LASER SYSTEM AND METHOD FOR OPERATING THE LASER SYSTEM

Abstract

An apparatus and a method for cleaning a cavity filled with a liquid are disclosed. An apparatus (1) for applying pulses of electromagnetic radiation to a cavity (2) filled with a liquid (3) may comprise a source (4, 4) for generating a first pulse and a second pulse of electromagnetic radiation and a control unit (22) adapted to control a time between the first pulse and the second pulse as a function of a diameter D and/or a cross-sectional area of the cavity (2).

Claims

1. An apparatus for applying pulses of electromagnetic radiation to a cavity filled with a liquid, comprising: a source for generating a first pulse and a second pulse of electromagnetic radiation; a control unit adapted to control a time between the first pulse and the second pulse as a function of a diameter D and/or a cross-sectional area of the cavity.

2. The apparatus according to claim 1, further comprising a user interface for receiving information on the diameter and/or cross-sectional area of the cavity.

3. The apparatus according to claim 1, further comprising means for determining the diameter and/or cross-sectional area of the cavity.

4. The apparatus according to claim 1, wherein the control unit is further adapted to control the time between the first pulse and the second pulse such that it varies with the inverse root of the diameter of the cavity.

5. The apparatus according to claim 1, wherein the control unit is further adapted to control the time between the first pulse and the second pulse as a function of a predetermined parameter that is specific to at least an energy of the first pulse and/or to the liquid.

6. The apparatus according to claim 5, wherein the predetermined parameter is independent of the geometry of the cavity.

7. The apparatus according to claim 5, wherein the predetermined parameter corresponds to an unconstrained oscillation period T.sub.0 of a bubble that would be generated by the first pulse in an infinitely large cavity filled with the liquid.

8. The apparatus according to claim 5, wherein the control unit is adapted to determine the predetermined parameter by accessing a data storage device of the apparatus and/or a remote data storage device.

9. The apparatus according to claim 5, wherein the control unit is adapted to control the time between the first pulse and the second pulse such that it is proportional to the predetermined parameter.

10. The apparatus according to claim 5, wherein the control unit is adapted to control the time according to the function K.sub.DT.sub.oD.sup.0.5, wherein K.sub.D is selected from the range 2 mm.sup.0.5 to 4.8 mm.sup.0.5, preferably from the range 2.5 mm.sup.0.5 to 3.8 mm.sup.0.5, and more preferably from the range 2.7 mm.sup.0.5 to 3.8 mm.sup.0.5.

11. The apparatus according to claim 1, wherein the first pulse is adapted to generate a first bubble within the liquid, and the second pulse is adapted to generate a second bubble within the liquid, such that a shock wave is generated within the liquid.

12. The apparatus according to claim 1, further comprising means for providing the liquid to the cavity.

13. The apparatus according to claim 1, wherein the control unit is adapted to determine an optimal time T.sub.p-opt and adapted to vary times between subsequent pairs of pulses within the range from T.sub.p-opt.sub.1 to T.sub.p-opt+.sub.2, wherein .sub.1 and .sub.2 are selected from the range 10 s to 300 s, preferably from 20 is to 75 s and more preferably from 25 s to 75 s.

14. A method for applying pulses of electromagnetic radiation to a cavity filled with a liquid, comprising the steps of: generating a first pulse and a second pulse of electromagnetic radiation; controlling a time between the first pulse and the second pulse as a function of a diameter D and/or a cross-sectional area of the cavity.

15. The method according to claim 14, wherein the cavity is an endodontic access opening of a dental root canal.

16. The method according to claim 14, wherein the cavity is a periodontal pocket.

17. The method according to claim 14, wherein the cavity is a bone cavity.

18. The method according to claim 14, wherein the cavity surrounds and implant.

19. The method according to claim 14, further including controlling the time between the first pulse and the second pulse as a function of a predetermined parameter that is specific to at least an energy of the first pulse and to the liquid.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0083] Embodiments of the invention will be explained in the following with the aid of the drawings in more detail. With reference to the following description, appended claims, and accompanying drawings:

[0084] FIG. 1 illustrates an exemplary inventive laser system with both an optical fiber laser delivery system and an articulated arm laser delivery system;

[0085] FIG. 2a illustrates an exemplary handpiece fed by an articulated arm in contact operational mode;

[0086] FIG. 2b illustrates an exemplary handpiece fed by a delivery fiber in contact operational mode;

[0087] FIG. 3a illustrates an exemplary handpiece fed by an articulated arm in non-contact operational mode;

[0088] FIG. 3b illustrates an exemplary handpiece fed by a delivery fiber in non-contact operational mode;

[0089] FIG. 4a illustrates an exemplary optical exit component of a handpiece fed by an articulated arm, having a flat tip geometry, and showing the resultant laser beam path;

[0090] FIG. 4b illustrates an exemplary optical exit component of a handpiece fed by an articulated arm, having a conical tip geometry, and showing the resultant laser beam path;

[0091] FIG. 5a illustrates an exemplary vapor bubble in generally spherical form;

[0092] FIG. 5b illustrates an exemplary vapor bubble in generally elongate form;

[0093] FIG. 6 illustrates an exemplary vapor bubble oscillation sequence under influence of one short laser pulse;

[0094] FIG. 7a illustrates an exemplary dependence of a single laser pulse vapor bubble oscillation period on the diameter of a confined cylindrical liquid;

[0095] FIG. 7b illustrates an exemplary dependence according to FIG. 7a of the ratio between the single laser pulse vapor bubble oscillation period in a confined cylindrical liquid, and the single laser pulse vapor bubble oscillation period in a large reservoir, on the diameter of the cylindrical cavity;

[0096] FIG. 7c illustrates an exemplary dependence according to FIG. 7a of the ratio between the single laser pulse vapor bubble oscillation period in a confined cylindrical liquid, and the single laser pulse vapor bubble oscillation period in a large reservoir, on the lateral surface of the cylindrical cavity;

[0097] FIG. 8a illustrates an exemplary collapse and shock wave emission of a vapor bubble under the influence of an expanding subsequent bubble in confined reservoir, according to the present invention;

[0098] FIG. 8b illustrates an exemplary sequence of laser pulses, and exemplary development of vapor bubbles and emission of a shock wave, according to the present invention;

[0099] FIG. 9a illustrates an exemplary arbitrarily shaped cavity being cleaned by an exemplary handpiece fed by a delivery fiber;

[0100] FIG. 9b represents an enlarged diagrammatic illustration of a lateral surface of an arbitrarily shaped cavity according to FIG. 9a.

[0101] FIG. 10a illustrates an exemplary endodontic access opening being cleaned by an exemplary handpiece fed by a delivery fiber;

[0102] FIG. 10b illustrates an exemplary endodontic access opening according to FIG. 10a;

[0103] FIG. 11a illustrates an exemplary dependence of a single laser pulse vapor bubble oscillation period on the average diameters of endodontic access cavities;

[0104] FIG. 11b illustrates an exemplary dependence according to FIG. 11a of the ratio between the single laser pulse vapor bubble oscillation period in a confined and unconfined endodontic access cavity, on the average diameter of the endodontic access cavity.

[0105] FIG. 11c illustrates an exemplary dependence according to FIG. 11a of the ratio between the single laser pulse vapor bubble oscillation period in a confined and unconfined endodontic access cavity, on the area of the lateral surface of the endodontic access cavity.

[0106] FIG. 12 represents a diagrammatic illustration of the temporal course of pulse sets in accordance with various embodiments of the invention;

[0107] FIG. 13 represents an enlarged diagrammatic illustration of a detail of a pulse set according to FIG. 12 with the temporal course of individual pulses with sweeping pulse repetition rates from pulse to pulse within one pulse set;

[0108] FIG. 14 represents an enlarged diagrammatic illustration of a detail of the temporal course of pulse sets according to FIG. 12 with the temporal course of individual pulses with sweeping pulse repetition rates from pulses to pulse set; and

[0109] FIG. 15 represents an enlarged diagrammatic illustration of a detail of an alternative pulse set according to FIG. 12 with the temporal course of individual pulses with sweeping pulse energy from pulse to pulse within one pulse set.

DETAILED DESCRIPTION OF PRESENTLY PREFERRED EMBODIMENTS

[0110] With reference now to FIG. 1, in various embodiments, an electromagnetic radiation system comprising a radiation source for generating a radiation beam is shown. In the following, both the inventive electromagnetic radiation system and an inventive method of operating said electromagnetic radiation system are described.

[0111] In the shown preferred embodiment, the apparatus is implemented as electromagnetic radiation system, and more particularly, laser system 1. The source for generating pulses is implemented as laser source 4, generating a radiation beam, more particularly a laser beam 5, e.g. including laser pulses. Laser system 1 comprises at least one laser source 4 for generating at least one laser beam 5 (cf. FIGS. 4a and 4b for more detail), and at least one optical delivery system 6 for the laser beam(s) 5.

[0112] Laser system 1 further comprises a schematically indicated control unit 22 for controlling laser beam 5 parameters, wherein control unit 22 includes again schematically indicated adjusting means 10 for adjusting the laser beam 5 parameters as described herein, particularly for controlling the pulse repetition time.

