CN115192228A - Control system of invisible orthodontic cycle - Google Patents
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Abstract
Description
Translated fromChinese技术领域technical field
本发明属于牙齿矫正技术领域，具体为隐形矫治周期的控制系统。The invention belongs to the technical field of orthodontic treatment, and particularly relates to a control system for an invisible orthodontic treatment cycle.
背景技术Background technique
随着无托槽隐形矫治技术的日渐发展，隐形矫治器拥有摘戴方便、临床易用、有利于口腔卫生清理等特点，使得无托槽隐形矫治技术越来越受欢迎。With the gradual development of bracket-free invisible orthodontic technology, invisible appliances have the characteristics of convenient removal and wearing, clinical ease of use, and favorable oral hygiene cleaning, making bracket-free invisible orthodontic technology more and more popular.
目前的各家隐形矫治技术中，单副矫治器的佩戴时间从5天——15天各有不同。佩戴天数差距较大，再加上隐形矫治的累加效果，导致患者的整个治疗周期相差较大，相同类型病例的治疗周期可能相差50％以上。但是，患者本身身体条件存在差异，不能完全地统一为某一个佩戴天数，否则会导致患者出现牙齿松动、牙龈出血，甚至牙齿脱落、临床效果和矫治目标相差太大等不良情况。Among the current invisible orthodontic technologies, the wearing time of a single pair of aligners varies from 5 days to 15 days. The large gap in wearing days, coupled with the cumulative effect of invisible orthodontics, leads to a large difference in the entire treatment cycle of patients, and the treatment cycle for the same type of cases may differ by more than 50%. However, there are differences in the physical conditions of the patients themselves, and the number of wearing days cannot be completely unified. Otherwise, the patients will suffer from tooth loosening, bleeding gums, or even tooth loss, and the clinical effect and treatment goals are too different.
比如：两个情况类似的简单拥挤病例，患者均为12岁，矫治步数同样是20步。为其中一个1患者制定的单副矫治器佩戴时间为7天，而另一个患者因为自身因素“A”，单副矫治器的佩戴天数为14天，这样就会出现14X20-7X20＝140天，两个患者的矫治周期相差140天。For example: two simple crowded cases with similar conditions, both patients are 12 years old, and the number of corrective steps is also 20 steps. The wearing time of a single pair of appliances for one of the 1 patients is 7 days, while the other patient wears a single pair of appliances for 14 days because of its own factor "A", so there will be 14X20-7X20=140 days, There was a 140-day difference in the treatment cycles of the two patients.
比如：两个情况类似的双牙颌前突病例，一个患者15岁，一个患者30岁，矫治步数同样是50步。因为各自的自身因素“B”，医生为15岁患者设定的单副矫治器佩戴时间为8天，而30岁患者为12天，12X50-8X50＝200天，两个患者的矫治周期相差200天。For example: two cases of biprotrusion with similar conditions, one patient is 15 years old, the other is 30 years old, and the number of corrective steps is also 50 steps. Because of their own factors "B", the doctor set the wearing time of a single pair of appliances for a 15-year-old patient to be 8 days, while that of a 30-year-old patient is 12 days. sky.
比如：两个情况类似的深覆合病例，一个患者15岁，一个患者30岁，矫治步数同样是40步。因为各自的自身因素“C”，医生为15岁患者设定的单副矫治器佩戴时间为10天，而30岁患者也为10天，那么两个患者的矫治周期一样。For example: two similar cases of deep overburden, one patient is 15 years old, the other is 30 years old, and the number of corrective steps is also 40 steps. Because of their own factors "C", the doctor set the wearing time of a single pair of appliances for a 15-year-old patient to be 10 days, and for a 30-year-old patient, it is also 10 days, so the correction cycle for the two patients is the same.
鉴于此类情况，我们有必要设计一个控制系统，通过收集整理各种因素，统计分析结果，并依据分析结果，为每一位患者制定适合其自身条件的单副矫治器佩戴天数，优化矫治周期，提升用户体验感。In view of such situations, it is necessary for us to design a control system. By collecting and sorting out various factors, statistically analyzing the results, and based on the analysis results, we can formulate the wearing days of a single pair of appliances suitable for each patient's own conditions and optimize the correction period. , to enhance the user experience.
