{"id":1973,"date":"2023-07-29T15:03:04","date_gmt":"2023-07-29T19:03:04","guid":{"rendered":"https:\/\/faculty.wcu.edu\/mtanaka\/?page_id=1973"},"modified":"2026-05-26T15:49:44","modified_gmt":"2026-05-26T19:49:44","slug":"design-of-medical-devices","status":"publish","type":"page","link":"https:\/\/faculty.wcu.edu\/mtanaka\/design-of-medical-devices\/","title":{"rendered":"Design of Medical Devices Course"},"content":{"rendered":"\n<div class=\"et_pb_section_0 et_pb_section et_section_regular et_block_section\"><div class=\"et_pb_row_0 et_pb_row et_block_row\"><div class=\"et_pb_column_0 et_pb_column et_pb_column_4_4 et-last-child et_block_column et_pb_css_mix_blend_mode_passthrough\"><div class=\"et_pb_text_0 et_pb_text et_pb_bg_layout_light et_pb_module et_block_module\"><div class=\"et_pb_text_inner\"><p><span style=\"font-size: xx-large;\"><strong><\/strong><\/span><\/p>\n<h4 style=\"text-align: center;\"><span style=\"font-size: x-large;\"><strong>New Course at WCU - Spring 2022<\/strong><\/span><\/h4>\n<p style=\"text-align: center;\"><span style=\"font-size: xx-large;\"><strong>Design of Medical Devices<\/strong><\/span><\/p>\n<h3 style=\"text-align: center;\"><span style=\"color: #666666;\"><strong>Martin Tanaka, PhD, PE<\/strong><\/span><\/h3>\n<p><strong>Course Description: <\/strong>Design of Medical Devices is a special topics course which provides an overview of several important biomedical engineering topics.\u00a0 It includes the processes used to design and develop commercial products, biomaterials and their applications in medical devices, and content to understanding regulatory requirements. It also includes elements of human anatomy and physiology, engineering calculations, human subject testing, and business and ethical considerations related to the topic.\u00a0\u00a0 Credits 3<\/p>\n<p><strong>Prerequisites: <\/strong>Materials Science, Computer Utilization, Mechanics of Materials, Probability and Statistics, and Ordinary Differential Equations<\/p>\n<p><strong>Course Aims and Objectives: <\/strong><span style=\"font-size: 14px;\">This course is a technical elective for students who have completed their fundamental training in mathematics and basic engineering courses.\u00a0 The course is designed for a junior or senior in mechanical engineering but may be suitable for students in other majors who meet the required prerequisites necessary to be successful in the course.\u00a0 Students will learn fundamental information about biomedical engineering through lectures and interactive classroom discussions. Several group projects will be used to address challenging material and foster collaborative effort essential in this interdisciplinary field.<\/span><\/p>\n<p>By the end of this course, students will; <span style=\"font-size: 14px;\">Develop foundational knowledge in commercial product design; <\/span><span style=\"font-size: 14px;\">Develop a fundamental understanding of basic human anatomy, mechanical properties of bones and joints, and the ability to calculate stress in a biological system; <\/span><span style=\"font-size: 14px;\">Understand how biomedical devices are developed and the federal regulations that control the development and sale of these products; <\/span><span style=\"font-size: 14px;\">Read technical articles in the field of biomedical engineering and describe the content contained within.<\/span><\/p>\n<\/div><\/div><div class=\"et_pb_text_1 et_pb_text et_pb_bg_layout_light et_pb_module et_block_module\"><div class=\"et_pb_text_inner\"><p><strong>Summary of Course Topics<\/strong><\/p>\n<p><span style=\"text-decoration: underline;\">Commercial Product Design Topics:<\/span> \u00a0<span style=\"font-size: 14px;\">Voice of the Customer; <\/span><span style=\"font-size: 14px;\">Product Specifications; <\/span><span style=\"font-size: 14px;\">Conceptual Design; <\/span><span style=\"font-size: 14px;\">Initial Product Design; <\/span><span style=\"font-size: 14px;\">Design Optimization; <\/span><span style=\"font-size: 14px;\">Design Review; <\/span><span style=\"font-size: 14px;\">Prototyping and Testing; <\/span><span style=\"font-size: 14px;\">Problem based learning; <\/span><span style=\"font-size: 14px;\">Critical Thinking in Engineering; <\/span><span style=\"font-size: 14px;\">Human centered design; <\/span><span style=\"font-size: 14px;\">Divergent Thinking<\/span><\/p>\n<p><span style=\"text-decoration: underline;\">Biomaterials &amp; Medical Devices Topics:<\/span> \u00a0<span style=\"font-size: 14px;\">Introduction to