高質量解析度的質譜儀(mass spectrometer)對於許多領域的研究是強而有力的重要工具，因此提高質譜儀的質量解析度是一項至關重要的課題。到目前為止，高質量解析度的質譜儀有軌道阱質譜儀(orbitrap mass spectrometer)、離子迴旋共振式質譜儀(FTICR mass spectrometer)與多圈式飛行時間式質譜儀(multi-turn time-of-flight mass spectrometer)等。這些高質量解析度的質譜儀有一共通缺點，在高質荷比(mass-to-charge ratio)範圍分析之靈敏度會大幅度下降，因此這個問題會導致儀器無法在高m/z範圍作質量分析。線性飛行時間式質譜儀(linear time-of-flight mass spectrometer)對於高範圍質荷比有極佳的靈敏度，同時對於質量量測的速度也非常快，但其質量解析度不佳。現有的最佳化方法對此類型儀器的並不是非常有效，或者必須通過犧牲質量範圍和靈敏度來實現高質量解析度。
本研究發展出耦合空間與速度聚焦之理論，能夠使線性飛行時間式質譜的質量解析度大幅度上升。這個聚焦理論結合大數據之分析，可以充分了解到儀器中各種實驗參數與質量解析度關係，進而預測出最恰當的儀器設計。除此之外，這個研究結果對線性飛行時間式質譜儀中兩大普遍的迷思: 「質量解析度正比於離子的飛行時間」與「質量解析度與質量並無明顯相關性」，提出不同的看法與解釋所造成的原因。過往的研究因為運算資源與最佳化方法不足，很難歸納出質量解析度與儀器中各種參數之關聯性。
在建立此聚焦理論前，必須先了解游離源產生離子的原理。不同游離的方法導致質量解析度下降的因素會不同，所以最佳化過程中需要離子聚焦的方式也會因此不同。此研究會著重於基質輔助雷射脫附游離法(matrix-assisted laser desorption/ionization)，因為此技術是飛行時間式質譜儀在高m/z範圍的分析最常使用游離源之一。此技術在高分子量物質的檢測有很好的靈敏度與便利性，所以此技術被廣泛地應用在各種領域的研究上。此游離源是利用雷射脫附的原理，使物質從固態直接昇華成為氣態離子。這個過程會使同質量的離子有不同的初始動能，而這些初始動能的差異會導致儀器的質量解析度大幅度下降。耦合空間與速度聚焦是能夠對離子初始動能差異進行有效的補償之方法，並且準確地預測出線性飛行時間式質譜儀中的最佳實驗參數，使質量解析度大幅度提升。這些實驗參數包括提取區域、加速區域與儀器整體等長度，此外還有儀器內各種電壓大小之配置與提取延遲之時間。
為了能系統性地進行實驗參數的最佳化，本論文首次引進飛行時間拓樸之概念。飛行時間拓樸是離子群在儀器中的飛行時間分布之特質，而且每一組實驗參數無論是否有經過最佳化都只會對應出一種飛行時間拓樸。經過大量的最佳化運算後，這些飛行時間拓樸型態可以藉由大數據分析來分類，目前歸納出的飛行時間拓樸種類為「無轉折點」、「一最大飛行時間轉折點」、「一最小飛行時間轉折點」與「一最大與一最小飛行時間轉折點」等四種。不同型態的飛行時間拓樸會有不同程度的離子聚焦效果，因此彼此之間的質量解析度上限差距非常大，可以從數倍至數千倍以上。
在此計算模型的預測下，要獲得最佳的飛行時間拓樸型態與高的質量解析度，線性MALDI-TOF MS游離源中的提取長度(s0)與加速區域的長度(d)，必須增加至一般質譜儀好幾倍以上，並且與儀器的總長(L)達到特殊比率。這些特殊比率的範圍會隨著m/z不同而有所不同。當m/z越大時，此特殊比率範圍也會隨之縮小。這個研究指出高質量m/z 100,000要達到高質量解析度，則游離源中各區域長度對於總長之特殊比率範圍都必須被嚴格規範(2.33% > s0/L > 1.33%與28% > d/L > 14.33%)，然而此實驗參數範圍可以適用m/z 100,000以內任意質量的最佳化。
從這些結果我們首創出高解析度線性MALDI-TOF MS通用原理: 1. 最佳提取延遲必須遵守耦合空間與速度聚焦之條件。2. 相同m/z之離子在不同長度的儀器中要保持相同的最佳質量解析度之數值，則最佳化後提取與加速區域的長度對於儀器總長之比率必須保持不變，提取延遲之大小必須按照此比率延長或者縮短，同時提取電壓範圍之數值也需要保持一樣。這兩個通用原理相較於過往的最佳化方法，能提供更恰當的實驗參數，有效地解決線性飛行時間式質譜儀在高m/z範圍的質量解析度不佳之問題。此聚焦理論可應用於任意m/z離子、任意尺度線性MALDI-TOF MS的最佳化，因此對於高質量解析度質譜儀的開發與應用是具有突破性。

High-resolution mass spectrometers are powerful and essential tools for research in many fields of research, thus enhancing the mass resolving power of mass spectrometers is a crucial project. High-resolution mass spectrometers include the orbitrap mass spectrometer, fourier-transform ion cyclotron resonance mass spectrometer, and multi-turn time-of-flight mass spectrometer, among others. These high-resolution mass spectrometers have the same drawback: their sensitivity greatly decreases when the mass analysis is across a high mass-to-charge ratio range. The linear time-of-flight mass spectrometer has excellent sensitivity for a high range of mass-to-charge ratios and the speed of mass measurement is also very fast. However, its mass resolving power is not good. Traditional optimization methods for this type of instrument are not very effective, or achieving high mass resolving power must be accomplished by sacrificing the range of mass detection and sensitivity.