[0113] The control unit may be implemented as a computer-related entity, either hardware, firmware, a combination of hardware and software and/or firmware, software, or software in execution, e.g. as a computer. The various functions of the control unit may be implemented in hardware, software, firmware, or any combination thereof. If implemented in software, the functions can be stored on or transmitted over as one or more instructions or code on a data store. A data store can be any available media that can be accessed by a computer. By way of example, and not limitation, such computer-readable media can comprise RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to carry or store desired program code in the form of instructions or data structures and that can be accessed by a computer. Also, any connection is properly termed a computer-readable medium. For example, if the software is transmitted from a website, server, or other remote source using a coaxial cable, fiber optic cable, twisted pair, or digital subscriber line (DSL), or wireless technologies such as infrared, radio, and microwave, then the coaxial cable, fiber optic cable, twisted pair, or DSL are included in the definition of medium.

[0114] Optical delivery system 6 preferably includes an articulated arm 14 and/or a handpiece 7, wherein the laser beam 5 is transmitted, relayed, delivered, and/or guided from the laser source 4 through the articulated arm 14 and the handpiece 7 to a target. The articulated arm 14 might preferably be an Optoflex brand articulated arm available from Fotona, d.o.o. (Slovenia, EU). In the shown preferred embodiment, a second laser source 4 and a second optical delivery system 6 with a second handpiece 7 is provided, wherein instead of the articulated arm a flexible elongated delivery fiber 19 for guiding the laser beam 5 is incorporated. Despite both laser sources 4, 4 and delivery systems 6, 6 being shown in combination, one of both in the alternative may be provided and used within the scope of the present invention.

[0115] Moreover, laser system 1 may be configured with any appropriate components and/or elements configured to facilitate controlled application of laser energy, for example, in order to create vapor bubbles in a liquid 3 within a cavity 2 for cleaning (including debridement, material removal, irrigation, disinfection, and/or decontamination of said cavity 2 and/or fragmenting particles within such cavities), as shown and described herein.

[0116] With reference now to FIGS. 2 and 3, it is to be understood that the cleaning according to the invention is intended for a cavity 2 (FIGS. 2, 3) filled with a liquid 3. In case of medical or dental applications, cavity 2 may be filled spontaneously with blood or other bodily fluids by the body itself. Alternatively, the cavity may be filled with water, or other liquids such as disinfecting solutions, by the operator and/or the apparatus. In the embodiments of FIGS. 2 and 3, the apparatus may be designed to include a liquid delivery system 26 configured to fill the volume of the cavity with the liquid. Preferably, said liquid 3 is an OH-containing liquid, for example a liquid with its major portion being water. In other examples, the liquid 3 may include abrasive materials or medication, such as antibiotics, steroids, anesthetics, anti-inflammatory medication, antiseptics, disinfectants, adrenaline, epinephrine, astringents, vitamins, herbs, and minerals. Furthermore, the liquid 3 may contain an additive enhancing the absorption of introduced electromagnetic radiation.

[0117] The laser source 4 may be a pulsed laser. The laser source 1 may be solid state laser source and configured with a pulse duration of less than 500 s. The laser pulse duration is defined as the time between the onset of the laser pulse, and the time when 50% of the total pulse energy has been delivered to the liquid. The pulse duration may be fixed; alternatively, the pulse duration may be variable and/or adjustable. The pulse energy may be fixed; alternatively, the pulse energy may be variable and/or adjustable. The wavelength of the laser beam 5 may be in a range from (above) 0.4 m to 11.0 m inclusive. As illustrated in FIGS. 9, 13, 14 and 15, the laser system 1 may be adapted to be operated in pulsed operation with pulse sets containing at least two and maximally twenty individual pulses p of a temporally limited pulse duration t.sub.p, wherein a temporal separation T.sub.s between the pulse sets typically is 10 ms, and wherein the individual pulses p follow one another with a pulse repetition time T.sub.p within a range of 50 s, inclusive, to 1000 s, inclusive.

[0118] The laser source 4, 4 may desirably be configured to generate coherent laser light having a wavelength such that the laser beam 5 is highly absorbed in the liquid 3, wherein the laser pulse duration is in the range of us and 500 s, and preferably of 10 s and <100 s.

[0119] Preferably, the laser source 4, 4 is one of an Er:YAG solid state laser source having a wavelength of 2940 nm, an Er:YSGG solid state laser source having a wavelength of 2790 nm, an Er:Cr:YSGG solid state laser source having a wavelength in a range of 2700 to 2800 nm, an Er:YAlO3 solid state laser having a wavelength of 2690 nm, a Ho:YAG solid state laser having a wavelength of 2100 nm, a CO.sub.2 or CO gas laser source having a wavelength of 9000 nm to 10600 nm, all of them providing a laser beam 5 highly absorbed in water and other OH-containing liquids.

[0120] In particular, the laser source 4 and/or laser source 4 may be an Er:YAG laser having a wavelength of 2940 nm, wherein the laser pulse energy is in a range from 1 mJ to 100 mJ, preferably from 1 mJ to 40 mJ, and more preferably within a range from 5.0 mJ to 20.0 mJ. This type of laser source may be combined with an exit component 8 that is cylindrical, having a diameter between 200 m and 1000 m, wherein the conical output surface 13 has a conical half angle being in the range from 16 to 38, preferably from 34 to 38, wherein the temporal separation T.sub.s between pulse sets 21 is <0.5 s, and wherein the cumulative delivered energy during a cleaning session is below iso J.

[0121] Additionally or alternatively, laser source 4 and/or laser source 4 is configured to generate coherent light having a wavelength highly absorbed in OH-containing liquids, e.g., by means of one of an Er:YAG laser source having a wavelength of 2940 nm, an Er:YSGG laser source having a wavelength of 2790 nm, an Er:Cr:YSGG laser source having a wavelength of 2780 nm or 2790 nm, or a CO.sub.2 laser source having a wavelength of about 9300 to about 10600 nm. The laser pulse energy may be in a range from 1 mJ to 500 mJ.

[0122] Other examples of laser sources 4,4 with a laser wavelength highly absorbed in water and other liquids include quadrupled Nd:YAG laser which generates light having a wavelength of 266 nm; an ArF excimer laser which generates light having a wavelength of 193 nm, an XeCl excimer laser which generates light having a wavelength of 308 nm, and a KrF excimer laser which generates light having a wavelength of 248 nm.

[0123] In another embodiment, laser source 4 and/or laser source 4 may be one of a frequency doubled Nd:YAG laser source having a wavelength of 532 nm, a dye laser source having a wavelength of 585 nm, or a Krypton laser source having a wavelength of 568 nm, all of them providing a laser beam 5 highly absorbed in oxyhemoglobin within blood vessels.

[0124] Alternatively, the laser source 4, 4 may be configured to generate coherent laser light having a wavelength such that the laser beam 5 is weakly absorbed in the liquid 3, wherein the laser pulse duration is in the range of 1 fs and <100 ns, and preferably of 1 ns and <25 ns. To this end, the laser source 4 and/or the laser source 4 may be one of a Q-switched Nd:YAG laser source having a wavelength of 1064 nm, a Q-switched ruby laser source having a wavelength of 690 nm, or an alexandrite laser source having a wavelength of 755 nm, including laser sources 4, 4 with frequency doubled wavelengths of these laser sources 4, 4, all of them providing a laser beam 5 weakly absorbed in water and other OH-containing liquids. For such weakly absorbed wavelength the pulse energy of one individual laser pulse p is in the range from 0.05 mJ to 1000 mJ, preferably in the range from 0.5 to 200 mJ, and in particular from 1 mJ to 20 mJ.

[0125] Moreover, any other suitable laser source 4, 4 may be utilized, as desired. In certain embodiments, the laser source may be installed directly into the handpiece 7, 7, and no further laser light delivery system 6, 6 such as the articulated arm 14 or elongated delivery fiber 19 is required. Additionally, such handpiece may not be intended to be held in hand but may be built into a table-top or similar device as is the case with laser photo-disruptors for ocular surgery.

[0126] Laser system 1 comprises a user interface 3o. User interface 3o comprises a screen and a plurality of keys and/or buttons.

[0127] The handpiece 7, 7 includes an exit component 8, through which the laser beam 5 exits the delivery system 6, 6 for entering the liquid 3, as shown in FIGS. 2a, 2b, 3a and 3b. The handpiece 7, 7, and in particular its exit component 8 may be configured to deliver the laser light to the liquid 3 in a contact, and/or non-contact manner. Turning now to FIG. 2a, when the handpiece 7 is configured for a contact delivery, the laser light is from the said contact handpiece 7 directed into a contact exit component 8 which is configured to be at least partially immersed into the liquid 3 within the anatomical cavity 2 in such a manner that the laser light exits the exit component 8 within the liquid 3, at a depth of at least 1 mm, and preferably of at least 3 mm, in order to generate vapor bubbles 18 within the liquid 3, and in order for the laser generated vapor bubble(s) 18 to interact with the liquid-to-cavity surface. In various embodiments, the contact exit component 8 may comprise or consist of an optical fiber tip as shown in and described along with FIG. 2b and FIG. 3b or a larger diameter exit tip 24 as shown in and described along with FIGS. 4a and 4b. In certain embodiments (FIG. 2a), the handpiece 7 together with a contact exit component 8 comprises a H14 tipped laser handpiece model available from Fotona, d.d. (Slovenia, EU). And in certain embodiments, an ending of an elongated delivery fiber 19 of the laser light delivery system 6 may be immersed into the liquid 3, thus serving the function of a contact exit component 8 (FIG. 2b).

[0128] For the contact scenario as shown in FIGS. 2a and 2b one of the above described highly absorbed or weakly absorbed wavelengths including all other above described parameters is preferably used, thereby generating at least two vapor bubbles 8 within the liquid 3.