biomaterials; <\/span><span style=\"font-size: 14px;\">Biocompatibility; <\/span><span style=\"font-size: 14px;\">Hydrogels; <\/span><span style=\"font-size: 14px;\">Tissue Engineering Fundamentals; <\/span><span style=\"font-size: 14px;\">Scaffolds, cells, biologically active molecules, and bioprinting; <\/span><span style=\"font-size: 14px;\">Adult stem cells, embryonic stem cells, induced pluripotent stem cells (IPSC); <\/span><span style=\"font-size: 14px;\">Therapeutic cloning &amp; controversy; <\/span><span style=\"font-size: 14px;\">Chemical signals, autographs, allographs, xenografts, synthetic tissue grafts, transplant rejection; <\/span><span style=\"font-size: 14px;\">Human Structural Anatomy - bones, ligaments, cartilage, tendons, biomechanical properties; <\/span><span style=\"font-size: 14px;\">Musculoskeletal System \u2013 muscles, joints, etc.; <\/span><span style=\"font-size: 14px;\">Prosthetics and Orthotics, and Exoskeletons; <\/span><span style=\"font-size: 14px;\">Artificial vision devices; <\/span><span style=\"font-size: 14px;\">Cardiovascular system Part 1 \u2013 Anatomy of the heart, and flow through arteries and veins, Pressure gradients and osmotic pressure in capillary beds, Oxygen partial pressure, diffusion, equilibrium, and hemoglobin; <\/span><span style=\"font-size: 14px;\">Cardiovascular system Part 2 - Blood pH, CO2, and bicarbonate, aneurisms and strokes, balloon angioplasty and stents<\/span><\/p>\n<p><span style=\"text-decoration: underline;\">Regulatory Science &amp; Ethics topics:<\/span>\u00a0 <span style=\"font-size: 14px;\">Origins of the FDA; <\/span><span style=\"font-size: 14px;\">Product Codes, Device Classes, Exempt, 510k, PMA, etc.; <\/span><span style=\"font-size: 14px;\">Guest Speaker from Industry; <\/span><span style=\"font-size: 14px;\">Guest Speaker From FDA; <\/span><span style=\"font-size: 14px;\">Business Aspects in BME (Product Dev. Process, CGMP, Reimbursement, V&amp;V 40); <\/span><span style=\"font-size: 14px;\">Human Subject Research - biomedical engineering ethics, Institutional Review Boards; <\/span><span style=\"font-size: 14px;\">Data Analysis \u2013 review of statistics, t-test, ANOVA; <\/span><span style=\"font-size: 14px;\">Course Review Discussion and integration of concepts<\/span><\/p>\n<p><a href=\"https:\/\/youtu.be\/musmgKEPY2o\" style=\"font-size: 14px;\"><\/a><\/p>\n<\/div><\/div><div class=\"et_pb_text_2 et_pb_text et_pb_bg_layout_light et_pb_module et_block_module\"><div class=\"et_pb_text_inner\"><p><strong><u>Module 1: Design and Development of Commercial Products <\/u><\/strong><\/p>\n<p>Commercial products are design and developed using a structured process.\u00a0 Medical devices are no exception. Some of the benefits of using a structured process include the following: <span style=\"font-size: 14px;\">Reduced risk of product failure; <\/span><span style=\"font-size: 14px;\">Lower overall product development costs; <\/span><span style=\"font-size: 14px;\">Faster time to market; <\/span><span style=\"font-size: 14px;\">Alignment of engineering and business objectives; <\/span><span style=\"font-size: 14px;\">Lower manufacturing costs; <\/span><span style=\"font-size: 14px;\">Higher product quality<\/span><\/p>\n<p>Thus, it is not surprising that major manufacturers use this process. Starting with the business roadmap and working around clockwise the process includes setting up a team, understanding the needs of your customers, developing engineering designs, optimizing and refining the designs, prototyping, testing, preparing for manufacturing, and finally production.<\/p>\n<p><a href=\"https:\/\/youtu.be\/musmgKEPY2o\" style=\"font-size: 14px;\"><\/a><\/p>\n<\/div><\/div><div class=\"et_pb_image_0 et_pb_image et_pb_module et_block_module\"><span class=\"et_pb_image_wrap\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Product_dev.jpg\" width=\"568\" height=\"427\" srcset=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Product_dev.jpg 568w, http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Product_dev-480x361.jpg 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) 568px, 100vw\" class=\"wp-image-2011\" \/><\/span><\/div><div class=\"et_pb_text_3 et_pb_text et_pb_bg_layout_light et_pb_module et_block_module\"><div class=\"et_pb_text_inner\"><p><a href=\"https:\/\/youtu.be\/musmgKEPY2o\"><\/a><\/p>\n<p>\u00a0<strong>Mechanical Engineering Design<\/strong><\/p>\n<p>Many people don\u2019t know how to design a mechanical system using engineering. Here is a simple breakdown.