发明内容SUMMARY OF THE INVENTION
本发明的目的在于提供隐形矫治周期的控制系统，以解决上述背景技术中提出的问题。The purpose of the present invention is to provide a control system for an invisible orthodontic period, so as to solve the above-mentioned problems in the background art.
为了实现上述目的，本发明提供如下技术方案：隐形矫治周期的控制系统，包括患者客户端、设计中心和医生客户端；In order to achieve the above purpose, the present invention provides the following technical solutions: a control system for an invisible correction cycle, including a patient client, a design center and a doctor client;
所述患者客户端包括有信息采集模块，用于采集患者身体数据并发送给设计中心的信息接收模块；The patient client includes an information collection module for collecting patient body data and sending it to the information receiving module of the design center;
所述医生客户端包括有医生信息模块、选择模块、方案显示模块和输入模块，用于输入患者对应的医生信息、医生习惯偏好、掌握力度等信息并将该信息发送给设计中心的信息接收模块；The doctor client includes a doctor information module, a selection module, a plan display module and an input module, which are used to input the information of the doctor corresponding to the patient, the doctor's habitual preference, grasping strength, etc. and send the information to the information receiving module of the design center. ;
所述设计中心包括有数据库、信息接收模块、检索模块、设计模块、修改模块、对比模块、审核模块和延时模块，设计中心用于综合患者客户端和医生客户端发来的数据为患者制定设计治疗方案。The design center includes a database, an information receiving module, a retrieval module, a design module, a modification module, a comparison module, an audit module and a delay module. Design a treatment plan.
优选的，所述信息接收模块用于接收信息采集模块和医生信息模块发送的数据并将该数据发送给检索模块、设计模块和修改模块；Preferably, the information receiving module is configured to receive data sent by the information collection module and the doctor information module and send the data to the retrieval module, the design module and the modification module;
所述设计模块用于对患者的牙齿进行三维建模、设计初始方案，并将信息发送给方案显示模块和数据库的缓存单元；The design module is used for 3D modeling of the patient's teeth, designing an initial plan, and sending the information to the plan display module and the cache unit of the database;
所述修改模块用于从数据库中调出初始方案，并将方案数据和信息接收模块的发送数据进行结合，得到当前修改方案，并将该当前修改方案发送给方案显示模块和数据库的缓存单元；The modification module is used to call out the initial plan from the database, and combine the plan data with the data sent by the information receiving module to obtain the current modified plan, and send the current modified plan to the plan display module and the cache unit of the database;
所述对比模块用于从数据库的缓存单元中调出初始方案和修改方案，并将初始方案和修改方案进行对比，得到差距信息，并将差距信息发送给方案显示模块，所述方案显示模块接收到对比模块发送的差距信息并显示出来。The comparison module is used to call out the initial plan and the modified plan from the cache unit of the database, and compare the initial plan and the modified plan to obtain gap information, and send the gap information to the plan display module, and the plan display module receives The gap information sent to the comparison module and displayed.
优选的，所述设计中心还包括延时模块；Preferably, the design center further includes a delay module;
所述输入模块还包括时间输入单元和数据输入单元，时间输入单元用于向延时模块发送预定时间信息，数据输入单元于向信息接收模块发送矫治方案数据。The input module further includes a time input unit and a data input unit, the time input unit is used for sending predetermined time information to the delay module, and the data input unit is used for sending correction plan data to the information receiving module.
优选的，所述医生客户端还包括选择模块；Preferably, the doctor client further includes a selection module;
所述选择模块用于向设计模块发送高速成像信息；The selection module is used for sending high-speed imaging information to the design module;
所述设计模块接收到选择模块发送的高速成像信息后，从数据库中匹配出最接近身体数据的病例信息，并根据对应该病例信息的初始建模信息结合身体数据，进行修改，从而得到对应该身体数据的初始建模信息。After the design module receives the high-speed imaging information sent by the selection module, it matches the case information closest to the body data from the database, and modifies it according to the initial modeling information corresponding to the case information in combination with the body data, so as to obtain the corresponding body data. Initial modeling information for body data.