[0129] In one of the embodiments of our invention, the laser system 1 comprises a sensor system 9 to determine a characterizing dimension of the cavity, e.g. of its lateral surface 27. For example, the sensor may determine information on a diameter and/or a cross-sectional area of the cavity and provide it to the control unit. The sensor system 9 preferably comprises an optical and/or an acoustical measurement sensor for sensing the lateral surface size.

[0130] Furthermore, the laser system 1 comprises control unit 22 for controlling the pulse repetition time T.sub.p to achieve at least approximately that the subsequent bubble 18, i.e., the bubble 18 generated by the subsequent laser pulse p.sub.b, starts to expand when the volume of the prior bubble 18 has already contracted to the desired size as described above. This control may be implemented by control unit 22, e.g. via its adjusting means 10 adapted to adjust the repetition time of pulses emitted by laser source 4 and/or 4. For example, the control unit may determine a specific repetition time, and trigger the adjusting means 10 to control the laser source accordingly. For example, the adjusting means may be an actuator of the laser source or it may simply an electronic control input of the laser source that alters the pulse repetition time according to steps as known in the art. The control unit may thus automatically ensure that pulses are delivered at the appropriate T.sub.p-opt depending on the cavity dimension (e.g. diameter, cross-sectional area) and/or one or more controlled parameters. However, the laser pulse repetition time T.sub.p might also be manually adjusted by the user, e.g. to be approximately equal to T.sub.p opt, e.g., corresponding to the cavity dimension and/or one or more controlled parameters.

[0131] When the handpiece 7, 7, and its exit component 8 are configured for a non-contact delivery (FIGS. 3a, 3b), the non-contact exit component 8 of the said non-contact handpiece 7 is configured to be positioned above the surface of the liquid 3 reservoir, with the laser energy being directed through air and possible other transparent materials (such as, for example an eye lens in case of ophthalmic applications) into the liquid 3 reservoir. In certain embodiments, a laser source 4 with a highly absorbed wavelength might be used as described above, and the exiting laser beam 5 is substantially focused onto the liquid 3 surface. In the shown non-contact scenario, however, preferably a laser source 4 with a weakly absorbed wavelength is used as described above, and the beam is substantially focused to a point located below the liquid surface by means of an appropriate focusing device, e.g. a lens system 20. The weak absorption allows the laser beam 5 to penetrate the liquid 3 until a certain penetration depth where the focal point is located. In the area of the focal point the laser energy concentration is high enough to generate the desired at least one vapor bubble 18, despite the weak absorption. In certain embodiments (FIG. 3a), non-contact handpiece 7, together with a non-contact exit component 8 comprises an H02 tip-less handpiece model available from Fotona, d.d. (Slovenia, EU). And in certain embodiments, an exit component 8 consists of an ending of an elongated laser light delivery fiber 19, which is positioned above the surface of a liquid 3 reservoir (FIG. 3b). Of course, a separate exit component 8 as described along with FIG. 2a might be used for the embodiments of FIGS. 2b, 3a and 3b as well. In yet other embodiments, the exit component 8 may represent a focusing optical system consisting of one or more lenses, such as is the case in ocular surgery photo-disruption procedures.

[0132] Moreover, handpiece 7 may comprise any suitable components or elements configured for targeted and/or controllable delivery of laser energy to a liquid 3. Preferably, the laser system 1 comprises a scanner 15 as schematically indicated in FIGS. 2a, 3a, which allows scanning of the exit component 8 cross section with the laser beam 5, as shown in FIGS. 4a, 4b.

[0133] Turning now to FIGS. 4a and 4b, in various embodiments the exit component 8, preferably but not coercively configured for contact delivery, may consist of an exit tip 24 (FIGS. 4a, 4b) or any other optical element, which extends along a longitudinal axis and is made of a material which is transparent to the laser beam. The exit component 8 preferably has a generally circular cross section, which leads to a generally cylindrical shape. However, any other suitable cross section may be chosen. The exit tip 24 may be of a variety of different shapes (e.g., flat, pointed, conical, angled, beveled, double-beveled), sizes, designs (e.g., side-firing, forward-firing) and materials (e.g. glass, sapphire, quartz, hollow waveguide, liquid core, quartz silica, germanium oxide). Further, the exit component 8 may comprise mirrors, lenses, and other optical components.

[0134] In one preferred embodiment the exit tip 24 of the exit component 8 has a flat output surface 11 (FIG. 4a). The exit tip 24 of the exit component 8 has a diameter d.sub.c, while the laser beam 5 has a diameter d.sub.L. The diameter dc of the exit component 8 can be equal to the diameter of the elongated delivery fiber 19 and in particular equal to the diameter di, of the laser beam 5. In the embodiment of FIG. 4a, where the exit component 8 is in the form of a larger diameter exit tip 24, the diameter d.sub.c of the exit component 8 is substantially greater than the diameter di, of the laser beam 5. In connection with the a.m. scanner 15 a certain scanning pattern on the flat output surface 11 can be achieved, thereby generating exiting beam portions 12 and as a result vapor bubbles 18 at corresponding locations within the liquid 3 (FIGS. 2a, 3a), as may be desired.

[0135] In another embodiment as shown in FIG. 4b, the exit component 8, again in the form of a larger diameter exit tip 24, has a pointed end with conically shaped output surface 13 being disposed around the longitudinal axis and having an apex facing away from the incoming beam section, wherein the conically shaped output surface 13 has a half opening angle being adapted to provide partial or preferably total reflection of the incoming beam section into a reflected beam section within the exit component 8 and to provide refraction of the reflected beam section into an exiting beam portion 12 emerging from the exit component 8 through the conically shaped output surface 13 in approximately radial direction relative to the longitudinal axis. In various embodiments, the angle is expediently in the range 60120, and preferably about 90.

[0136] Typically, when fiber tips with output surface 13 are used, the laser beam 5 extends substantially across the whole output surface 13. This will result in a circumferentially spread exiting beam portion 12. In certain embodiments, however, as shown in FIG. 4b, the exit component 8 may have a diameter d.sub.C substantially larger than the diameter di, of the laser beam 5, providing space for the laser beam to be scanned over the exit component's conical output surface 13. In such embodiments, the exit component 8 base is preferably of a cylindrical shape. However, any other suitable 3D shape, such as a cube, cuboid, hexagonal prism or a cone, can be used. Scanning the conical output surface 13 with the incoming laser beam 5 allows for generation of multiple exiting beam portions 12 and corresponding vapor bubbles located circumferentially around the exit component 8. Since more than one laser pulse p, i.e. a synchronized train of pulses p (FIGS. 8a, 9, 13, 14 and 15) needs to be delivered to the same spot, one could deliver one pulse p exiting beam portion 12 to a related vapor bubble 18 spot, then move to the next vapor bubble 18 spot on the circumference, and so on, and then return to the same initial vapor bubble 18 spot just in time for the next pulse p within the pulse train. This would enable faster procedures since the laser repetition rate would not be limited by the bubble oscillation period T.sub.B=(t.sub.min1t.sub.01) (FIG. 6) but only by the maximum repetition rate of the laser system 1. In some examples, the apparatus may thus comprise a scanner that directs subsequent pulses to different positions but revisits each position at least once to deliver at least a second pulse there, wherein the pulse repetition rate at each position is controlled by the control unit as described.

[0137] With reference now to FIGS. 4a, 4b, in accordance with various embodiments, when laser energy is delivered into a highly absorbing liquid 3 through an exit component 8 having a flat output surface 11 (FIG. 4a), that is immersed into the liquid 3, the above described vapor bubble 18 turns into a channel-like, extended or elongate vapor bubble 16, as schematically indicated in FIG. 5b. A channel-like bubble formation may be generated also when laser energy is delivered to a tubular cavity. On the other hand, when highly absorbed laser energy is delivered into a liquid 3 through an immersed conical output surface 13, or a flat output surface 11 of sufficient small diameter compared to the beam diameter d, or when weakly absorbed laser energy is delivered in non-contact mode and focused within the liquid 3 as described above, a generally spherical vapor bubble 18 develops, as schematically indicated in FIG. 5a. It is to be appreciated, however, that in reservoirs with small dimensions, the bubble's shape will be influenced more by the reservoir's geometry, and less by the fiber tip's output surface.

[0138] It is also to be appreciated that with shock waves generated according to present invention, conically shaped tips may get more quickly damaged during the violent shock wave emission, and therefore it may be advantageous to use flat surface fiber tips with the present invention.

[0139] Moreover, it is to be appreciated, that when in certain embodiments a weakly absorbed laser beam is delivered to a liquid 3 in a non-contact manner, and the beam's focus is located within the liquid 3, and away from the liquid surface, no bubble gets formed at or near the liquid's surface. Instead, the beam gets transmitted deeper into the liquid, and providing that the pulse duration is sufficiently short (100 ns), and the power density at the focal point within the liquid is sufficiently high, a bubble 18 is generated only when the laser beam 5 reaches its focal point deeper within the liquid 3.

[0140] Turning now to FIG. 6, in various embodiments, the system, apparatus and method described herein utilizes an improved scientific understanding of the interaction of pulsed laser light with a highly absorbing liquid 3. When one pulse p of a pulsed laser beam 5 is delivered to such a liquid 3 at an onset time t.sub.01, a bubble oscillation sequence develops. In the 1st phase of the bubble oscillation sequence (from time t.sub.01 to time t.sub.max1), laser energy deposition into the liquid 3 via absorption causes superheating of the liquid 3, and boiling induces a vapor bubble 18. The vapor bubble 18 expands rapidly, and thereafter reaches its maximum size at t.sub.max1, when the internal pressure matches the pressure in the surrounding liquid 3.