\u00a0 It\u2019s not the only way and your approach could differ based on the type of product you are engineering.\u00a0 But if you have limited experience, it may help you get started.<\/p>\n<p>&nbsp;<\/p>\n<ol>\n<li>Begin by thinking about the functions that your product needs to satisfy. Consider different approaches \/ ways to solve each problem and come up with an initial design.<\/li>\n<li>Begin designing the product from the inside out. Focus on the interactions of the individual components, motors, gears, belts, buttons, etc. Model the parts in 3D CAD and assemble them together. Optimize the design to avoid long shafts under bending loads or other areas that induce high stress (no math yet), and optimize the part configuration for a compact design.<\/li>\n<li>Take measurements of your assembly and begin to design the housing that will hold it. Focus on the internal geometry needed to properly hold your important functional parts, not on the outside \u201cbox\u201d. In good mechanical design the outer housing will often look like you poured a thick layer of cement over the functional parts. Add feet for mounting and clean up the aesthetics.<\/li>\n<li>Now that the design concept is solidified, its time for the engineering. Use the geometry in the model to obtain dimensions for your calculations. Look for areas of high stress, calculate it, and compare it to the material strength. If it is less, move to the next area.\u00a0 If it is more, modify the geometry or the material and repeat the analysis. If it is far lower, consider reducing the size to reduce cost and weight and run the analysis again. This process is the key to engineering. The goal is to solve problems through calculation, not trial and error.<\/li>\n<li>Once you have checked everything that you can think to check, it\u2019s time to verify your work. Build a prototype and test it. This can take a long time and be expensive, so hopefully you will only need to do this once.<\/li>\n<li>Assuming that the design passes the tests, you can now begin building production tooling and manufacturing equipment to make your product.<a href=\"https:\/\/youtu.be\/musmgKEPY2o\"><\/a><a href=\"https:\/\/youtu.be\/BHMUXFdBzik\"><\/a><\/li>\n<\/ol>\n<\/div><\/div><div class=\"et_pb_text_4 et_pb_text et_pb_bg_layout_light et_pb_module et_block_module\"><div class=\"et_pb_text_inner\"><p><a href=\"https:\/\/youtu.be\/musmgKEPY2o\"><\/a><\/p>\n<p><strong style=\"font-size: 14px;\">Human Centered Design<\/strong><\/p>\n<p>In human centered design, emphasis is placed on people rather than the product. It includes meeting with the end users of the product and getting to know them before the product is designed.\u00a0 Making quick prototypes and placing them in the hands of the customers to get feedback.\u00a0 Iterating and optimizing toward a final solution. <a href=\"https:\/\/youtu.be\/musmgKEPY2o\">https:\/\/youtu.be\/musmgKEPY2o<\/a><\/p>\n<\/div><\/div><div class=\"et_pb_image_1 et_pb_image et_pb_module et_block_module\"><span class=\"et_pb_image_wrap\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Human_centered_design.jpg\" width=\"624\" height=\"323\" srcset=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Human_centered_design.jpg 624w, http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Human_centered_design-480x248.jpg 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) 624px, 100vw\" class=\"wp-image-2010\" \/><\/span><\/div><div class=\"et_pb_text_5 et_pb_text et_pb_bg_layout_light et_pb_module et_block_module\"><div class=\"et_pb_text_inner\"><p><a href=\"https:\/\/youtu.be\/musmgKEPY2o\"><\/a><\/p>\n<p><strong>Divergent Thinking<\/strong><\/p>\n<p>Divergent thinking enables people to discover new ways to solve problems. Unlike convergent thinking where possibilities are narrowed down until only one idea remains, divergent thinking aims to spread out our thoughts. Thinking in new ways can reveal new solution approaches. Good used of this method in product design includes first thinking divergently to explore the design space, then thinking convergently to identify a solution approach that satisfies the requirements. <a href=\"https:\/\/youtu.be\/BHMUXFdBzik\">https:\/\/youtu.be\/BHMUXFdBzik<\/a><\/p>\n<\/div><\/div><div class=\"et_pb_image_2 et_pb_image et_pb_module et_block_module\"><span class=\"et_pb_image_wrap\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Divergent_Thinking.jpg\" width=\"469\" height=\"244\" srcset=\"https:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Divergent_Thinking.jpg 