优选的，所述数据库包括有缓存单元、进行中单元和已完成单元。Preferably, the database includes a cache unit, an ongoing unit and a completed unit.
优选的，所述设计中心还包括检索模块；Preferably, the design center further includes a retrieval module;
所述信息接收模块还用于将身体数据发送给检索模块；The information receiving module is also used for sending the body data to the retrieval module;
所述查找模块用于接收信息接收模块的身体数据，并根据该身体数据从数据库的缓存单元中匹配出最接近身体数据的病例信息，并将该病例信息发送给显示模块；The search module is used for receiving the body data of the information receiving module, and matches the case information closest to the body data from the cache unit of the database according to the body data, and sends the case information to the display module;
所述显示模块还用于接收查找模块发送的病例信息并显示出来。The display module is also used to receive and display case information sent by the search module.
优选的，所述设计中心包括审核模块，所述审核模块用于数据库的缓存单元中调出初始模拟信息、当前模拟信息和未来模拟信息，从数据库的进行中单元中调出最接近身体数据的病例信息，并将当前模拟信息和未来模拟信息与病例信息进行对比，得到审核信息，并将该审核信息发送个显示模块；Preferably, the design center includes an audit module, and the audit module is used to call out initial simulation information, current simulation information and future simulation information from the cache unit of the database, and call out the data closest to the body data from the in-progress unit of the database. Case information, and compare the current simulation information and future simulation information with the case information to obtain review information, and send the review information to a display module;
所述显示模块用于接收点评模块发送的点评信息并显示出来。The display module is used for receiving and displaying the review information sent by the review module.
本发明的有益效果如下：The beneficial effects of the present invention are as follows:
1、本发明通过患者客户端的采集模块采集患者的身体数据，而后利用设计中心对该身体数据进行三维建模，从而模拟出该患者的身体状况，并显示在医生客户端，可将患者按年龄段分类，根据分类，制定可行的矫治周期和方案，并根据既定的年龄段统计牙齿移动速度，治疗效果，可优化的矫治方案，以达到缩短矫治周期的目的，还可以在治疗过程中，利用先进的仪器，定时对比治疗效果，如有需要，根据治疗效果来优化矫治方案，缩短矫治周期。1. The present invention collects the patient's body data through the acquisition module of the patient client, and then uses the design center to carry out three-dimensional modeling of the body data, thereby simulating the patient's physical condition and displaying it on the doctor's client. Segment classification, according to the classification, formulate a feasible treatment cycle and plan, and calculate the tooth movement speed, treatment effect, and optimize the treatment plan according to the established age group to achieve the purpose of shortening the treatment cycle, and can also be used in the treatment process. Advanced instruments, regularly compare the treatment effect, if necessary, optimize the treatment plan according to the treatment effect, and shorten the treatment period.
附图说明Description of drawings
图1为本发明控制系统模块图。FIG. 1 is a block diagram of the control system of the present invention.
具体实施方式Detailed ways
下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.