[0141] In the 2.sup.nd phase (from time t.sub.max1 to time t.sub.min1), the internal pressure is lower than the pressure in the surrounding liquid 3, and this difference in pressures forces the vapor bubble 18 to collapse.

[0142] When the vapor bubble 18 collapse completes at time Limn, a rebound occurs thereafter, and the vapor bubble 18 starts to grow again up until time t.sub.max2. This 3.sup.rd phase (from time t.sub.min1 to time t.sub.max2) is followed again by a collapse in the 4.sup.th phase (from time t.sub.max2 to time t.sub.min2). This oscillation process of the vapor bubble 18 continues, decreasing in amplitude and temporal period each time as illustrated in FIG. 6.

[0143] In various embodiments, a temporal bubble oscillation period T.sub.B may be defined as the time between t.sub.01 and t.sub.min1. Temporal bubble oscillation period T.sub.B varies based at least in part on the thermo-mechanical properties of the liquid 3, the shape and volume of the liquid 3 reservoir, the laser beam 5 emission profile, pulse duration, pulse energy, and so forth. Specifically, when the liquid 3 medium is contained in an endodontic access opening, e.g. in a body cavity 2 as shown in FIGS. 2a, 2b 3a, 3b, and 5, the bubble's oscillation period T.sub.B is prolonged, the bubble's collapse is slowed down, and no shock wave is emitted, as already explained.

[0144] The exemplary dependence of the bubble's oscillation period T.sub.B on the cavity dimensions is shown in FIG. 7a, as measured in a cylindrical model of a cavity. A LightWalker branded laser system available from Fotona, d.o.o., Slovenia was used in the measurement. The liquid 3 within the cavity 2 was water, and the laser source 4 was an Er:YAG laser with the wavelength of 2940 nm which is strongly absorbed in water. The laser pulse duration was about 50 sec and the laser pulse energy E.sub.L was 5 mJ, 7.5 mJ, 19 mJ or 26 mJ. The laser beam 5 was delivered from the laser source 4 through the Fotona Optoflex brand articulated arm 14 and the handpiece 7 (Fotona H14) to a water filled model of a root canal cavity 2 through a flat fiber tip 24 (Fotona Flat Sweeps400) with its flat surface ending a submersed in water to a depth h of about 3 mm. The fiber tip's diameter was 0.4 mm, and the lateral diameter (D) of the cylindrical cavity model was equal to D=3 mm or D=6 mm. It is to be appreciated that because of the slowing down of the bubble dynamics at D=3 mm and D=6 mm, no shock waves were observed when the bubble 18 imploded at t=t.sub.min1.

[0145] Referring again to FIG. 7a, the depicted lines represent numerical fits to the oscillation period data using a function

T.sub.B=KD.sup.0.5(1)

with best fits obtained with K=475, 671, 1145 and 1320 s.Math.mm.sup.0.5, for pulse energies E.sub.L=5, 7.5, 19 and 26 mJ, correspondingly.

[0146] The dependence of T.sub.B on the square root of D resembles the dependence of the oscillating period T.sub.lin of a standard damped linear oscillator on a damping factor , as

T.sub.lin=T.sub.lino(1(T.sub.lino/2).sup.2).sup.0.5(2)

where T.sub.lino is the oscillating period of the linear oscillator in the absence of damping (=0). Even though the oscillation dynamics of a three-dimensional bubble in a fluid within a constrained environment is much more complex than that of an ideal linear oscillator, we have thus found that the square root dependence applies to the bubble dynamics as well, providing that the oscillation period of an unconstrained bubble in a large reservoir (T.sub.o) is assigned to a relatively large but not infinite cavity diameter of about D=14 mm. Above this diameter, the square root approximation breaks down, and the imaginary damping factor becomes negative. We attribute this observation to the bubble characteristics according to which the bubble oscillation period starts to increase appreciably and with the square root dependence only after the cavity diameter becomes smaller than about D=14 mm.

[0147] According to the above, the data points for D=14 mm in FIG. 7a represent the bubble oscillation periods as obtained in a large water reservoir. The same laser parameters and delivery system as described above were used for all liquid reservoir geometries. In the large reservoir, e.g. in a free liquid geometry, bubble oscillations can be accommodated by displacing the liquid at long distances, and therefore the oscillations were faster, with a bubble period T.sub.B being up to about two times shorter than in the cylindrical cavity model. In the confined cavity model, a free expansion of the bubble laterally is not possible, and hence the water is pushed forward and backward in the root canal. Since the water obstructs the expansion of the vapor in the forward direction, the bubble grows backwards along the fiber, as can be seen from the insert in FIG. 6 at time t.sub.max1, The pressure inside the bubble remains high for a long time, since it has to fight against the resistance of the water which has to be displaced in the small canal. This process delays the dynamics of expansion and implosion, and introduces additional losses compared to a free water situation. In the cavity, the lateral and forward bubble expansion is limited by the cavity wall, while the backward expansion is blocked by the fiber making the lumen of the cavity even smaller. These differences with a free water situation are considered to be the reason of a measured approximately two times longer bubble oscillation time T.sub.B and in up to approximately three times smaller bubble size (VB) in the cavity as compared to a large reservoir, resulting altogether in about six times slower rate of the bubble collapse (VB/T.sub.B)/2. Consequently, no shock wave emission was detected during single pulse experiments in the confined cavity model geometry (for D=3 and 6 mm). In turn, in the free reservoir, shock wave emission was present during the collapse of the (first) bubble without the need for a second pulse.

[0148] It is to be appreciated that the bubble implosion begins near the fiber tip where the expansion started, resulting in a separation of the bubble 18 from the fiber, as can be seen from the insert in FIG. 6 at time t.sub.sep. Referring now to FIG. 8a and FIG. 8b, according to present invention, at first a first laser pulse pa and then a second laser pulse p.sub.b with the same characteristics as the prior laser pulse p.sub.a may be delivered into the root canal model at the respective onset times t.sub.oa and t.sub.ob with a pulse repetition time T.sub.p in between such that the second bubble 18 starts to expand at a time when the prior bubble 18 has already contracted to a certain size. This leads to a violent implosion of the prior bubble 18, and consequently to an emission of a shock wave 25 by the prior bubble 18 at the time of its collapse, even in confined geometries.

[0149] The foregoing oscillation dynamics of vapor bubbles 18 and 18 and associated relation to shock wave emission, facilitate the improved inventive system for and methods of cleaning utilizing delivery of laser pulses p, for example cleaning of root canals, drilled bone, and/or the like anatomical cavities 2 preferably with D.sub.ave less than 8 mm and even more preferably with D.sub.ave6 mm. Moreover, and referring now to FIGS. 8a, 8b, in various embodiments, shock wave emission can be facilitated or enhanced in confined geometries preferably with D.sub.ave<8 mm and even more preferably with D.sub.ave6 mm, and/or in highly viscous liquids by delivering a minimum of two laser pulses p.sub.a, p.sub.b in a sequence whereas the pulse repetition time T.sub.p is controlled as described herein. It is to be appreciated that the illustrations in FIGS. 8a, 8b are made only for the purposes of describing the invention, and do not necessarily depict amplitudes and shapes of laser pulses, bubble volumes or shock waves, as would be observed in actual embodiments of the invention.

[0150] FIG. 8b shows an exemplary inventive laser pulse sequence with pulse durations t.sub.p and inventive pulse repetition time T.sub.p, and the resulting dynamics of the resulting vapor bubbles and shock wave emissions. Individual pulses p.sub.a and p.sub.b within one sequence follow each other by a pulse repetition time T.sub.p. The first pulse p.sub.a starts at an onset time t.sub.oa and generates, starting at the same onset time t.sub.oa, a first vapor bubble 18. The size or volume V of the vapor bubble 18 oscillates in an expansion phase from a minimal volume at the first t.sub.oa to a maximal volume V.sub.max-a at a maximum volume time.sub.tmax1-a, and in a subsequent contraction phase from a maximal volume V.sub.max-a at the maximal volume time t.sub.max1-a a to a minimal volume at a minimum volume time t.sub.mint1-a. When within the inventive pulse sequence the pulse repetition time T.sub.p is adjusted to match T.sub.p-opt, in other words adjusted such that an onset time t.sub.ob of the subsequent laser pulse p.sub.b is delivered at about the time when the first vapor bubble 18 formed by the prior laser pulse pa has partially collapsed as outlined herein (e.g. to a value from about 0.7V.sub.max-a to about 0.2V.sub.max-a, preferably from about 0.7V.sub.max-a to about 0.3V.sub.max-a, expediently in a range from about 0.6V.sub.max-a to about 0.4V.sub.max-a, and according to FIG. 8b of about 0.5V.sub.max-a), two effects happen in parallel: As a first effect the first bubble 18 has separated from the exit component 8 and moved away downwards (FIG. 8a), in consequence of whichalthough the exit component 8 has not movedthe second pulse p.sub.b is introduced at a location different to the location where the first vapor bubble 18 is now present at the time of introducing the second laser pulse p.sub.a, thereby generating the second vapor bubble 18 within the liquid 3. As a second effect the liquid pressure exerted on the collapsing prior bubble 18 by the expanding subsequent bubble 18, i.e., the bubble resulting from the subsequent laser pulse p.sub.b, forces the prior bubble 18 to collapse faster, thus enabling or enhancing the emission of a shock wave 25 by the prior bubble 18, as indicated in FIG. 8a. The inventive control of the pulse repetition time T.sub.p, as outlined herein, ensures that when the subsequent bubble starts substantially expanding i) the prior bubble is already in the fast collapse phase, and is therefore sensitive to the sudden additional pressure caused by the expanding subsequent bubble; and ii) in embodiments with a contact delivery of the laser energy into a liquid, the prior bubble has already substantially separated and moved away from the exit component 8, and therefore the laser energy of the subsequent laser pulse does not get absorbed within the prior bubble. However, in any case where the created vapor bubbles 18, 18 have no sufficient tendency to separate from the exit component or to otherwise change their location, and also in embodiments with a non-contact delivery, the exit component 8 or laser focal point may be spatially moved in between the pulses, for example by a scanner, as explained above, in order to avoid the laser energy of the subsequent laser pulse p.sub.b to be absorbed within the prior bubble 18.

