(351 days)
PERSEUS is a computer-controlled system, intended to assist in distal femoral resection and tibial resection during Total Knee Arthroplasty, determining reference alignment axes in relation to anatomical and instrumentation structures during stereotaxic orthopaedic surgical procedures.
PERSEUS is a computer assisted system, that helps surgeon in the positioning of implant components, during total knee implant surgical procedure, according to the conventional reference axes in relation to anatomical landmarks. Perseus System is configured to detect, measure, and display angular and positional measurement changes in a triaxial format. The device assists the surgeon in: Establishing the mechanical axis of the femur, determining the varus/valgus angle and the flexion/extension angle of the cutting block relative to the femur. Establishing the mechanical axis of the tibia, determining the varus/valgus angle and the posterior slope angle of the cutting block relative to the tibia. Perseus system utilizes triaxial accelerometer and triaxial gyroscope to determine, through limb movement, reference axes of femur and tibia and relative orientation of distal femoral and tibial cutting guide with respect to frontal and sagittal planes of the limb.
Here's a detailed breakdown of the acceptance criteria and the studies proving the device's performance, based on the provided text:
Acceptance Criteria and Device Performance
1. Table of Acceptance Criteria and Reported Device Performance
| Measure | Acceptance Criteria | Reported Device Performance |
|---|---|---|
| HKA (Hip-Knee-Ankle) angle deviation | within 3° (for final leg alignment) | Average post-operative HKA angle deviation: 0.3 ± 1.5° |
| Average post-operative HKA alignment deviation: 0.7° (range 0-2°) | ||
| Femoral distal resection deviation | within 2° (for distal femoral resection, frontal and lateral planes) | Femoral distal resection deviation: < 2° (frontal and lateral planes) |
| Femoral implant flexion | Not explicitly stated | Average femoral implant flexion: 0.8 ± 0.8° |
| Tibial slope | Not explicitly stated | Average tibial slope: 0.1 ± 1.7° |
| Blood loss | Reduced blood loss compared to conventional technique | Confirmed reduced blood loss compared to conventional technique |
2. Sample Sizes Used for Test Sets and Data Provenance
The document mentions several studies, primarily clinical evaluations. The provenance is Europe (aftermarket clinical evaluation). All studies appear to be prospective clinical evaluations or retrospective analysis of post-operative data.
- Study 1 (Aftermarket Clinical Evaluation - Europe):
- Test Set Sample Size: 3 cohorts of 10 patients each (total 30 patients)
- EM Perseus: 10 patients
- EM Nav: 10 patients (surgical navigation system)
- IM Conv: 10 patients (conventional mechanical instrumentations)
- Data Provenance: Europe (aftermarket clinical evaluation), the specific country is not mentioned. Data is from patients operated by the same surgical team.
- Test Set Sample Size: 3 cohorts of 10 patients each (total 30 patients)
- Study 2 (Aftermarket Clinical Evaluation - Europe):
- Test Set Sample Size: 2 cohorts of 18 patients each (total 36 patients)
- Perseus: 18 patients
- Conventional instrumentation: 18 patients
- Data Provenance: Europe, multicentric study involving two centers.
- Test Set Sample Size: 2 cohorts of 18 patients each (total 36 patients)
- Study 3 (Aftermarket Clinical Evaluation - Europe):
- Test Set Sample Size: Single cohort of 20 patients.
- Data Provenance: Europe.
- Study 4 (Retrospective analysis of post-operative X-rays):
- Test Set Sample Size: 20 cases.
- Data Provenance: Not explicitly stated, but likely from European clinical practice given the context of aftermarket clinical evaluations.
- Study 5 (Retrospective analysis of post-operative X-rays):
- Test Set Sample Size: 53 patients operated with Perseus vs. 52 patients operated with conventional technique (total 105 patients).
- Data Provenance: Not explicitly stated, but likely from European clinical practice.
3. Number of Experts Used to Establish Ground Truth for the Test Set and Qualifications
The document does not specify the number of experts, their qualifications, or their role in establishing ground truth for the test sets (patient data). It mentions that "Clinical evaluation has been done with the same performance requirement when possible or, in alternative, looking at final leg alignment with post-operative x-rays." This suggests that the ground truth for clinical outcomes like HKA angle, femoral implant flexion, and tibial slope was derived from post-operative X-rays, which are generally interpreted by qualified medical professionals (e.g., orthopedic surgeons or radiologists), but the specific details are not provided.