如图1所示，本发明实施例提供了隐形矫治周期的控制系统，包括患者客户端、设计中心和医生客户端；患者客户端包括信息采集模块；设计中心包括数据库、信息接收模块、检索模块、设计模块、修改模块、对比模块、审核模块、延时模块；医生客户端包括显示模块、选择模块、输入模块；As shown in FIG. 1 , an embodiment of the present invention provides a control system for an invisible correction cycle, including a patient client, a design center, and a doctor client; the patient client includes an information acquisition module; the design center includes a database, an information receiving module, and a retrieval module , design module, modification module, comparison module, review module, delay module; doctor client includes display module, selection module, input module;
所述数据库包括缓存单元、进行中单元和已完成单元；进行中单元和已完成单元用于存储以往的病例信息，病例信息包括患者基本信息、患者身体信息、矫治方案信息、成骨细胞活性信息、破骨细胞活性信息、颌骨骨密度信息、其他信息等，且病例信息不限于以上内容；The database includes a cache unit, an in-progress unit and a completed unit; the in-progress unit and the completed unit are used to store past case information, and the case information includes patient basic information, patient body information, treatment plan information, and osteoblast activity information. , osteoclast activity information, jaw bone mineral density information, other information, etc., and the case information is not limited to the above content;
信息采集模块用于采集患者的身体数据并发送给信息接收模块；输入模块用于输入患者对应的医生信息、医生习惯偏好、掌控力度等信息，并将该信息发送给设计中心的信息接收模块；The information collection module is used to collect the patient's body data and send it to the information receiving module; the input module is used to input the patient's corresponding doctor information, doctor's habitual preference, control strength and other information, and send the information to the information receiving module of the design center;
信息接收模块用于接收采集模块发送的身体数据并发送给设计模块，信息接收模块还用于接收输入模块发送的信息并发送给设计模块和修改模块；The information receiving module is used to receive the body data sent by the acquisition module and send it to the design module, and the information receiving module is also used to receive the information sent by the input module and send it to the design module and the modification module;
设计模块用于接收信息接收模块和医生选择模块发送的数据，对患者的牙齿进行三维建模、设计初始方案，并将信息发送给方案显示模块和数据库的缓存单元，且有多种初始方案可供查看选择；The design module is used to receive the data sent by the information receiving module and the doctor's selection module, carry out 3D modeling of the patient's teeth, design the initial plan, and send the information to the plan display module and the cache unit of the database, and there are various initial plans. for viewing options;
修改模块用于接收信息接收模块发送的修改数据，从数据库中调出初始方案信息，并将方案数据和信息接收模块的发送数据进行结合，得到当前修改信息，并将该当前模拟信息发送给方案显示模块和数据库的缓存单元；The modification module is used to receive the modification data sent by the information receiving module, retrieve the initial scheme information from the database, combine the scheme data with the data sent by the information receiving module, obtain the current modification information, and send the current simulation information to the scheme Display module and database cache unit;
对比模块用于从数据库的缓存单元中调出初始方案和修改方案，并将初始方案和修改方案进行对比，得到差距信息，并将差距信息发送给显示模块，显示模块接收到对比模块发送的差距信息并显示出来。The comparison module is used to call out the initial scheme and the modified scheme from the cache unit of the database, and compare the initial scheme and the modified scheme to obtain the gap information, and send the gap information to the display module, and the display module receives the gap sent by the comparison module. information and display it.
本方案中，通过对比模块得出治疗前和治疗后之间的差距，并将这个差距通过显示模块显示出来，便于医护人员更明确地了解到治疗效果，从而判断该矫治方案的优劣。In this scheme, the difference between before and after treatment is obtained through the comparison module, and the difference is displayed through the display module, so that medical staff can more clearly understand the treatment effect, so as to judge the pros and cons of the treatment plan.
其中，所述设计中心还包括延时模块；所述输入模块包括时间输入单元和数据输入单元，时间输入单元用于向延时模块发送预定时间信息，数据输入单元于向信息接收模块发送矫治方案数据；Wherein, the design center further includes a delay module; the input module includes a time input unit and a data input unit, the time input unit is used to send predetermined time information to the delay module, and the data input unit is used to send the correction plan to the information receiving module data;
方案显示模块用于接收设计模块发送的初始建模信息，并将初始建模信息显示出来，显示模块还用于接收修改模块发送的当前模拟信息，并将当前模拟信息显示出来。The scheme display module is used to receive the initial modeling information sent by the design module, and display the initial modeling information. The display module is also used to receive the current simulation information sent by the modification module, and display the current simulation information.
本方案的基础原理及效果为：本方案中，病例信息中的患者基本信息、患者身体信息、初始建模信息、矫治方案信息、当前模拟信息和未来模拟信息，均是相互关联的。The basic principle and effect of this scheme are: in this scheme, the basic information of the patient, the patient's body information, the initial modeling information, the correction plan information, the current simulation information and the future simulation information in the case information are all interrelated.