469w, https:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Divergent_Thinking-300x156.jpg 300w\" sizes=\"(max-width: 469px) 100vw, 469px\" class=\"wp-image-2009\" \/><\/span><\/div><div class=\"et_pb_text_6 et_pb_text et_pb_bg_layout_light et_pb_module et_block_module\"><div class=\"et_pb_text_inner\"><p>\u00a0<strong><u>Module 2: Biomaterials and Medical Devices<\/u><\/strong><\/p>\n<p>The field of biomaterials is over 70 years old with some of the first medical devices being used in the late 1940s and early 1950s. Medical devices have had a significant impact on human health and the economy, saving millions of lives and improving the quality of life for millions more.<\/p>\n<p><strong>Biomaterial<\/strong> - A biomaterial is a nonviable material used in a medical device intended to interact with biological systems.\u00a0The original biomaterials were \u201coff the shelf\u201d.\u00a0 These were standard materials like stainless steel developed for other applications. Using them for a medical application made them \u201cbiomaterials\u201d. Next came passive materials specifically design to improve biocompatibility. An example is 316L, surgical stainless steel. It\u2019s a modified version of 316 stainless steel that has low carbon content to further enhanced corrosion resistance. Having found ways to minimize adverse reactions, the next phase of biomaterials was to enhance positive interactions. Coronary stents coated with drug releasing chemicals not only keep blood vessels open, but also provide medication directly to the inside of the vessel. The latest innovation in biomaterials include self-assembling structures and materials that facilitate functional remodeling.<\/p>\n<p><strong>Biocompatibility<\/strong> \u2013 For a material to be biocompatible it must have the ability to perform with an appropriate host response in a specific application. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Examples of \u201cappropriate host responses\u201d include resistance to blood clotting, resistance to bacterial colonization, and normal uncomplicated healing. Notice that it is specific to the application, so the same material may be biocompatible when used as a skin patch, but not biocompatible when used as a contact lens or an implanted tissue mesh.<\/p>\n<p><strong>Biological Biomaterials -\u00a0<\/strong>Solid porous scaffolds infused with cell and drugs can be used to develop regenerated tissue. This tissue can be developed within a bioreactor (in vitro - outside the body) or within the body (in vivo). Fibrous scaffolds, decellularized scaffolds, and hydrogels may also be used<\/p>\n<\/div><\/div><div class=\"et_pb_image_3 et_pb_image et_pb_module et_block_module\"><span class=\"et_pb_image_wrap\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Biomaterials.jpg\" width=\"608\" height=\"252\" srcset=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Biomaterials.jpg 608w, http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Biomaterials-480x199.jpg 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) 608px, 100vw\" class=\"wp-image-2012\" \/><\/span><\/div><div class=\"et_pb_image_4 et_pb_image et_pb_module et_block_module\"><span class=\"et_pb_image_wrap\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Biological_materials.jpg\" width=\"489\" height=\"434\" srcset=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Biological_materials.jpg 489w, http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Biological_materials-480x426.jpg 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) 489px, 100vw\" class=\"wp-image-2013\" \/><\/span><\/div><div class=\"et_pb_text_7 et_pb_text et_pb_bg_layout_light et_pb_module et_block_module\"><div class=\"et_pb_text_inner\"><p><strong>Medical Devices<\/strong><\/p>\n<p><strong>Prosthetic Heart Valves <\/strong>\u2013 4.5 million replacement valves are implanted each year worldwide. They may be mechanical valves such as the bileaflet tilting disk or made from biological tissue such as a xenograft from a pig.<\/p>\n<p><strong>Total Hip Replacement <\/strong>- Mechanical stress, degenerative diseases, overuse, or natural aging can lead to joint dysfunction. Over 300,000 total hip replacements are performed in the USA each year. Many people can walk a few days after surgery and resuming athletic activities may also be possible.<\/p>\n<p><strong>Ventricular Assist Device <\/strong>- Nearly 5,000,000 Americans are living with seriously failing hearts. Yet, there are only about 3,500 donor hearts available in the US each year. VADs may be used to prolong and improve the quality of life.