4. Adjudication Method for the Test Set
The document does not explicitly describe an adjudication method (like 2+1 or 3+1) for the clinical outcomes or the interpretation of post-operative X-rays. The analysis of X-rays for angular deviations is likely based on standard radiographic measurement techniques.
5. Multi-Reader Multi-Case (MRMC) Comparative Effectiveness Study
No multi-reader multi-case (MRMC) comparative effectiveness study is explicitly described. The clinical studies compare patient outcomes (e.g., HKA alignment, blood loss) between those treated with Perseus and those with conventional techniques or other navigation systems, not specifically focusing on how human readers improve with vs. without AI assistance in interpretation.
6. Standalone (Algorithm Only) Performance Study
Yes, standalone performance was evaluated through bench tests and pre-clinical evaluation testing:
- Bench tests: Conducted to quantify device accuracy and repeatability. These involved controlled setups to verify:
- Measurement repeatability with different cursor positions.
- Error introduced by mispositioning of ankle instrumentation.
- Repeatability with different sensors.
- Repeatability with different instrument positioning.
- Pre-clinical evaluation testing: Verified accuracy, repeatability, and reproducibility in a simulated OR setup and consistency of the procedure with different users/experience levels.
These tests evaluate the algorithm and device's performance in a controlled environment, separate from human-in-the-loop clinical scenarios.
7. Type of Ground Truth Used
- Bench Tests & Pre-clinical Evaluation: Ground truth was established using controlled variables within appropriate test setups, likely using precise measurement tools, and simulated surgical scenarios with known desired outcomes.
- Clinical Studies: The primary ground truth for measuring clinical outcomes (e.g., HKA angle, femoral distal resection deviation, tibial slope) was derived from post-operative X-rays. Blood loss was also measured as an outcome.
8. Sample Size for the Training Set
The document does not provide details on a specific "training set" for the PERSEUS device. PERSEUS is described as a "computer-controlled system" using inertial sensors and physical positions for positional information. While such systems are developed based on algorithms, the document focuses on the validation studies rather than the development phase's data sets. Therefore, the sample size for an explicit training set is not reported.
9. How the Ground Truth for the Training Set Was Established
Since no specific training set is mentioned in the document, the establishment of ground truth for a training set is not described. The device's operation, based on accelerometers and gyroscopes, suggests it relies on engineering principles and sensor data processing rather than learning from a labeled training dataset in the way a typical AI/ML system for image classification might. The "performance tests" and "bench tests" served to validate the system's accuracy against established physical measurement standards and simulated scenarios.
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September 9, 2020
Orthokey Italia S.r.l. % Guido Bonapace Regulatory Affair Isemed srl Via P. Togliatti, 19/X Imola, 40026 Italy
Re: K192653
Trade/Device Name: Perseus Regulation Number: 21 CFR 882.4560 Regulation Name: Stereotaxic Instrument Regulatory Class: Class II Product Code: OLO Dated: August 6, 2020 Received: August 10, 2020
Dear Guido Bonapace:
We have reviewed your Section 510(k) premarket notification of intent to market the device referenced above and have determined the device is substantially equivalent (for the indications for use stated in the enclosure) to legally marketed predicate devices marketed in interstate commerce prior to May 28, 1976, the enactment date of the Medical Device Amendments, or to devices that have been reclassified in accordance with the provisions of the Federal Food, Drug, and Cosmetic Act (Act) that do not require approval of a premarket approval application (PMA). You may, therefore, market the device, subject to the general controls provisions of the Act. Although this letter refers to your product as a device, please be aware that some cleared products may instead be combination products. The 510(k) Premarket Notification Database located at https://www.accessdata.fda.gov/scripts/cdrh/cfdocs/cfpmn/pmn.cfm identifies combination product submissions. The general controls provisions of the Act include requirements for annual registration, listing of devices, good manufacturing practice, labeling, and prohibitions against misbranding and adulteration. Please note: CDRH does not evaluate information related to contract liability warranties. We remind you, however, that device labeling must be truthful and not misleading.
If your device is classified (see above) into either class II (Special Controls) or class III (PMA), it may be subject to additional controls. Existing major regulations affecting your device can be found in the Code of Federal Regulations, Title 21, Parts 800 to 898. In addition, FDA may publish further announcements concerning your device in the Federal Register.