[0151] It is to be appreciated that the invention is not limited to the emission of only two subsequent pulses within a pulse set. A third pulse following a second laser pulse, and fulfilling both conditions, may be delivered resulting in an emission of a shock wave by the previous (second) bubble. Similarly, an n.sup.th subsequent laser pulse will result in an emission of a shock wave by the (n1).sup.th bubble, and so on as further laser pulses are being added to the set of pulses. The more laser pulses are delivered in one pulse set, the higher is the laser-to-shock wave energy conversion, with the energy conversion efficiency being proportional to the ratio (n1)/n where n is the total number of laser pulses delivered in one pulse set 21 (FIG. 10).

[0152] Our experiments show that the optimal repetition time (T.sub.p-opt) is the pulse repetition time where the subsequent bubble starts to develop during the second half of the bubble's period (T.sub.B), i.e., when T.sub.p=T.sub.p-opt=F.sub.ST.sub.B where the shock wave enhancing factor (F.sub.S) is in a range from about 0.6 to about 1.2, preferably in a range from about 0.75 to 0.95, and expediently in a range from about 0.8 to about 0.95. When the same device is intended to be used for cleaning differently sized cavities, containing different liquids, and with different device parameters (laser pulse energy, for example), as mentioned, this poses a challenge since as shown in FIG. 7 the bubble oscillation time (T.sub.B), and consequently the optimal pulse repetition time (T.sub.p-opt) depend critically on these conditions, being longer, for example, for smaller reservoirs and larger laser pulse energies.

[0153] However, for most procedures there is typically only a limited set of cavity dimensions which vary from one cleaning session to another and are not under the control of the operator or the device, as opposed to controlled parameters, i.e., the parameters which are under the control, at least to a sufficient degree, by the device and/or the operator. Examples of controlled parameters are the wavelength of the electromagnetic source, its pulse energy and duration, or the characteristics of the employed (contact or non-contact) delivery. Therefore when keeping all the controlled parameters the same, the optimal repetition time (T.sub.p-opt) varies from cleaning session to cleaning session only as a function of the uncontrolled cavity dimensions. The present invention is based on the finding that particularly the lateral diameter or cross-section be advantageously used to adapt the pulse repetition time accordingly. Moreover, an aspect is also the finding that the influence of the controlled parameters, i.e., of the parameters which are at least in principle under the control of the device and the operator, can be approximately characterized by a single parameter, the unconstrained or free bubble oscillation period (T.sub.o) representing the bubble dynamics under the conditions when the uncontrolled cavity dimensions are infinitely large, i.e., when the bubble dynamics is not affected by the uncontrolled spatially limited cavity dimensions. Further, it is our discovery that the optimal pulse repetition time (T.sub.p-opt) can be determined with sufficient accuracy solely from the known unconstrained (free) bubble oscillation period (T.sub.o) in combination with a characteristic cavity dimension (S), the characteristic cavity dimension S characterizing the damping influence of the constraining cavity environment (e.g. the diameter and or cross-section).

[0154] This is demonstrated in FIG. 7b that provides a different perspective on the bubble oscillation data presented in FIG. 7a. When for each laser pulse energy E.sub.L, the bubble oscillation period data points T.sub.B are divided by the unconstrained oscillation period T.sub.o belonging to that pulse energy (i.e., by the value of T.sub.B at D.sub.ave=14 mm), the obtained ratio T.sub.B/T.sub.o is found to be approximately independent of the laser pulse energy E.sub.L, for all average diameters D.sub.ave, the diameter D.sub.ave thus representing a characteristic dimension S for the employed cylindrical cavity model. The full line represents the fitted function:

T.sub.B/T.sub.o=CaveD.sub.ave.sup.0.5(3)

[0155] With the best fit obtained for the average diameter coefficient C.sub.ave=3.74 mm.sup.0.5, with the statistical coefficient of determination of R.sup.2=0.99. Typically a fit is considered good when R.sup.20.7.

[0156] Similarly, and as shown in FIG. 7c, when the area of the lateral surface (A.sub.L) of the cylindrical cavity is considered to represent a characteristic dimension, the best fit, represented by a full line in FIG. 7c, is obtained when the data is fitted to the function:

T.sub.B/T.sub.o=C.sub.lsA.sub.ls.sup.0.25(4)

with the lateral area coefficient C.sub.ls=3.50 mm.sup.0.5, with R.sup.2=0.98.

[0157] Therefore, for an ideal cylindrically shaped cavity, the characteristic dimension is represented either by S=D=D.sub.ave or S=A.sub.ls=D.sup.2/4, and the optimal pulse separation (T.sub.p) can be calculated for any value of the characteristic dimension using the predetermined unconstrained bubble oscillation period T.sub.o characterizing the influence of the controlled parameters (such as the laser pulse energy in FIGS. 7a-c), according to:

T.sub.p-opt=F.sub.ST.sub.oC.sub.aveD.sub.ave.sup.0.5(5)

or

T.sub.p-opt=F.sub.ST.sub.oC.sub.lsA.sub.ls.sup.0.25(6)

where T.sub.o can be predetermined by a measurement and/or calculation for any combination of controlled parameters under free reservoir conditions.

[0158] It should be appreciated that in real situations the cavities may not be cylindrical but can be of any shape, an exemplary shape being illustrated in FIG. 9a. If we define the vertical direction of a cavity as the direction parallel to the direction of the delivered electromagnetic radiation (optical axis of first and/or second pulse), then the cavity's lateral surface 27 which is schematically depicted in FIG. 9a, is defined as a lateral cross section of the cavity at the location of the bubble. For the purposes of this invention, the size and shape of the lateral surface may be characterized by the lateral surface's minor (D.sub.min) and major (D.sub.max) diameters. As depicted in FIGS. 9a and 9b, the major diameter may be the line segment of the lateral surface that runs through the bubble and the optical axis and connects the most separated points on the cavity's inner surface. The minor diameter may be the line perpendicular to the major axis, crossing the major axis and the bubble, and extending on both sides to the cavity's inner surface. For a cylindrically shaped cavity, with lateral surface 27 being circular, D.sub.min=D.sub.max=D=D.sub.ave.

[0159] For an arbitrarily shaped lateral surface 27, it will be assumed that in most situations the characteristic cavity dimension S can be sufficiently well represented by either the average of the minor and major axes of the lateral surface, S=D.sub.ave=(D.sub.min+D.sub.max)/2, Also the cross-section area according to the present invention may be represented by the area of the lateral surface S=A.sub.ls=D.sub.minD.sub.max/4. It is to be noted that for a case of an elliptically shaped lateral, the minor and major diameters may correspond to the major and minor axes of such ellipse. For circularly shaped surface, the characteristic dimension may be represented by the diameter of the circle, and the cross-sectional area may be represented by A.sub.ls=D.sup.2/4. However, other definitions of the characteristic cavity dimension may be appropriate when so required by the type of the procedure and of the cavity shape, including potential influence of the cavity dimension in the vertical direction.

[0160] As an example, in endodontic root canal cleaning, and as shown in FIGS. 10a and 10b, the endodontist makes an access opening 28 (also access cavity or chamber) in the crown of the tooth, in order to enable cleaning and shaping of the interior of each of its root canals 29. Clinically, the size and shape of the lateral surface 27 of the access cavity 28 depends on the tooth type, the patient and also on the endodontist's skill and preference. For upper central and lateral incisors, the shape of the lateral surface is typically approximately circular. For first, second and third molars the shape of the lateral surface is quadrangular with rounded corners. And for other teeth, the shape of the lateral surface is approximately elliptical. The size and shape of the lateral surface 27 is typically described by the mesiodistal (minor) and buccolingual (major) cavity diameter, where as shown in FIG. 11b the mesiodistal cavity diameter (D.sub.min) is the diameter along the line joining the mesial and distal tooth surface, and the buccolingual cavity diameter (D.sub.max) is the diameter along the line joining the buccal and lingual tooth surface.

[0161] Very roughly, the clinically encountered range from small to large minor diameters, and from small to large major diameters for different tooth types and patients is depicted in in Table 1.