<\/p>\n<p><strong>CT Scanner <\/strong>\u2013 Some medical devices are used for diagnosis. A computerized tomography (CT) scanner combines a series of X-ray images taken from different angles around your body and uses a computer to assemble a 3D image of your bones and other radiopaque materials.<\/p>\n<\/div><\/div><div class=\"et_pb_text_8 et_pb_text et_pb_bg_layout_light et_pb_module et_block_module\"><div class=\"et_pb_text_inner\"><h3><strong><u>Module 3: Understanding the regulatory requirements<\/u><\/strong><\/h3>\n<p>The information contained below was generated from CDRH learn on the FDA website. <a href=\"https:\/\/www.fda.gov\/training-and-continuing-education\/cdrh-learn\">https:\/\/www.fda.gov\/training-and-continuing-education\/cdrh-learn<\/a>\u00a0<\/p>\n<\/div><\/div><\/div><\/div><div class=\"et_pb_row_1 et_pb_row et_block_row\"><div class=\"et_pb_column_1 et_pb_column et_pb_column_4_4 et-last-child et_block_column et_pb_css_mix_blend_mode_passthrough\"><div class=\"et_pb_image_5 et_pb_image et_pb_module et_block_module\"><span class=\"et_pb_image_wrap\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Reg1-2.jpg\" width=\"624\" height=\"350\" srcset=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Reg1-2.jpg 624w, http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Reg1-2-480x269.jpg 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) 624px, 100vw\" class=\"wp-image-2004\" \/><\/span><\/div><div class=\"et_pb_image_6 et_pb_image et_pb_module et_block_module\"><span class=\"et_pb_image_wrap\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Reg2.jpg\" width=\"624\" height=\"350\" srcset=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Reg2.jpg 624w, http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Reg2-480x269.jpg 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) 624px, 100vw\" class=\"wp-image-1988\" \/><\/span><\/div><div class=\"et_pb_image_7 et_pb_image et_pb_module et_block_module\"><span class=\"et_pb_image_wrap\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Reg3.jpg\" width=\"624\" height=\"350\" srcset=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Reg3.jpg 624w, http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Reg3-480x269.jpg 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) 624px, 100vw\" class=\"wp-image-1989\" \/><\/span><\/div><div class=\"et_pb_image_8 et_pb_image et_pb_module et_block_module\"><span class=\"et_pb_image_wrap\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Reg4.jpg\" width=\"624\" height=\"352\" srcset=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Reg4.jpg 624w, http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Reg4-480x271.jpg 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) 624px, 100vw\" class=\"wp-image-1990\" \/><\/span><\/div><div class=\"et_pb_image_9 et_pb_image et_pb_module et_block_module\"><span class=\"et_pb_image_wrap\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Reg5.jpg\" width=\"624\" height=\"351\" srcset=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Reg5.jpg 624w, http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Reg5-480x270.jpg 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) 624px, 100vw\" class=\"wp-image-1991\" \/><\/span><\/div><div class=\"et_pb_image_10 et_pb_image et_pb_module et_block_module\"><span class=\"et_pb_image_wrap\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Reg6.jpg\" width=\"624\" height=\"350\" srcset=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Reg6.jpg 624w, http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Reg6-480x269.jpg 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) 624px, 100vw\" class=\"wp-image-1992\" \/><\/span><\/div><div class=\"et_pb_image_11 et_pb_image et_pb_module et_block_module\"><span class=\"et_pb_image_wrap\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Reg7.jpg\" width=\"624\" height=\"351\" srcset=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Reg7.jpg 624w, http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Reg7-480x270.jpg 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) 624px, 100vw\" class=\"wp-image-1993\" \/><\/span><\/div><div class=\"et_pb_image_12 et_pb_image et_pb_module et_block_module\"><span class=\"et_pb_image_wrap\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Picture8.jpg\" width=\"624\" height=\"352\" srcset=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Picture8.jpg 