本方案中，通过患者客户端的采集模块采集患者的身体数据，而后利用设计中心对该身体数据进行三维建模，从而模拟出该患者的身体状况，并显示在医生客户端；接着医生将对应预备手术策略的矫治方案数据通过输入模块发送给设计中心，设计中心根据矫治方案数据改变从数据库调出的初始建模信息，完成对初始三维建模的修改，得到模拟手术后的当前模拟信息，并发送给医生客户端进行显示。In this scheme, the patient's body data is collected through the acquisition module of the patient client, and then the body data is 3D modeled by the design center, so as to simulate the patient's body condition and display it on the doctor's client; then the doctor will prepare the corresponding The correction plan data of the surgical strategy is sent to the design center through the input module, and the design center changes the initial modeling information called from the database according to the correction plan data, completes the modification of the initial three-dimensional modeling, and obtains the current simulation information after the simulated operation. Sent to the doctor client for display.
因此本方案实现了，模拟患者身体状况和模拟患者预备手术策略的矫治方案后的身体状况。使得医生人员，在不进行手术的情况下，能够预测到术后患者的身体情况，并根据该预测进行相关调整，有利于医生人员的学习和矫治方案的合理选择。Therefore, this scheme realizes the physical condition after simulating the patient's physical condition and simulating the patient's preparation surgery strategy. This enables doctors to predict the physical condition of patients after surgery without performing surgery, and make relevant adjustments according to the prediction, which is conducive to doctors' learning and reasonable selection of treatment plans.
其中，所述医生客户端还包括选择模块；所述选择模块用于向设计模块发送高速成像信息；设计模块接收到选择模块发送的高速成像信息后，从数据库的进行中单元中匹配出最接近身体数据的病例信息，并根据对应该病例信息的初始建模信息结合身体数据，进行修改，从而得到对应该身体数据的初始建模信息。Wherein, the doctor client also includes a selection module; the selection module is used to send high-speed imaging information to the design module; after the design module receives the high-speed imaging information sent by the selection module, it matches the most recent units from the ongoing units of the database. The case information of the body data is modified according to the initial modeling information corresponding to the case information combined with the body data, thereby obtaining the initial modeling information corresponding to the body data.
本方案中，通过选择模块对设计模块的建模方式进行选择，当选择模块发送高速成像信息时，设计模块就在原先类似的初始建模信息结合本患者的身体数据进行修改；选择模块不发送信息的话，设计模块就会根据身体数据自己完成建模；通过选择模块对建模方式进行切换，医生人员可以根据需求切换建模方式，从而提高建模效率。In this scheme, the modeling method of the design module is selected through the selection module. When the selection module sends high-speed imaging information, the design module modifies the original similar initial modeling information combined with the patient's body data; the selection module does not send If the information is available, the design module will complete the modeling by itself according to the body data; by selecting the module to switch the modeling method, doctors can switch the modeling method according to their needs, thereby improving the modeling efficiency.
所述延时模块用于接收时间输入单元发送的预定时间信息，延时模块从数据库的已完成单元中调出骨质生长规律数据以，延时单元还从数据库的缓存单元中调出当前模拟信息，并根据骨质生长规律、当前模拟信息和预定时间信息，推算出对应该预定时间信息的未来模拟信息，延时模块将预定时间信息和未来模拟信息发送给显示模块，延时模块还将未来模拟信息发送个数据库的缓存单元；The delay module is used to receive the predetermined time information sent by the time input unit, the delay module retrieves the bone growth regularity data from the completed unit of the database, and the delay unit also retrieves the current simulation from the cache unit of the database. According to the bone growth law, the current simulation information and the predetermined time information, the future simulation information corresponding to the predetermined time information is calculated. The delay module sends the predetermined time information and future simulation information to the display module, and the delay module will also In the future, the simulated information is sent to a cache unit of the database;
显示模块还用于接收延时模块发送的预定时间信息和未来模拟信息并显示出来。The display module is also used for receiving and displaying the predetermined time information and future simulation information sent by the delay module.
本方案中，延时模块利用已完成单元的骨质生长规律，推断出使用该矫治方案后患者的情况，并通过显示模块显示出来，从长远角度而言，了解到术后的情况，便于提前排除手术隐患，有利于矫治方案的合理选择。In this scheme, the delay module uses the bone growth law of the completed unit to infer the patient's condition after using the correction scheme, and displays it through the display module. From a long-term perspective, knowing the post-operative condition is convenient in advance. Elimination of hidden dangers of surgery is conducive to a reasonable choice of orthodontic treatment.
