全國中小學科展

2019年

Improving Spinal Fusions: Redesigning the Pedicle Probe to Prevent Vertebral Breaches

Pedicle probes are medical devices used by surgeons during spinal fusions for patients with conditions such as scoliosis and spinal fractures. The probe creates pilot holes to guide the placement of pedicle screws in vertebrae. The screws are then connected with a metal rod to stabilize the spine. Twenty-nine percent of patients who undergo spinal fusions suffer from vertebral breaches – accidental damage to the spinal cord – which cause complications such as infection, motor defects, and in many cases paralysis. My goal was to make spinal fusions safer by redesigning the pedicle probe to provide surgeons with instantaneous feedback on the probe’s location, enabling them to more accurately place pedicle screws. The pedicle probe I developed takes advantage of the difference in density between the inner cancellous (spongy) bone and the outer cortical (compact) bone found in vertebrae. Cortical bone is avoided by monitoring the cannulation force – the force required to insert the probe. When the probe contacts denser cortical tissue, it warns the user by providing tactile and visual feedback through a vibration motor and an LED. This enables the surgeon to redirect the probe and advance down the optimum path, preventing a possible breach. It proved successful in preventing breaches on lamb vertebrae, which closely resemble human vertebrae. This novel device improves feedback to the surgeon and eliminates the need for costly and potentially harmful ionizing radiation exposure. Furthermore, it does not depend on, or require, any preoperative imaging. The cost of manufacturing the improved probe is less than $42 USD (NT$1297). Results of patent searches for 加拿大, the 美國, and Europe suggest that the redesigned probe is unique in predicting and preventing breaches in spinal fusions based on predetermined force threshold values. The probe is also unique in enabling personalized procedures in spinal fusions for those with complications, through calibrating a control (force) limit based on tissue samples prior to the procedure. Enhancing a surgeon’s ability to determine an appropriate path for pedicle screws through a sensor-enabled probe has the potential to significantly reduce the incidence of vertebral breaches during spinal fusion surgery.

BA-ADA based ROS-responsive nanoparticles for selective drug delivery in cancer cells

Current medical intervention in cancer therapeutic methods has shown risks and side effects with normal tissues. This includes incomplete cancer eradication. In reference to numerous studies and literature reviews, a stimuli-responsive drug delivery system is selected as an innovative, safe and more assured treatment due to its site-specific release ability. This allows specific intervention upon the given stimulus which response to the presenting disease symptoms. Hence, we designed a ROS(Reactive Oxygen Species)-responsive BA-ADA(4-Hydroxyphenylboronic acid pinacol ester and 1-Adamantanecarboxylic acid bonded molecule) nanoparticle delivery system. In our study, ROS-responsive nanoparticle was designed and prepared based on a synthetic molecule from BA and ADA. A therapeutic payload, Doxorubicin, can be loaded into the nanoparticles and it can be selectively released within cancerous tissues whereby ROS level is over-expressed. This will enhance both therapeutic efficiency and reduce side effects. The stability and ROS-responsiveness of the particle were proven in a series of evidence-based experiments. The results showed a significant difference in cell viability during the experiments with healthy and cancerous cell samples. Further research will be required to extend the experiment in vivo.

以狀態有向圖探討跳躍數列方法數

本篇研究針對跳躍進行數列本身意義的探討,用新的數列V表示跳躍數列的接球狀況,接著利用狀態有向圖定義出表示跳躍數列球在空中狀況的「頂點」以及表示跳躍數列內數值的「邊」,而迴圈狀況即為跳躍數列的情況下我們利用鄰接矩陣的想法進行探討,並且最後利用跡數的方式進行跳躍數列形式的討論。不同於文獻中僅針對用球數b和跳躍數列字串長度n做為討論,本篇研究增加了代表著跳躍數列中數值可達到的最大數值s(也代表著表示跳躍數列球在空中狀況的「頂點」長度),針對用球數為1顆的情況下為k階盧卡斯數的數值,而在其他用球數也有好的結果,並且針對不同情況下的跳躍數列整理出遞迴關係式以及生成函數。最後,在本篇研究中也找到許多在OEIS上所沒有的數列,並且給予這些數列有不同的解釋。