624w, http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Picture8-480x271.jpg 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) 624px, 100vw\" class=\"wp-image-1994\" \/><\/span><\/div><div class=\"et_pb_image_13 et_pb_image et_pb_module et_block_module\"><span class=\"et_pb_image_wrap\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Picture9.jpg\" width=\"624\" height=\"351\" srcset=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Picture9.jpg 624w, http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Picture9-480x270.jpg 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) 624px, 100vw\" class=\"wp-image-1995\" \/><\/span><\/div><div class=\"et_pb_image_14 et_pb_image et_pb_module et_block_module\"><span class=\"et_pb_image_wrap\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Picture10.jpg\" width=\"624\" height=\"349\" srcset=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Picture10.jpg 624w, http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Picture10-480x268.jpg 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) 624px, 100vw\" class=\"wp-image-1996\" \/><\/span><\/div><div class=\"et_pb_image_15 et_pb_image et_pb_module et_block_module\"><span class=\"et_pb_image_wrap\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Picture11.jpg\" width=\"624\" height=\"352\" srcset=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Picture11.jpg 624w, http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Picture11-480x271.jpg 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) 624px, 100vw\" class=\"wp-image-1997\" \/><\/span><\/div><div class=\"et_pb_image_16 et_pb_image et_pb_module et_block_module\"><span class=\"et_pb_image_wrap\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Picture12.jpg\" width=\"624\" height=\"351\" srcset=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Picture12.jpg 624w, http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Picture12-480x270.jpg 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) 624px, 100vw\" class=\"wp-image-1998\" \/><\/span><\/div><div class=\"et_pb_image_17 et_pb_image et_pb_module et_block_module\"><span class=\"et_pb_image_wrap\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Picture13.jpg\" width=\"624\" height=\"350\" srcset=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Picture13.jpg 624w, http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Picture13-480x269.jpg 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) 624px, 100vw\" class=\"wp-image-1999\" \/><\/span><\/div><div class=\"et_pb_image_18 et_pb_image et_pb_module et_block_module\"><span class=\"et_pb_image_wrap\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Picture14.jpg\" width=\"624\" height=\"350\" srcset=\"http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Picture14.jpg 624w, http:\/\/faculty.wcu.edu\/mtanaka\/files\/2023\/07\/Picture14-480x269.jpg 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) 624px, 100vw\" class=\"wp-image-2000\" \/><\/span><\/div><div class=\"et_pb_text_9 et_pb_text et_pb_bg_layout_light et_pb_module et_block_module\"><div class=\"et_pb_text_inner\"><p><strong><em>Faculty are encouraged to contact me directly to obtain detailed information about syllabus, lectures, assignments, projects, and exams.\u00a0 Verification of credentials is required.<\/em><\/strong><\/p>\n<p><strong><em>Martin Tanaka received support from the National Science Foundation (Award #2149517) that contributed to this work.<\/em><\/strong><\/p>\n<\/div><\/div><\/div><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":180,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1973","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/faculty.wcu.edu\/mtanaka\/wp-json\/wp\/v2\/pages\/1973","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/faculty.wcu.edu\/mtanaka\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/faculty.wcu.edu\/mtanaka\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/faculty.wcu.edu\/mtanaka\/wp-json\/wp\/v2\/users\/180"}],"replies":[{"embeddable":true,"href":"https:\/\/faculty.wcu.edu\/mtanaka\/wp-json\/wp\/v2\/comments?post=1973"}],"version-history":[{"count":14,"href":"https:\/\/faculty.wcu.edu\/mtanaka\/wp-json\/wp\/v2\/pages\/1973\/revisions"}],"predecessor-version":[{"id":2716,"href":"https:\/\/faculty.wcu.edu\/mtanaka\/wp-json\/wp\/v2\/pages\/1973\/revisions\/2716"}],"wp:attachment":[{"href":"https:\/\/faculty.wcu.edu\/mtanaka\/wp-json\/wp\/v2\/media?parent=1973"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}