TABLE-US-00001 TABLE 1 Minor diameter D.sub.min Major diameter D.sub.max (mm) (mm) Tooth type Small Large Small Large Upper central incisor 1.2 0.3 1.9 0.3 1.2 0.3 1.9 0.3 Upper lateral incisor 0.9 0.3 1.6 0.3 1.2 0.3 1.9 0.3 Upper canine 1.2 0.3 1.9 0.3 2.2 0.3 2.9 0.3 Upper first premolar 1.1 0.3 1.8 0.3 5.0 0.3 5.7 0.3 Upper second premolar 1.2 0.3 1.9 0.3 3.2 0.6 4.5 0.6 Upper molars 5.0 1.5 6.6 1.5 5.0 1.5 6.6 1.5 Lower incisors 0.5 0.2 1.0 0.2 1.4 0.3 2.1 0.3 Lower canine 1.2 0.3 1.9 0.3 2.0 0.3 2.7 0.3 Lower first premolar 1.2 0.3 1.9 0.3 2.2 0.4 3.1 0.4 Lower second premolar 1.1 0.3 1.8 0.3 2.2 0.4 3.1 0.4 Lower molars 5.0 1.5 6.6 1.5 5.0 1.5 6.6 1.5

[0162] The exemplary measured dependence of the bubble's oscillation period T.sub.B on the average diameter of the lateral surface, D.sub.ave=(D.sub.min+D.sub.max)/2 of the endodontic access opening is shown in FIG. 11a. A LightWalker branded laser system available from Fotona, d.o.o., Slovenia was used in the measurement. The liquid 3 within the cavity 2, 28 was water, and the laser source 4 was an Er:YAG laser with the wavelength of 2940 nm which is strongly absorbed in water. The laser pulse duration was about 25 sec and the laser pulse energy E.sub.L was either 10 mJ or 20 mJ. As depicted in FIGS. 11a and 11b, the laser beam 5 was delivered from the laser source 4 through the Fotona Optoflex brand articulated arm 14 and the handpiece 7 (Fotona H14) to seventy-four water filled access openings 28 of extracted teeth of different tooth types, through a flat fiber tip 24 (Fotona Flat Sweeps400) with its flat surface ending 11 submersed in water to an insertion depth h.sub.f of either 2 mm or 4 mm. The fiber tip's diameter was 0.4 mm, and the average diameter of the lateral surface (D.sub.ave) ranged from about 1 mm to about 6.5 mm, with D.sub.min ranging from about 1 mm to about 6 mm, and D.sub.max ranging from about 1.5 mm to about 7.5 mm.

[0163] Referring again to FIG. 11a, the depicted lines represent numerical fits to the oscillation period data using the function T.sub.B=KD.sub.ave.sup.0.5, analogously to Eq. 1 and FIG. 7a. It is to be noted that the values of the numerical fits for Dave=14 mm define the unconstrained oscillation periods T.sub.o. The obtained values are: K=1010 s.Math.mm.sup.0.5 and T.sub.o=270 s (for E.sub.L=20 mJ and h=4 mm); K=830 s.Math.mm.sup.0.5 and T.sub.o=214 s (for E.sub.L=20 mJ and h=2 mm); K=800 s.Math.mm.sup.0.5 and T.sub.o=222 s (for E.sub.L=10 mJ and h=4 mm); and K=620 s.Math.mm.sup.0.5 and T.sub.o=166 s (for E.sub.L=10 mJ and h=2 mm).

[0164] When analogously to FIG. 7b, the bubble oscillation period data T.sub.B according to FIG. 11a, is divided by the corresponding unconstrained oscillation periods T.sub.o, the obtained ratios T.sub.B/T.sub.o shown in FIG. 11b are found to be approximately independent of the laser pulse energy E.sub.L and insertion depth h for all average diameters D.sub.ave. The full line in FIG. 11b represents the result of fitting all data for all access openings and for both values of laser energy and both insertion depths to the function of Eq. 3. The best fit is obtained with T.sub.B/T.sub.o=C.sub.aveD.sub.ave.sup.0.5, where the average diameter coefficient for endodontic cavities is equal to C.sub.ave=3.75 mm.sup.0.5 with the statistical coefficient of determination, R.sup.2=0.76, in excellent agreement with the average diameter coefficient for cylindrical cavities of C.sub.ave=3.74 mm.sup.0.5 (FIG. 7b).

[0165] Similarly, when the bubble oscillation period data T.sub.B according to FIG. 11a, is divided by the corresponding unconstrained oscillation periods T.sub.o, the obtained ratios T.sub.B/T.sub.o shown in FIG. 11c are found to be approximately independent of the laser pulse energy E.sub.L and insertion depth h for all lateral surfaces A.sub.ls=D.sub.minD.sub.max/4. The full line in FIG. 11c represents the result of fitting all data for all access openings and for both values of laser energy and both insertion depths to the function of Eq. 4. The best fit is obtained with T.sub.B/T.sub.o=C.sub.lsA.sub.ls.sup.0.25, where the lateral surface coefficient for endodontic cavities (C.sub.ls) is equal to C.sub.ls=3.47 mm.sup.0.5 with R.sup.2=0.76, also in excellent agreement with the lateral surface coefficient of C.sub.ls=3.50 mm.sup.0.5 for the ideal cylindrically shaped cavity (FIG. 7c).

[0166] Therefore, for the embodiments of our invention where the size and shape of the lateral surface 27 represent the most significant uncontrolled varying cavity size influencing the bubble dynamics, the pulse separation times which are about optimal for most of the cavities can be taken to be the same as for an ideal cylindrical cavity, and are thus determined according to Eq. 3 using D.sub.ave=(D.sub.min+D.sub.max)/2, and C.sub.ave=3.74 mm.sup.0.5 or according to Eq. 4 using A.sub.ls=D.sub.minD.sub.max/4, and C.sub.ls=3.50 mm.sup.0.5.

[0167] However, for some procedures where there exists a sufficiently strong correlation between sizes of D.sub.min and D.sub.max, the minor or major diameter alone can represent a statistically significant characteristic dimension. For example, for the endodontic data according to FIG. 11a, a good fit was obtained also with:

T.sub.B/T.sub.o=C.sub.minD.sub.min.sup.0.5(7)

where C.sub.min=3.45 mm.sup.0.5 with R.sup.2=0.75; and

T.sub.B/T.sub.o=C.sub.maxD.sub.max.sup.0.5(8)

where C.sub.max=3.95 mm.sup.0.5 with R.sup.2=0.70, resulting in

T.sub.p-opt=F.sub.ST.sub.oC.sub.minD.sub.min.sup.0.5(9)

and

T.sub.p-opt=F.sub.ST.sub.oC.sub.maxD.sub.max.sup.0.5(10)

[0168] It is noted that the ranges indicated above for parameters K.sub.D and KA approximately correspond to the ranges of the products F.sub.SC.sub.ave, F.sub.SC.sub.min, F.sub.SC.sub.max, and of the product F.sub.SC.sub.ls respectively.

[0169] Further, it is also within the present scope that more specific ranges of K.sub.D relate to ranges of each of F.sub.SC.sub.ave, F.sub.SC.sub.min, and/or F.sub.SC.sub.max individually, wherein F.sub.s varies within the preferred ranges as outlined herein and D.sub.ave, D.sub.mi.sub.n, D.sub.max would be used as D (in the formula K.sub.DT.sub.oD.sup.0.5). Similarly, the ranges specified for K.sub.D may also be used instead of those for K.sub.A (in K.sub.AT.sub.oA.sup.0.25), providing that the units for K.sub.D (in mm.sup.0.5) are replaced by units for K.sub.A (in mm.sup.0.25).

[0170] It is to be appreciated that the function as given by Eq. 1 represents only one of possible fitting functions to the oscillation data. For example, our analysis shows that a very good fit to the oscillation data can be obtained also by using the following function:

T.sub.B=T.sub.o(1+K.sub.i/D.sub.i),(11)

leading to

T.sub.p-opt=F.sub.sT.sub.o(1+K.sub.i/D.sub.i),(12)

wherein D.sub.i represents one of the main lateral dimensions of a treated cavity, D.sub.min, D.sub.max or D.sub.ave, and K.sub.min, K.sub.max and K.sub.ave are the corresponding fitting parameters. As above, the time T.sub.o represents the bubble oscillation time for the infinitely wide cavity (D.sub.i).

[0171] For the oscillation times in endodontic access cavities, as shown for example for D.sub.ave in FIG. 11 a, the fitting parameters to Eq. (11) are, for D.sub.min, D.sub.max and D.sub.ave, equal to K.sub.min=2.90.3 (R.sup.2=0.7), K.sub.max=3.70.3 (R.sup.2=0.6) and K.sub.ave=3.40.3 (R.sup.2=0.7), correspondingly.

[0172] In one of the exemplary embodiments an Er:YAG laser was used to perform enhanced irrigation of the access opening and root canals, where the set of relevant controlled parameters includes laser pulse energy (E.sub.L), laser pulse duration (t.sub.p), the fiber tip geometry: a flat fiber with output shape 11 or a pointed fiber with output shape 13, the fiber tip's diameter D, and the depth of insertion h. The corresponding values of the bubble oscillation period for an infinitely large lateral surface 27 of the endodontic access cavity 28, as obtained using the same fitting technique as presented in FIG. 11a, are shown in Table 2. The data presents an embodiment where the laser beam 5 extends substantially across the whole cross section of the fiber tip 23.

