiac assist device 1000. Similarly, the middle of the cardiac assist device 1000— i.e., the portion generally located within region 1012— may charge slower than the portion located in region 1010 but quicker than the portion located in 1014, and may exhibit a weaker contraction force than the portion generally located in region 1010 but a greater contraction force that the portion generally located in region 1014.

Accordingly, in this embodiment the cardiac assist device 1000 will contract first (and/or with the most force) at the bottom region 1010, followed sequentially by portions of the device 1000 located in region 1012 and ultimately region 1014. This results in a ventricle contraction that mimics the natural contraction of a human heart 402.

Although cardiac assist device 1000 is shown with a basket-type metallic mesh 1008, the cardiac assist device 1000 may instead use a different structured metallic mesh 1008— e.g., a spiral, parallel-ring, or any other suitable patterned mesh. Moreover, although for simplicity cardiac assist device 1000 is shown with three regions 1010, 1012, and 1014, in practice the cardiac assist device 1000 may be controlled using more or less regions. Additionally, in some embodiments that voltage and/or material properties of the cardiac assist device 1000 may be configured with no such discrete regions, but instead configured such that during use, a gradually increasing contraction force is applied to the metallic mesh 1008 in the direction extending from the bottom of the heart 402 towards the top of the heart 402 as it is depicted in Fig. 10.

Although the novel EAP actuator 200 is described for use in connection with heart assist devices 400, 600, 800, and 1000 above, in other embodiments of the invention the novel EAP actuator 200 may be employed in other biomedical applications. For example, in one embodiment, the EAP actuator 200 may configured to be inserted inside the ventricle in a minimally invasive manner. In this embodiment, the EAP actuator 200 may be formed into a ring- or scaffold-like structure and inserted into a failing ventricle to assist with ventricular contraction.

In another embodiment, the EAP actuator 200 may be used in applications designed to assist in locomotion. For example, the EAP actuator 200 can be configured to assist in human movement by inserting the EAP material into the sole of a shoe or configured as a kinesio- assistive tape or woven into garments. Garments may include but are not limited to peripheral or central compression sleeves for arms, legs, torso, hands, feet, etc. Peripheral sleeves that can compress and relax may be effective at creating an internal pressure change resulting in increased blood flow. This may be beneficial for people with chronic disease. This may also improve the peripheral blood flow in environments such as zero-gravity. Additional advantages of the various embodiments of the invention will be apparent to those skilled in the art upon review of the disclosure herein. It will be appreciated that the various embodiments described herein are not necessarily mutually exclusive unless otherwise indicated herein. For example, a feature described or depicted in one embodiment may also be included in other embodiments, but is not necessarily included. Thus, the present invention encompasses a variety of combinations and/or integrations of the specific embodiments described herein.

As used herein, the phrase "and/or," when used in a list of two or more items, means that any one of the listed items can be employed by itself or any combination of two or more of the listed items can be employed. For example, if a composition is described as containing or excluding components A, B, and/or C, the composition can contain or exclude A alone; B alone; C alone; A and B in combination; A and C in combination; B and C in combination; or A, B, and C in combination.

The present description also uses numerical ranges to quantify certain parameters relating to various embodiments of the invention. It should be understood that when numerical ranges are provided, such ranges are to be construed as providing literal support for claim limitations that only recite the lower value of the range as well as claim limitations that only recite the upper value of the range. For example, a disclosed numerical range of about 10 to about 100 provides literal support for a claim reciting "greater than about 10" (with no upper bounds) and a claim reciting "less than about 100" (with no lower bounds).

Further, while the drawings illustrate, and the specification describes, certain preferred embodiments of the invention, it is to be understood that such disclosure is by way of example only. Embodiments of the present invention are described herein with reference to cross-section illustrations that are schematic illustrations of idealized embodiments of the present invention. As such, variations from the shapes of the illustrations as a result, for example, of manufacturing techniques and/or tolerances, are to be expected. There is no intent to limit the principles of the present invention to the particular disclosed embodiments. For example, in the drawings, the size and relative sizes of layers and regions may be exaggerated for clarity. In addition, embodiments of the present invention should not be construed as limited to the particular shapes of regions illustrated herein but are to include deviations in shapes that result, for example, from manufacturing. For ease of description, terms of direction such as "upwards," "lower," "bottom," "top," etc., may be used to describe the relative position of certain structures. Such descriptions should not be taken as limiting on the invention, unless otherwise noted.