Improving Communication for the Visually Impaired Through an Innovative Arabic Writing System

Visual impairment is a major global health problem. In 2017, WHO estimated that there were 253 million people worldwide with this ailment. According to the journal of the American Medical association, the prevalence of visual impairment in the Saudi population is 9.3%. Learning Braille by families of students with visual impairments remains a major obstacle, which precipitates several communication issues. Moreover, difficulties for the students themselves lie in learning braille with languages that include diacritical marks; consequently, affecting their academic progress. My main objective of this project is to help improving life quality of these individuals, and the focus is to advance their social productivity and adaptation. This was accomplished through creating a new simpler Arabic writing system using geometrical shapes. As a part of this project, fifteen participants with visual impairments were interviewed and tried this new writing system; two of them are adults between 25 and 40 years old while the rest are students from 9 to 17 years old. Additionally, 100 participants with visual impairments completed a survey. The data showed that students learned this system in two hours in comparison with students that mastered braille in a few months. This shows that this system is easier to learn and subsequently saves time and effort. The most important value added to this project is that diacritical marks were combined with the alphabet, thereby considerably reducing book sizes compared to Braille-written books. This project presents a novel system that helps people with visual impairments to increase their confidence and independence.

旋轉方塊路橋問題之探討

本研究為一迷宮遊戲和旋轉方塊所組合成的問題。在給定行列數的可旋轉方塊上,置入「路」和「橋」,指定起點,並透過方塊的旋轉改變路徑,探討所有可能到達的終點以及抵達各終點的最短路線數。 此研究中,首先透過問題簡化和圖形討論,發現旋轉方塊以迴圈和無法繞行的路線(構造S)交錯形成,得到所有可能的終點位置。接著,整理所有簡化圖形的規律,利用加法原理推算出最短路線數。透過找出圖形對稱特性,得到不同終點之最短路徑數的關係。而後將不同規格的旋轉方塊的最短路線數關係,以遞迴關係式表示,並且找出其生成函數,希望透過生成函數得到最短路徑數的一般式。研究時,我們不僅發現不同規格之最短路線數生成函數的關係,從而能探討每一規格的最短路線數。更進一步發現無論方塊行數取至極限時或方塊行列數相同時,其最短路徑數的數列與卡特蘭數列(the Catalan numbers)有關。

水稻根表鐵膜對植體營養元素吸收的影響

鐵是植物生長的必要營養元素之一,土壤中的鐵含量雖然不低,但受限於含鐵礦物的溶解度使得鐵的有效性低,植物對鐵的吸收因此受限,進而影響人類的鐵攝取量並造成相關的健康問題。欲提高植物對鐵的利用效率,必須先了解植物對其吸收之相關機制,主要關鍵之一為植物根如何改變根圈環境以控制鐵吸收的有效性。 本研究以水稻為對象,探討水稻不同根部泌氧能力,對水稻根部鐵膜組成、鐵吸收效率,及其對其他營養元素吸收的影響。我們藉由遺傳篩選方法,選殖出較不易生成鐵膜之突變株(#878),透過比較野生型與突變株 (#878)水稻生理性狀之差異,發現通氣組織的生成為控制根系泌氧的影響因子;此泌氧能力會使根系周圍的鐵氧化,並於根表形成一層含有鐵氧化物的沉澱 (即鐵膜);而鐵膜的生成會影響水稻營養元素的吸收,其中鐵膜對陽離子型態的營養元素有較好吸持效果。

Convert pixel image into paths saves in XYZ format to use in CNC machines using innovative algorithms.