The purpose of this dissertation- is to develop the theory of coupled space- and velocity- focusing based on the concepts of space and velocity focusing. By integrating this focusing theory with the analysis of big data, we can effectively and quickly optimize the parameters of linear time-of-flight mass spectrometer. Furthermore, the results of calculation indicate that high mass resolving power for low to high mass-to-charge ratio (m/z) range is achieved by this optimization. After completing the big data analytics, we are able to fully comprehend the relationship between the mass resolving power and the experimental parameters of instrument, and predict the most appropriate design of instrument. This research also offers some different perspectives for the two myths in time-of-flight mass spectrometry: "mass resolving power is proportional to the flight time of ion" and "mass resolving power has no obvious correlation with the mass of ion".
Before developing this focusing theory, it is necessary to understand the principle of ion generation from the ionization source first. Different ion sources require different focusing conditions to improve mass resolving power. This study will focus on matrix-assisted laser desorption/ionization (MALDI) because this technology is one of the most used ion sources for linear time-of-flight mass spectrometers in high m/z range. Linear TOF MS also offers excellent sensitivity for ion detection in high m/z range, so this technology can be applied to various fields of research. This ion source primarily utilizes laser desorption to directly sublimate the substance from a solid state into gaseous ions. During this process, ions of same mass have different initial kinetic energies leading to a significant drop in the mass resolving power. The main purposes of this focusing theory are to compensate for the spread of the initial kinetic energy and predict the optimal experimental parameters in the linear MALDI time-of-flight mass spectrometer. These experimental parameters include the length of the extraction region, the acceleration region, and the total length of instrument, as well as the configuration of various voltages in the instrument and the extraction delay.
In order to systematically optimize the experimental parameters, the concept of flight-time topology needs to be discussed first. The flight-time topology is the characteristic of the flight time distribution of ion population in the instrument. Each set of experimental parameters will only correspond to one type of flight-time topology, whether the extraction delay has been optimized or not. These flight-time topologies must be classified by the statistics of a large number of calculation results. At present, the types of flight-time topology can be mainly divided into four types. Different types of flight-time topology have very large differences in the upper limit of mass resolving power, ranging from several times to thousands of times.
Under the prediction of this calculation model, in order to obtain the best flight-time topology and the highest mass resolving power, the extraction length s0 and the acceleration length d in the ion source must be increased to above ten times of traditional mass spectrometer or reach a specific ratio to the total length L of the instrument. The range of these special ratios will vary with m/z, and the range of special ratios for the ions of larger m/z is smaller. This study pointed out that to achieve high resolving power for m/z 100,000, the specific ratio range of each region in the ion source to the total length must be strictly regulated (2.33% > s0/L > 1.33% and 28% > d/ L > 14.33%).
These results summarize the general principles of linear MALDI-TOF MS: 1. Optimal extraction delay can be rapidly determined through coupled space- and velocity- focusing. 2. The values of mass resolving power in the different lengths of instrument are maintained the same when the ratio of the length of the extraction and acceleration region to the total length of instrument must remain unchanged, and the range of the extraction voltage also keeps the same. Finally, the extraction delay needs to be lengthened or shortened by this ratio. These two general principles can be applied to the optimization of any m/z ion and any scale of linear time-of-flight mass spectrometer, so it is a breakthrough for the development and application of high-resolution mass spectrometers, solving the issues of insufficient resolution and sensitivity at high m /z range detection.

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