其中，所述设计中心还包括检索模块；所述信息接收模块还用于将身体数据发送给检索模块；所述检索模块用于接收信息接收模块的身体数据，并根据该身体数据从数据库的缓存单元中匹配出最接近身体数据的病例信息，并将该病例信息发送给显示模块；显示模块还用于接收查找模块发送的病例信息并显示出来。Wherein, the design center further includes a retrieval module; the information receiving module is also used for sending the body data to the retrieval module; the retrieval module is used for receiving the body data of the information receiving module, and according to the body data from the cache of the database The unit matches the case information closest to the body data, and sends the case information to the display module; the display module is also used to receive and display the case information sent by the search module.
本方案中，查找模块根据患者的身体信息查找进行中单元中相近的病例信息，并通过显示模块进行显示；有利于医生人员制定适合该患者身体信息的矫治方案。In this solution, the search module searches for the similar case information in the ongoing unit according to the patient's body information, and displays it through the display module, which is helpful for doctors to formulate a correction plan suitable for the patient's body information.
其中，所述设计中心包括点评模块，点评模块用于数据库的缓存单元中调出初始模拟信息、当前模拟信息和未来模拟信息，从数据库的进行中单元中调出最接近身体数据的病例信息，并将当前模拟信息和未来模拟信息与病例信息进行对比，得到点评信息，并将该点评信息发送个显示模块；显示模块用于接收点评模块发送的点评信息并显示出来。Wherein, the design center includes a review module, and the review module is used to call out the initial simulation information, current simulation information and future simulation information from the cache unit of the database, and call out the case information closest to the physical data from the ongoing unit of the database, The current simulation information and future simulation information are compared with the case information to obtain review information, and the review information is sent to a display module; the display module is used to receive and display the review information sent by the review module.
本方案中，点评模块将进行中单元中的病例信息中的当前模拟信息与代表实施该矫治方案后当前治疗效果的当前模拟信息进行对比，并且将病例信息中未来模拟信息与代表实时该矫治方案后未来治疗效果的未来模拟信息分别进行对比，从而得到对比结果，将该对比结果作为点评信息，点评模块将点评信息发送给显示模块进行显示；实现多方位的对比，从而便于医生人员进行分析该矫治方案的优劣，从而提高医疗经验，选择更优秀的矫治方案。In this scheme, the commenting module compares the current simulation information in the case information in the ongoing unit with the current simulation information representing the current treatment effect after implementing the correction scheme, and compares the future simulation information in the case information with the current simulation information representing the real-time correction scheme The future simulation information of the future treatment effect is compared respectively, so as to obtain the comparison result, and the comparison result is used as the comment information, and the comment module sends the comment information to the display module for display; multi-directional comparison is realized, which is convenient for doctors to analyze the information. The pros and cons of orthodontic programs can improve medical experience and choose better orthodontic programs.
需要说明的是，在本文中，诸如第一和第二等之类的关系术语仅仅用来将一个实体或者操作与另一个实体或操作区分开来，而不一定要求或者暗示这些实体或操作之间存在任何这种实际的关系或者顺序。而且，术语“包括”、“包含”或者其任何其他变体意在涵盖非排他性的包含，从而使得包括一系列要素的过程、方法、物品或者设备不仅包括那些要素，而且还包括没有明确列出的其他要素，或者是还包括为这种过程、方法、物品或者设备所固有的要素。It should be noted that, in this document, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any relationship between these entities or operations. any such actual relationship or sequence exists. Moreover, the terms "comprising", "comprising" or any other variation thereof are intended to encompass a non-exclusive inclusion such that a process, method, article or device that includes a list of elements includes not only those elements, but also includes not explicitly listed or other elements inherent to such a process, method, article or apparatus.
尽管已经示出和描述了本发明的实施例，对于本领域的普通技术人员而言，可以理解在不脱离本发明的原理和精神的情况下可以对这些实施例进行多种变化、修改、替换和变型，本发明的范围由所附权利要求及其等同物限定。Although embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, and substitutions can be made in these embodiments without departing from the principle and spirit of the invention and modifications, the scope of the present invention is defined by the appended claims and their equivalents.
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