CNC machines use vector graphics or vector image programs that take time and effort on hobbyists. Therefore, it is important to provide accurate techniques for converting ordinary images available on the Internet or can be designed with easy programs. In order to have precise drill paths read by CNC machines directly and produce a product that does not contain rattles at the edges. This depends on the accuracy of processing the extracted paths. The development of algorithms has been completed Transforms Pixel image into Paths with XYZ extension, which is used to drill material and cut it through CNC machines. And the algorithms are based on transfer images with low quality. And Its Advantage that it can create high Paths with as few points as possible. The program can convert the pixel image into paths, and then converted into g-code, and use it in CNC machines directly.

波濤洶湧的玻璃杯—玻璃杯共振之研究

一個裝有水的玻璃杯,用喇叭撥出大聲的聲音,便能觀察到共振的現象發生,玻璃杯將會不停的震動,甚至導致破裂。本研究將會藉由傅立葉轉換(Fourier transform)來分析玻璃杯的振動的本徵頻率,並進一步探討頻譜的峰值。另外我們也研究了不同水位的高低以及液體密度對於共振頻率的影響,並以能量守恆的觀點進一步推導出玻璃杯的震動方程式。最後我們也近一步討論higher harmonic,並且發現non-linear dispersion relation的現象,有別於我們對於f∝n的觀念。

The Study of the Relationship between Global Warming and Acid Rain

The purpose of this project are 1)To study the relationship between global warming and acid rain with chemical model and mathematics model from temperature changing and pH of carbonic acid. 2) To create a pH measurement tool of carbonic acid in gaseous state.3) To study the impact of human activities in Loei province that affect to the relationship between global warming and acid rain. The procedures are 1)Do an experiment for studying the relationship between temperature changing and pH of carbonic acid. 2) Proof the mathematics model by using the result of experiment, the chemical reaction equation of carbonic acid solution. 3)Create a pH measurement tool of Carbonic acid by using Arduino and sensor with new formula in the computer program. 4) Using a pH measurement tool of Carbonic acid for studying impact of human activities in Loei province including industrial area, agricultural area, tourism area and forest area. The result of the mathematical model of the relationship between temperature changing and pH of carbonic acid is in form of Cubic equation in Equilibrium state and STP state. (Standard condition for Temperature and Pressure) So, we found that in this state has pH of carbonic acid is about 5.644. When the temperature rises up the effect of rainfall has a lower pH of carbonic acid solution. We also proof the new formula that create a pH measurement tool of Carbonic acid in gaseous state. The impact of human activities in Loei province found that the areas most affected by acid rain are the industrial areas, agricultural areas, tourism areas and forest areas respectively. In conclusion, when the temperature rises, it will dissolve acid solutions in the water on the earth. The loss of [H+] made the pH increases and the greenhouse gases become more atmospheric. These gases are more likely to react with atmospheric vapor. When these vapor form a cloud and condensation falls as rain, the rainfall has a lower pH, that is, global warming can result in the phenomenon of acid rain is greater.

費馬多邊形數定理之延伸探討

本研究旨在對費馬多邊形數定理(任意非負整數皆可表成n個n邊形數的和)進行更進一步的延伸探討,更精確地說,即是:對於給定的二次式an2+bn+c,定義一數列〈an 〉n=-1∞=〈a-1=0,an=an2+bn+c, ∀n≥0〉,而若存在一最小正整數γ,使得對於所有非負整數x,可由數列〈a_n 〉_(n=-1)^∞中取出共γ項,滿足x恰為這γ項之和。這時,我們稱正整數γ為二次式an^2+bn+c的指標值,定義函數Yi使得γ=Yi(an2+bn+c)。 在本研究中,首先先行探討函數Yi的一些基本性質,再藉由電腦以暴力法算出一些二次式指標值的下界,從這些指標值中找出規律,將其推廣至所有我們所討論的二次式,並證明之,至於再探討二次式指標值的上界的部分,我將數學家MelvynB.Nathanson證明費馬多邊形數定理的證明技巧,稍作改寫,使其能夠應用至更為一般的情況,藉此系統性的求得二次式指標值的可能上界。最後,經由不斷的優化上界與下界,即可求得二次式的指標值。