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Please be advised that FDA's issuance of a substantial equivalence determination does not mean that FDA has made a determination that your device complies with other requirements of the Act or any Federal statutes and regulations administered by other Federal agencies. You must comply with all the Act's requirements, including, but not limited to: registration and listing (21 CFR Part 807); labeling (21 CFR Part 801); medical device reporting of medical device-related adverse events) (21 CFR 803) for devices or postmarketing safety reporting (21 CFR 4, Subpart B) for combination products (see https://www.fda.gov/combination-products/guidance-regulatory-information/postmarketing-safety-reportingcombination-products); good manufacturing practice requirements as set forth in the quality systems (OS) regulation (21 CFR Part 820) for devices or current good manufacturing practices (21 CFR 4, Subpart A) for combination products; and, if applicable, the electronic product radiation control provisions (Sections 531-542 of the Act); 21 CFR 1000-1050.
Also, please note the regulation entitled, "Misbranding by reference to premarket notification" (21 CFR Part 807.97). For questions regarding the reporting of adverse events under the MDR regulation (21 CFR Part 803), please go to https://www.fda.gov/medical-device-safety/medical-device-reportingmdr-how-report-medical-device-problems.
For comprehensive regulatory information about medical devices and radiation-emitting products, including information about labeling regulations, please see Device Advice (https://www.fda.gov/medicaldevices/device-advice-comprehensive-regulatory-assistance) and CDRH Learn (https://www.fda.gov/training-and-continuing-education/cdrh-learn). Additionally, you may contact the Division of Industry and Consumer Education (DICE) to ask a question about a specific regulatory topic. See the DICE website (https://www.fda.gov/medical-device-advice-comprehensive-regulatoryassistance/contact-us-division-industry-and-consumer-education-dice) for more information or contact DICE by email (DICE@fda.hhs.gov) or phone (1-800-638-2041 or 301-796-7100).
Sincerely.
Shumaya Ali, M.P.H. Assistant Director DHT6C: Division of Restorative, Repair and Trauma Devices OHT6: Office of Orthopedic Devices Office of Product Evaluation and Ouality Center for Devices and Radiological Health
Enclosure
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Indications for Use
510(k) Number (if known) K192653
Device Name PERSEUS
Indications for Use (Describe)
PERSEUS is a computer-controlled system, intended to assist in distal femoral resection and tibial resection during Total Knee Arthroplasty, determining reference alignment axes in relation to anatomical and instrumentation structures during stereotaxic orthopaedic surgical procedures.
| Type of Use (Select one or both, as applicable) | |
|---|---|
| Prescription Use (Part 21 CFR 801 Subpart D) | Over-The-Counter Use (21 CFR 801 Subpart C) |
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510(k) Summary
This 510(k) Summary is being submitted as required by 21 CFR 807.92.
5.1 General Information
| Submitter : | ORTHOKEY Italia S.r.l |
|---|---|
| Piazza Nazioni Unite, 15 | |
| 54033 Carrara (MS)-Italy | |
| Tel. +39 055 354829 | |
| Fax +39 055 3246012 |
Consultant/ Contact:
Guido Bonapace ISEMED srl Via Palmiro Togliatti 19/X Imola, BO 40026 ITALY Tel. +39 0542 683803 Fax +39 0542 698456 Email: regulatory@isemed.eu
Summary Prepared Date:
September the 7th, 2020
5.2 Names
| Device Name: | PERSEUS |
|---|---|
| Common Name: | Orthopedic Stereotaxic Instrument |
| Regulation Name: | Stereotaxic Instrument |
| Product Code: | OLO |
| Classification: | 21 CFR 882.4560, Class II |
5.3 Predicate Devices
The medical device PERSEUS is substantially equivalent to the following device legally marketed in the US:
| Applicant | PREDICATE Device name | 510(k) Number |
|---|---|---|
| OrthAlign Inc. | KneeAlign 2 System | K163379 |
Moreover, the following reference device has been considered:
| Applicant | REFERENCE Device name | 510(k) Number |
|---|---|---|
| Zimmer CAS | iASSIST™ Knee System | K141601 |
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5.4 Device Description
PERSEUS is a computer assisted system, that helps surgeon in the positioning of implant components, during total knee implant surgical procedure, according to the conventional reference axes in relation to anatomical landmarks. Perseus System is configured to detect, measure, and display angular and positional measurement changes in a triaxial format.
