نوع مقاله: مقاله کامل پژوهشی

نویسندگان

1 دانشجوی دکتری مهندسی پزشکی، گروه بیومکانیک، دانشکده مهندسی پزشکی، دانشگاه صنعتی امیرکبیر، تهران

2 دانشیار، گروه بیومکانیک، دانشکده مهندسی پزشکی، دانشگاه صنعتی امیرکبیر، تهران

3 استاد مدعو، دانشکده مهندسی مکانیک، دانشگاه صنعتی شریف، تهران

10.22041/ijbme.2016.19419

چکیده

در مطالعه­ی حاضر، روشی نوین برای به­دست آوردن معادلات حاکم بر سیستم اسکلتی بدن انسان ارائه ‌شده­است. در این روش، رویکردی نوین برای وارد کردن ویژگی‌های سینماتیکی مفاصل زیستی و همچنین اثر زنجیره‌های پیچیده­ی سینماتیکی سیستم اسکلتی در معادلات حرکت ارائه ‌شده­است. روش پیشنهادی در این مقاله با استفاده از حساب دیفرانسیل توابع ماتریسی، معادلات حاکم بر سیستم اسکلتی را به‌صورت معادلات دیفرانسیل معمولی تحصیل می‌کند. علاوه ‌بر این، ازآنجا که معادلات حاصل به‌صورت بازگشتی ارائه‌شده‌اند، این روش برای به­دست آوردن معادلات دیفرانسیل حرکت سیستم اسکلتی بدن انسان، رویکردی کارا از نظر محاسباتی پیشنهاد می‌کند. به‌منظور بررسی صحت روابط پیشنهادشده در این مقاله، مکانیزمی استاندارد شامل سه حلقه­ی سینماتیکی بسته موردتوجه قرار گرفت. نتایج حاصل از حل دینامیک مستقیم این مکانیزم با استفاده از روش پیشنهادی، با نتایج ارائه‌شده در سایر مراجع معتبر مقایسه شدند و روش پیشنهادی صحت‌سنجی شد. به­علاوه، به‌منظور بررسی کاربرد روش پیشنهادی در شبیه‌سازی سیستم اسکلتی بدن انسان، مدل‌سازی دینامیکی کمربند شانه‌ای در حضور ریتم شانه در دستور کار قرار گرفت. برای توصیف ریاضی ریتم شانه از دو مدل ریاضی استفاده شد: مدل اصلی و مدل ساده‌شده. تفاوت میان نتایج شبیه‌سازی این دو مدل بر ضرورت استفاده از داده‌های آزمایشگاهی اصلی برای مدل‌سازی ریتم شانه تأکید می‌کرد. ازآنجا که علت علاقه‌مندی محققان به استفاده از داده‌های ساده‌شده­ی ریتم شانه ناشی از  محدودیت در فرمول‌های موجود برای مدل‌سازی سیستم اسکلتی می­شود، با استفاده از روش پیشنهادی در این مقاله این مشکل مرتفع می‌گردد.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

A Novel Method for Mathematical Modeling of the Skeletal System of the Human Body: Incorporating the Kinematic Characteristics of Biological Joints and the Effects of Complex Kinematic Chains of the Skeletal System

نویسندگان [English]

  • Hossein Ehsani 1
  • Mostafa Rostami 2
  • Mohammad Parnianpour 3

1 Ph.D Candidates, Biomechanic Department, Biomedical EngineeringFaculty, Amirkabir University of Technology, Tehran, Iran

2 Associate Professor, Biomechanic Department, Biomedical EngineeringFaculty, Amirkabir University of Technology, Tehran, Iran

3 Adjunct Professor, Mechanical Engineering Department, Sharif University of Technology, Tehran

چکیده [English]

In the current study, a novel method for deriving the governing equations of the skeletal system of the human body has been presented. In this method, a novel approach for incorporating the kinematic characteristics of biological joints and also the effects of complex kinematic chains of the skeletal system has been proposed. The suggested method while utilizing the calculus of matrix-valued functions, derives the governing equations of the skeletal system in the form of ordinary differential equations. Moreover, since the formulations were presented in a recursive fashion, this paper suggests a computationally efficient algorithm to derive the differential equations of motion for the skeletal system. In order to examine the validity of the proposed formulations, a benchmark mechanism with three closed-loop kinematic constraints were considered. We compared the results obtained from our formulations with the outcomes presented in other studies and validated the proposed formulations. Besides, in order to investigate the application of the suggested method in simulation of the skeletal system of the human body, dynamical modeling of the shoulder rhythm was taken into consideration. Two models were employed for describing the shoulder rhythm: Original model and simplified model. The discrepancies observed between the outcomes of these two models delineate the necessity of using the original data for the shoulder rhythm. While the limitations of the available formulations have compelled the researchers to employ the simplified model for the shoulder rhythm, with the method we propose in this study this problem is obviated.

کلیدواژه‌ها [English]

  • skeletal system
  • Mathematical modeling
  • shoulder rhythm

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