TABLE-US-00002 TABLE 2 Fiber tip geometry Flat Pointed Fiber tip diameter 300 m 400 m 500 m 600 m 400 m 600 m t.sub.p (s) E.sub.L (mJ) h (mm) T.sub.o (s) T.sub.o (s) T.sub.o (s) T.sub.o (s) T.sub.o (s) T.sub.o (s) 25 10 2 161 166 153 146 166 147 25 20 2 202 214 199 190 215 188 25 10 4 216 222 204 195 225 196 25 20 4 254 270 251 240 271 237 50 10 2 145 141 137 134 134 123 50 20 2 183 187 168 168 207 170 50 10 4 193 188 184 179 202 165 50 20 4 231 235 212 212 261 215

[0173] It is to be appreciated that the values of T.sub.o for E.sub.L, t.sub.p, h, and D which are not presented in Table 2, can be approximately obtained by constructing new data points within and as well below and above the range of the discrete set of values depicted in Table 2, using a linear or a suitable higher order interpolation or fitting method. In some examples, the control unit may be adapted to interpolate such values for T.sub.o based on two or more known values of T.sub.o. For example, a table including one or more values of Table 2 may be stored in a storage device as outlined above, and, depending on the controlled parameters, the control unit may select a value of T.sub.o from the table and/or interpolate a suitable value based on two or more values stored in the table. Additionally or alternatively, the operator of the apparatus may be provided with the table, and he/she may then enter a suitable value for T.sub.o via the user interface.

[0174] The control unit may be adapted to control the pulse repetition as a function of the unconstrained oscillation period T.sub.o of the first vapor bubble, which may depend on the wavelength of the radiation beam, and/or the energy of the first laser pulse (p.sub.a), and/or the pulse duration of the first pulse (t.sub.p), and/or the exit component 8 and/or the insertion depth, e.g. according to Table 2 or interpolations thereof, e.g. using one or more of the Eqs. 5, 6, 9 or 10, such that the interaction between the first vapor bubble 18 and the second vapor bubble 18 generates a shock wave within the liquid 3.

[0175] In one of the preferred embodiments, the apparatus, e.g. implemented as a cleaning system configured for cleaning of cavities, e.g., endodontic access opening cavities, filled with liquid. A cavity may have a lateral surface characterized by a minor and/or major inner diameter (D.sub.min, D.sub.max), that may vary from cavity to cavity. The cleaning system may comprise an electromagnetic radiation system, e.g. a laser system, wherein the electromagnetic radiation system is adapted to be operated in pulsed operation with at least one pulse set (21) containing at least two individual pulses (p) having each an individual pulse energy, wherein within the pulse set (21) a first pulse (p.sub.a) of the pulses (p), having a pulse duration (t.sub.p) and pulse energy (E.sub.L), is followed by a second pulse (p.sub.b) of the pulses (p) with a pulse repetition time (T.sub.p), wherein the pulses are adapted to generate a first vapor bubble (18) within the liquid (3) by means of the corresponding first pulse (pa) and to generate a second vapor bubble (18) within the liquid (3) by means of the

corresponding second pulse (p.sub.b). The pulse repetition time is controlled, e.g. by a control unit, based on the unconstrained oscillation period T.sub.o of the first vapor bubble as a function of the wavelength of the radiation beam, and/or the energy of the first laser pulse (p.sub.a), and/or the pulse duration of the first pulse (t.sub.p), and/or the exit component 8 and/or the insertion depth (h) according to Table 2 or by some other data characterizing the influence of the above said parameters. Preferably, the control unit 22 is adapted to adjust the pulse repetition time (T.sub.p) as a function of the unconstrained oscillation period T.sub.o of the first vapor bubble and of the cavity minor inner diameter (D.sub.min) and/or major inner diameter (D.sub.max), using at least one of the Eqs. 5, 6, 9 or 10, such that the interaction between the first vapor bubble (18) and the second vapor bubble (18) generates a shock wave within the liquid (3).

[0176] FIG. 12 shows in a schematic diagram an exemplary temporal course of pulse sets 21 according to the invention. In this connection, the course of the amplitude of the pulse sets 21 is illustrated as a function of time. The pulse sets 21 follow one another along one single optical path within the laser system 1 with a temporal pulse set spacing T.sub.S being the temporal difference between the end of one pulse set 21 and the beginning of the next pulse set 21. The temporal pulse set spacing T.sub.S is expediently 10 msT.sub.S500 ms, advantageously 10 msT.sub.S100 ms, and is in the illustrated embodiment of the inventive method approximately 10 ms. The lower temporal limit for temporal set spacing T.sub.S of 10 ms is set in order to allow sufficient time for the laser active material, such as, for example, a flash-lamp pumped laser rod, to cool off during the time between subsequent pulse sets 21. The individual pulse sets 21 have a temporal set length is of, for example, approximately 2 ms. Depending on the number of individual pulses p provided infra the value of the temporal set length is can vary. The maximal number of pulse sets 21, and correspondingly the maximal number of individual pulses p, that may be delivered during a cleaning session is limited at least by the maximal delivered cumulative energy below which the temperature increase of the liquid 3 does not exceed an allowed limit.

[0177] It is to be appreciated that, the bubble oscillation periods T.sub.B as defined by Eqs. 3, 4, 7, 8 represent only average oscillation periods, and that in practice the oscillation periods may be spread around those average values of the oscillation periods T.sub.B, as demonstrated in exemplary embodiments depicted in FIGS. 11b and 11c. Therefore, the T.sub.p-opt as calculated for the average bubble oscillation periods according to Eqs. 5 and 6, or 9 and m may not be perfectly optimal to generate a shock wave within a particular liquid-filled cavity.

[0178] This may be solved in yet another embodiment, where, in order to facilitate automatic adjustability of the pulse repetition time T.sub.p to an expected spread of the bubble oscillation period around the expected average oscillation period (e.g. corresponding to minor deviations due to the specifics of the cavity geometries), the apparatus (e.g. laser system 1) is configured with a laser source 4 having a (automatically) variable, sweeping pulse generation. In this manner, the shock wave emission may be automatically optimized for particular cavity dimensions and shapes and or for particular controlled parameters. The general idea of the inventive sweeping technique is to generate multiple pairs of first and second bubbles 18, 18 such, that the time difference between the onset time t.sub.ob of the second vapor bubble 18 and the onset time toa of the first vapor bubble 18 (FIG. 8b) is repeatedly varied in a sweeping manner. By varying said time difference it is made sure, that at least one pair of bubbles 18, 18 matches the required timing, as with the first and second bubbles 18, 18 of FIG. 8b, and thus emitting at least one shock wave 25 (FIG. 8a) during each sweeping cycle. By repeatedly performing such sweeping cycles, the generation of shock waves 25 may be repeated to an extent until the desired irrigation goal is achieved.

[0179] FIG. 13 shows an enlarged detail illustration of the diagram according to FIG. 12 in the area of an individual pulse set 21. Each pulse set 21 has expediently at least two and maximally 20 individual pulses p, advantageously two to eight individual pulses p, and preferably two to four individual pulses p, and in the illustrated embodiment according to FIG. 13 there are six individual pulses p. Maintaining the aforementioned upper limit of the number of individual pulses p per pulse set 21 avoids overheating of the laser active material. The individual pulses p have a temporal pulse duration t.sub.p and follow one another along one single optical path within the laser system in a pulse repetition time T.sub.P, the pulse repetition time T.sub.P being the time period from the beginning of one single pulse p to the beginning of the next, subsequent pulse p.

[0180] The pulse duration t.sub.p is for weakly absorbed wavelengths in the range of 1 ns and <85 ns, and preferably 1 ns and 25 ns. The lower temporal limit of the pulse duration t.sub.p for weakly absorbed wavelengths ensures that there are no shock waves created in the liquid 3 during the vapor bubble 18 expansion. And the upper pulse duration t.sub.p limit for weakly absorbed wavelengths ensures that the laser pulse power is sufficiently high to generate optical breakdown in the liquid.

[0181] For highly absorbed wavelengths, the pulse duration t.sub.p is in the range of 1 us and <500 s, and preferably of 10 s and <100 s. The lower temporal limit for highly absorbed wavelengths ensures that there is sufficient pulse energy available from a free-running laser. And the upper pulse duration limit for highly absorbed wavelengths ensures that the generated heat does not spread via diffusion too far away from the vapor bubble, thus reducing the laser-to-bubble energy conversion efficiency. Even more importantly, the upper pulse duration limit ensures that laser pulses are shorter than the vapor bubble rise time, t.sub.max1t.sub.01, in order not to interfere with the bubble temporal oscillation dynamics. In FIG. 10, the amplitude of the laser beam or of its individual pulses p is schematically plotted as a function of time wherein the temporal course of the individual pulses p, for ease of illustration, are shown as rectangular pulses. In practice, the pulse course deviates from the schematically shown rectangular shape of FIG. 13.

[0182] Referring now to FIG. 13, a first exemplary shock wave emission enhancing pulse (SWEEPS) set 21 according to the invention is proposed, wherein the pulse repetition time T.sub.P is varied or swept in discreet positive or negative steps from an initial pulse period T.sub.po to a final pulse period T.sub.pm, preferably + across a range from T.sub.p0=T.sub.p-opt.sub.1 to T.sub.pm=T.sub.p-opt+.sub.2 (or from T.sub.po=T.sub.p-opt+.sub.2 to T.sub.pm=T.sub.p-opt.sub.1 in the case of a negative ), where .sub.1 and .sub.2 are each preferably in a range from m to 300 sec, even more preferably in a range from 20 to 75 sec, and expediently in a range from 25 to 75 sec. In a preferred embodiment .sub.1=.sub.2. By using this inventive pulse repetition sweeping technique, it is ensured that at least one pair of pulses p within the number of multiple pulses p.sub.o to p.sub.n, p.sub.n+1 of FIG. 13 matches the required pulse repetition rate, thereby resembling the first and second pulses p.sub.a, p.sub.b of FIG. 8b with the required adjusted and optimal pulse repetition time T.sub.P=T.sub.p-opt in between, and thus generating at least one fitting pair of bubbles 18, 18 (FIG. 8b) for emitting at least one shock wave during each sweeping cycle. Notably, by sweeping within a small range around the estimated optimum pulse repetition time (e.g. determined from the unconstrained bubble oscillation period and a diameter of the cavity), it may be ensured that the true optimum pulse repetition time is achieved with certainty for the specific cavity at hand.