The device assists the surgeon in:
- Establishing the mechanical axis of the femur, determining the varus/valgus angle and the flexion/extension angle of the cutting block relative to the femur.
- Establishing the mechanical axis of the tibia, determining the varus/valgus angle and the posterior slope angle of the cutting block relative to the tibia.
Perseus system utilizes triaxial accelerometer and triaxial gyroscope to determine, through limb movement, reference axes of femur and tibia and relative orientation of distal femoral and tibial cutting guide with respect to frontal and sagittal planes of the limb.
5.5 Indications for Use
PERSEUS is a computer-controlled system, intended to assist in distal femoral resection and tibial resection during Total Knee Arthroplasty, by determining reference alignment axes in relation to anatomical and instrumentation structures during stereotaxic orthopedic surgical procedures.
| Proposed Device | Predicate Device | Reference Devices | |
|---|---|---|---|
| Product Name | PERSEUS | KneeAlign 2 System | iASSIST Knee System |
| Manufacturer | Orthokey Italia S.r.l. | OrthAlign Inc. | Zimmer CAS |
| 510(K) No. | K163379 | K141601 | |
| ClassificationName | Orthopedic StereotaxicInstrument | Orthopedic StereotaxicInstrument | Orthopedic StereotaxicInstrument |
| Figure | Image: PERSEUS | Image: KneeAlign 2 System | Image: iASSIST Knee System |
| RegulationNumber | 882.4560 | 882.4560 | 882.4560 |
| Regulatory Class | II | II | II |
| ClassificationProduct Code | OLO | OLO | OLO |
| Intended use | |||
| Indications foruse | PERSEUS is a computer-controlled system, intendedto assist in distal femoralresection and tibial | The OrthAlign Plus®System is acomputer-controlled systemintended to assist the surgeonin determining reference | The iASSIST Knee System is acomputer assisted stereotaxicsurgical instrument system toassist the surgeon in the |
| Proposed Device | Predicate Device | Reference Devices | |
| Product Name | PERSEUS | KneeAlign 2 System | iASSIST Knee System |
| resection during Total KneeArthroplasty, bydetermining referencealignment axes in relation toanatomical andinstrumentation structuresduring sterotacticorthopaedic surgicalprocedures. | alignment axes in relation toanatomical structures duringstereotactic orthopedic surgicalprocedures. The KneeAlignsystem facilitates the accuratepositioning of implants andinstrumentation, relative tothese alignment axes.Orthopedic surgical proceduresinclude but are not limited to:Total Knee ArthroplastyUnicompartmental KneeArthroplasty – Tibial TransverseResection | positioning of orthopedicimplant system componentsintra-operatively. It involvessurgical instruments andposition sensors to determinealignment axes in relation toanatomical landmarks and toprecisely position alignmentinstruments and implantcomponents relative to theseaxes. Example orthopedicsurgical procedures includebut are not limited to: TotalKnee Arthroplasty. | |
| Targetpopulation | Orthopedic surgicalprocedures include:Total knee arthroplasty | Orthopedic surgical proceduresinclude but are not limited to:Total Knee ArthroplastyUni-compartmental KneeArthroplasty - Tibial TransverseResection | Orthopedic surgicalprocedures include but arenot limited to:Total knee arthroplasty |
| Anatomical site | knee | knee | Knee |
| Where used(hospital, home,ambulance, etc) | For professional use inoperating room | For professional use inoperating room | For professional use inoperating room |
| Technology | |||
| Energy usedand/ordelivered | • Navigation unit, referencesensor: DC battery power.• Instruments: manualposition and orientation | • Navigation unit, referencesensor and laser module: DCbattery power• Instruments: manual positionand orientation | • Reference sensor: DCbattery power.• Instruments: manualposition and orientation |
| User Interface | Graphical user interface, oncomputer unit, outsidesterile field. | Integrated graphical userinterface, on an electronic unitthat attaches toinstrumentation. | Integrated graphical userinterface, on an electronicunit that attaches toinstrumentation. |
| ControlMechanism | Computer generation ofpositional information, usinginertial sensors,microcontroller, digitalsignal processor andphysical positions ofregistration instruments. | Computer generation ofpositional information, usinginertial sensors,microcontroller, digital signalprocessor and physicalpositions of registrationinstruments. | Computer generation ofpositional information, usinginertial sensors,microcontroller, digital signalprocessor and physicalpositions of registrationinstruments. |