[0183] The pulse repetition time T.sub.P may be swept within each pulse set 21 as exemplarily shown in FIG. 13 where the pulse repetition time T.sub.p is discretely swept from pulse p.sub.o to pulse p.sub.n+1 by changing the pulse repetition time T.sub.p from pulse to pulse by an additional discreet temporal step , while multiple pulse sets 21 of such or similar kind may follow one another. In the illustrated embodiment of the inventive method, pulse sets 21 consisting of six pulses p.sub.o to p.sub.n+1 are shown, but pulse sets 21 with a larger or smaller number of pulses p may be used as well.

[0184] Alternatively, as a second preferred sweeping pattern, a number of m pulse sets 21 may be applied, wherein the pulse repetition time T.sub.P may be varied or swept from pulse set 21 to pulse set 21 as exemplarily shown in FIG. 14: The pulse repetition time T.sub.p is discretely swept from pulse set 21 to pulse set 21 by starting at an initial repetition time T.sub.po, and then changing the pulse repetition time T.sub.p from pulse set 21 to pulse set 21, by a discreet temporal step to a final repetition time T.sub.pm. The sweeping cycle may be re-started each time the whole sweeping range has been covered. In the embodiment of the inventive method illustrated in FIG. 11, pulse sets consisting of two pulses p.sub.0, p.sub.1 are shown, but pulse sets with a larger number of pulses p may be used as well. In any case the same effect as with the sweeping pattern of FIG. 10 can be achieved: At least one pair of pulses p.sub.0, p.sub.1 within the number of m pulse sequences 21 of FIG. 14 matches the required pulse repetition rate, thereby resembling the first and second pulses p.sub.a, p.sub.b of FIG. 8b with the required adjusted and optimal pulse repetition time T.sub.P=T.sub.p-opt in between, and thus emitting at least one shock wave during each sweeping cycle.

[0185] A further preferred, third sweeping pattern is schematically depicted in FIG. 15: One pulse set 21 contains multiple pairs of two pulses p.sub.0, p.sub.1, wherein a subsequent pulse p.sub.2 of each pair follows a corresponding initial pulse p.sub.1, and wherein the pulse repetition times T.sub.p within all pairs is kept constant. However, from pair of pulses p.sub.0, p.sub.1 to a subsequent pair of pulses p.sub.0, p.sub.1, the pulse energy of each second pulse p.sub.1 is varied in a sweeping manner. In the shown example the pulse energy is increased from pair to pair by a certain delta. On the other hand, an energy decrease may be applied as well. Such pulse energy sweeping is based on the finding, that the lower the second pulsed p.sub.1 energy is, the longer it will take the second bubble 18 (FIG. 8a, 8b) to develop appreciably to influence the first bubble's 18 collapse, and vice versa. This way it can again be achieved, that at least one pair of bubbles 18, 18 matches the required timing, as with the first and second bubbles 18, 18 of FIG. 8b, and thus emitting at least one shock wave 25 (FIG. 8a) during each sweeping cycle. Additionally or alternatively, also the energy of the first pulse may be swept, similarly as described with reference to the second pulse.

[0186] A combined SWEEP method may be used as well, where the pulse repetition time T.sub.P is swept within pulse sets 21 from one pulse p to another, and/or from pulse set 21 to pulse set 21. Furthermore, the sweeping pulse energy of FIG. 15 may be combined with the sweeping pulse repetition times T.sub.P of FIG. 13 and/or of FIG. 14.

[0187] In order to facilitate improved adjustability and/or control, in various embodiments, the laser system 1 may be configured with a laser source 4 having variable pulse parameters, e.g. a variable pulse rate or repetition time, a variable pulse energy, a variable pulse set rate, and/or a variable temporal pulse set length is of the pulse set 21. In this manner, the shock wave emission may be optimized for particular cavity dimensions and shape, and also for a particular placement of the fiber tip or positioning of the laser focus in the different locations relative to the cavity. Namely, the placement of the fiber tip or positioning of the laser focus relative to the cavity may affect the properties of the bubble oscillations and shock wave emission. In one of the embodiments, a centering system may be used to center the fiber tip relative to the walls of the cavity, and/or to center the fiber tip near the entrance, or bottom of the cavity, or near an occlusion within the cavity.

[0188] The bubble oscillation period T.sub.B may for example vary from about 10 s to about 3000 is, based at least in part on the thermo-mechanical properties of the liquid.sub.3, the shape and volume of the liquid reservoir, the laser wavelength, beam emission profile, configuration of the head, and so forth. Accordingly, when the pulse repetition time T.sub.P will be adjusted to approximately match T.sub.p-opt (e.g. adjusted to a range between approximately 60% T.sub.B and approximately 95% T.sub.B), the pulse repetition rate FP, will be in the range from about 0.35 kHz to about 167 kHz, such that the laser source 1 may be adapted accordingly.

[0189] The laser pulse energy E.sub.L, according to the invention, may be fixed for all pulses within a pulse set 21. In certain embodiments, however, the energy of the subsequent pulse may be adjustable to automatically gradually decrease, for example linearly or exponentially, from pulse to pulse within each set 21. This approach may be especially advantageous for pulse sets with a pulse number of n=2, where the energy E.sub.L of the second pulse p.sub.b may be lower than that of the first pulse p.sub.a, since the function of the second bubble 18 is only to create an additional pressure on the collapsing bubble 18 during the initial expansion phase of the bubble 18.

[0190] Alternatively, the laser pulse energy E.sub.L may be adjustable to gradually increase from pulse to pulse within a pulse set 21, in order to increase even further the pressure of the subsequent bubbles on the prior bubbles.

[0191] Additionally or alternatively, in one of the embodiments of our invention, the laser system may comprise a feedback system to determine the bubble dynamics and feed it back to the control unit such as to control deviations of the pulse repetition time around the estimated optimum frequency to optimize shock wave generation.

[0192] For example, the amount of shock waves generated may be measured by sweeping, and the feedback system may be adapted to control the pulse repetition frequency such as to maximize the shock wave generation. In other words, a closed control loop control for automatically delivering a subsequent laser pulse at the appropriate T.sub.p-opt is formed. In other examples, as a result of the measured amount of shock waves, the laser pulse repetition time T.sub.p might be manually adjusted by the user to be approximately equal to T.sub.p-opt.

[0193] Several irrigants for the endodontic cleaning are available, and include sodium hypochlorite (NaOCl), chlorhexidine gluconate, alcohol, hydrogen peroxide and ethylenediaminetetraacetic acid (EDTA). However, in one of the preferred embodiments only water may be used instead of a potentially toxic irrigant since the generation of shock waves according to our invention reduces or eliminates the need for the use of chemicals.

[0194] It will be appreciated that, while the foregoing example methods are directed to cleaning of root canals and/or bone cavities, in accordance with principles of the present disclosure, similar methods and/or systems may be utilized to clean other body tissues, for example periodontal pockets, and/or the like. The method may be also used to clean selected small surfaces of electronic and precision mechanical components during manufacturing, maintenance and servicing, especially when it is not desirable or possible to expose the whole electronic or other component to a standard cleaning or irrigation procedure.

[0195] While the principles of this disclosure have been shown in various embodiments, many modifications of structure, arrangements, proportions, the elements, materials and components, used in practice, which are particularly adapted for a specific environment and operating requirements may be used without departing from the principles and scope of this disclosure. These and other changes or modifications are intended to be included within the scope of the present disclosure and may be expressed in the following claims.

[0196] The present disclosure has been described with reference to various embodiments. However, one of ordinary skill in the art appreciates that various modifications and changes can be made without departing from the scope of the present disclosure. Accordingly, the specification is to be regarded in an illustrative rather than a restrictive sense, and all such modifications are intended to be included within the scope of the present disclosure. Likewise, benefits, other advantages, and solutions to problems have been described above with regard to various embodiments. However, benefits, advantages, solutions to problems, and any element(s) that may cause any benefit, advantage, or solution to occur or become more pronounced are not to be construed as a critical, required, or essential feature or element of any or all the claims.

[0197] Systems, methods and computer program products are provided. In the detailed description herein, references to various embodiments, one embodiment, an embodiment, an example embodiment, etc., indicate that the embodiment described may include a particular feature, structure, or characteristic, but every embodiment may not necessarily include the particular feature, structure, or characteristic. Moreover, such phrases are not necessarily referring to the same embodiment. Further, when a particular feature, structure, or characteristic is described in connection with an embodiment, it is submitted that it is within the knowledge of one skilled in the art to affect such feature, structure, or characteristic in connection with other embodiments whether or not explicitly described. After reading the description, it will be apparent to one skilled in the relevant art(s) how to implement the disclosure in alternative embodiments.

[0198] As used herein, the terms comprises, comprising, or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Also, as used herein, the terms coupled, coupling, or any other variation thereof, are intended to cover a physical connection, an electrical connection, a magnetic connection, an optical connection, a communicative connection, a functional connection, and/or any other connection. When language similar to at least one of A, B, or C is used in the claims, the phrase is intended to mean any of the following: (1) at least one of A; (2) at least one of B; (3) at least one of C; (4) at least one of A and at least one of B; (5) at least one of B and at least one of C; (6) at least one of A and at least one of C; or (7) at least one of A, at least one of B, and at least one of C.