| OperatingPrinciplesRegistration ofanatomy | Electronics attached tomovable instruments,placed in specifiedprocedural positions, forrecording sensor data. | Electronics attached to movableinstruments, placed in specifiedprocedural positions, on or incontact with bony anatomy, forrecording sensor data. | Electronics attached tomovable instruments, placedin specified proceduralpositions, on or in contactwith bony anatomy, forrecording sensor data. |
| Measurementof change inangularorientations | • Computer displayedvalues based on internalcalculations.• Accelerometer | • Computer displayed valuesbased on internal calculation.• Accelerometer measurementof angular change in | • Computer displayed valuesbased on internalcalculation.• Accelerometer |
| Proposed Device | Predicate Device | Reference Devices | |
| Product Name | PERSEUS | KneeAlign 2 System | iASSIST Knee System |
| change in instrumentpositions. | change in instrumentpositions. | ||
| Patient interface | Instrument fixation to bonewith pins or screws.Instrument indications andengagement of bonyanatomy via physical surfacecontact | Instrument fixation to bonewith pins or screws. Instrumentindications and engagement ofbony anatomy via physicalsurface contact | Instrument fixation to bonewith pins or screws.Instrument indications andengagement of bony anatomyvia physical surface contact |
| Main SystemComponents | • Non sterile reusablecomputer unit• Navigation andmeasurement software• Reusable instrument sets• Single-use sensor | • Single-use computer unit• Navigation and measurementsoftware• Reusable instrument sets | • Non sterile reusablecomputer unit• Navigation andmeasurement software• Reusable instrument sets• Single-use sensor |
| Performance | HKA angle within 3° | HKA angle within 3° | HKA angle within 3° |
| Electrical Safetyand EMC | IEC 60601-1IEC 60601-1-2 | IEC 60601-1IEC 60601-1-2 | IEC 60601-1IEC 60601-1-2 |
| Materials | Stainless Steel gradescommon to orthopedicsurgical instrumentsPolymer grades common toorthopedic surgicalinstrumentsInternal electronics | Stainless Steel grades commonto orthopedic surgicalinstrumentsPolymer grades common toorthopedic surgical instrumentsInternal electronics | Stainless Steel gradescommon to orthopedicsurgical instrumentsPolymer grades common toorthopedic surgicalinstrumentsInternal electronics |
| Biocompatibility | Per ISO 10993-1, ExternalCommunicating Device,Tissue/Bone/DentinCommunicating, withsubsystems that havepotential indirect contactfor a limited contactduration (< 24 hours) | Per ISO 10993-1, ExternalCommunicating Device,Tissue/Bone/DentinCommunicating, withsubsystems that have directand potential indirect contactfor a limited contact duration (< 24 hours) | Per ISO 10993-1, ExternalCommunicating Device,Tissue/Bone/DentinCommunicating, withsubsystems that have directand potential indirect contactfor a limited contact duration(< 24 hours) |
| Compatibilitywith theenvironmentand otherdevices | Specified storage andoperating environments fortypical transport andsurgical environments. | Specified storage and operatingenvironments for typicaltransport and surgicalenvironments. | Specified storage andoperating environments fortypical transport and surgicalenvironments. |
| Sterilization | • Navigation unit: EOsterilization.• Instruments: autoclavesterilization | • Navigation unit: EOsterilization.• Instruments: autoclavesterilization | • Navigation unit: EOsterilization.• Instruments: autoclavesterilization |
5.6 Comparison with the predicate and the reference device
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ORTHOKEY ITALIA SRL 510(K) PREMARKET NOTIFICATION
The subject device PERSEUS fall under the same Regulation number, Regulatory Class and Product Code as the predicate device K163379 and the reference device K141601.
The indication for use of the subject device PERSEUS is similar to the one declared by the predicate device K163379 and the reference device K141601.
As per information provided in the table above, the technical and performance features of the proposed and predicate devices are similar or identical. In order to demonstrate the effective comparison related to clinical performance, biocompatibility, sterilization, packaging, shelf life, electrical and EMC safety, specific clinical evaluation and tests based on international standards have been performed.
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In light of evidence listed in the table above, the proposed device PERSEUS can be considered substantially equivalent to the predicate device K163379 and the reference device K141601.
5.7 Performance Data
In order to demonstrate the accuracy and repeatability of the proposed device PERSEUS in terms of alignment of the resection level, with respect to mechanical axis, performance tests have been conducted.
Bench tests performance evaluation of Perseus has been done, verifying the orientation of femoral or tibial resections. Clinical evaluation has been done with the same performance requirement when possible or, in alternative, looking at final leg alignment with post-operative x-rays. The clinical evaluation has been prepared considering:
- Bench testing
- Pre-clinical evaluation testing
- Aftermarket Clinical evaluation (Europe)
- Data generated from literature
Bench testing have been conducted introducing controlled variables within an appropriate test setup throughout the subject device's operational range, to quantify the accuracy of the device. A set of bench tests have been designed in order to:
- Verify the measurement repeatability on a controlled setup, with different cursor positions of the jig
- Verify the error introduced by mispositioning of the ankle instrumentation
- Verify the repeatability of the measurement with different sensors
- Verify the repeatability of the measurement with different instrument positioning
Pre-clinical activities have been conducted to verify accuracy, repeatability and reproducibility in a simulated OR setup and to verify the consistency of the procedure when performed by different users with different level of experience.
Aftermarket clinical evaluation. Since Perseus is CE marked, aftermarket clinical evaluation has been done in Europe. Studies were conducted involving research centers in order to verify clinical results and performances of Perseus.
A study involved 3 cohorts of 10 patients each randomly selected, operated by the same surgical equipe, where perseus was used only for distal femoral resection. The cohorts were dividend in:
- EM Perseus; patients operated with Perseus ●
- EM Nav; patients operated with surgical navigation system,
- IM Conv; patients operated with conventional mechanical instrumentations.
Final limb alignment on frontal and lateral planes and blood loss have been measured postoperatively. Perseus has demonstrated to fulfil surgical goal of final HKA alignment within 3° of deviation and femoral distal resection within 2° of deviation, and a reduced blood loss, compared to conventional technique.
A second study only on femoral resection has been performed on a multicentric study involving two centers. The goal of the study was to verify blood loss and angular deviation of femoral distal resection on frontal and lateral planes, for two cohorts of 18 patients: 1 operated with the use of Perseus; 2 operated with conventional instrumentation. Perseus for the femoral resection has confirmed to satisfy the requirements of have a deviation < 2° in both frontal and lateral planes.
A third study was a single cohort evaluation, on 20 patients, of final limb alignment, blood loss and surgical time. Results show an average femoral resection alignment of 91±0.5° varus in frontal plane and 1.5±1.0° on sagittal plane.
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Data on post-operative x-rays obtained from first 20 cases performed by the same user have been obtained. Results show an average post-operative deviation of HKA angle of 0.3±1.5°, femoral implant flexion of 0.8±0.8° and a tibial slope of 0.1±1.7°.
Data on post-operative x-rays obtained from 53 patients operated with Perseus and compared with 52 patients operated with conventional technique have been obtained. Results show and average post-operative deviation of HKA alignment of 0.7° with a range of 0-2°.
5.8 Conclusion
The comparison performed between the proposed device PERSEUS, the predicate device K163380 and the reference device K141601, is able to demonstrates that the device PERSEUS has similar technical features and clinical performance of the devices previously marketed in US. Particularly, even if the user interface is slightly different from the one proposed by the predicate device, this difference does not raise any new concern in terms of safety and effectiveness, as demonstrated through electrical safety, EMC, sterilization, packaging, shelf life and performance test reports.
In light of evidence summarized above and based on classification, intended use, technological characteristics, and performance data, the subject device PEPRSEUS may be found substantially equivalent to the predicate device KneeAlign 2 System (K163379) and the reference device iASSIST™ Knee System (K141601).
§ 882.4560 Stereotaxic instrument.
(a)
Identification. A stereotaxic instrument is a device consisting of a rigid frame with a calibrated guide mechanism for precisely positioning probes or other devices within a patient's brain, spinal cord, or other part of the nervous system.(b)
Classification. Class II (performance standards).