mathematics
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A Way for Smartwatches to Detect Depression Risks Devised by KAIST and U of Michigan Researchers
- A international joint research team of KAIST and the University of Michigan developed a digital biomarker for predicting symptoms of depression based on data collected by smartwatches
- It has the potential to be used as a medical technology to replace the economically burdensome fMRI measurement test
- It is expected to expand the scope of digital health data analysis
The CORONA virus pandemic also brought about a pandemic of mental illness. Approximately one billion people worldwide suffer from various psychiatric conditions. Korea is one of more serious cases, with approximately 1.8 million patients exhibiting depression and anxiety disorders, and the total number of patients with clinical mental diseases has increased by 37% in five years to approximately 4.65 million. A joint research team from Korea and the US has developed a technology that uses biometric data collected through wearable devices to predict tomorrow's mood and, further, to predict the possibility of developing symptoms of depression.
< Figure 1. Schematic diagram of the research results. Based on the biometric data collected by a smartwatch, a mathematical algorithm that solves the inverse problem to estimate the brain's circadian phase and sleep stages has been developed. This algorithm can estimate the degrees of circadian disruption, and these estimates can be used as the digital biomarkers to predict depression risks. >
KAIST (President Kwang Hyung Lee) announced on the 15th of January that the research team under Professor Dae Wook Kim from the Department of Brain and Cognitive Sciences and the team under Professor Daniel B. Forger from the Department of Mathematics at the University of Michigan in the United States have developed a technology to predict symptoms of depression such as sleep disorders, depression, loss of appetite, overeating, and decreased concentration in shift workers from the activity and heart rate data collected from smartwatches.
According to WHO, a promising new treatment direction for mental illness focuses on the sleep and circadian timekeeping system located in the hypothalamus of the brain, which directly affect impulsivity, emotional responses, decision-making, and overall mood.
However, in order to measure endogenous circadian rhythms and sleep states, blood or saliva must be drawn every 30 minutes throughout the night to measure changes in the concentration of the melatonin hormone in our bodies and polysomnography (PSG) must be performed. As such treatments requires hospitalization and most psychiatric patients only visit for outpatient treatment, there has been no significant progress in developing treatment methods that take these two factors into account. In addition, the cost of the PSG test, which is approximately $1000, leaves mental health treatment considering sleep and circadian rhythms out of reach for the socially disadvantaged.
The solution to overcome these problems is to employ wearable devices for the easier collection of biometric data such as heart rate, body temperature, and activity level in real time without spatial constraints. However, current wearable devices have the limitation of providing only indirect information on biomarkers required by medical staff, such as the phase of the circadian clock.
The joint research team developed a filtering technology that accurately estimates the phase of the circadian clock, which changes daily, such as heart rate and activity time series data collected from a smartwatch. This is an implementation of a digital twin that precisely describes the circadian rhythm in the brain, and it can be used to estimate circadian rhythm disruption.
< Figure 2. The suprachiasmatic nucleus located in the hypothalamus of the brain is the central biological clock that regulates the 24-hour physiological rhythm and plays a key role in maintaining the body’s circadian rhythm. If the phase of this biological clock is disrupted, it affects various parts of the brain, which can cause psychiatric conditions such as depression. >
The possibility of using the digital twin of this circadian clock to predict the symptoms of depression was verified through collaboration with the research team of Professor Srijan Sen of the Michigan Neuroscience Institute and Professor Amy Bohnert of the Department of Psychiatry of the University of Michigan.
The collaborative research team conducted a large-scale prospective cohort study involving approximately 800 shift workers and showed that the circadian rhythm disruption digital biomarker estimated through the technology can predict tomorrow's mood as well as six symptoms, including sleep problems, appetite changes, decreased concentration, and suicidal thoughts, which are representative symptoms of depression.
< Figure 3. The circadian rhythm of hormones such as melatonin regulates various physiological functions and behaviors such as heart rate and activity level. These physiological and behavioral signals can be measured in daily life through wearable devices. In order to estimate the body’s circadian rhythm inversely based on the measured biometric signals, a mathematical algorithm is needed. This algorithm plays a key role in accurately identifying the characteristics of circadian rhythms by extracting hidden physiological patterns from biosignals. >
Professor Dae Wook Kim said, "It is very meaningful to be able to conduct research that provides a clue for ways to apply wearable biometric data using mathematics that have not previously been utilized for actual disease management." He added, "We expect that this research will be able to present continuous and non-invasive mental health monitoring technology. This is expected to present a new paradigm for mental health care. By resolving some of the major problems socially disadvantaged people may face in current treatment practices, they may be able to take more active steps when experiencing symptoms of depression, such as seeking counsel before things get out of hand."
< Figure 4. A mathematical algorithm was devised to circumvent the problems of estimating the phase of the brain's biological clock and sleep stages inversely from the biodata collected by a smartwatch. This algorithm can estimate the degree of daily circadian rhythm disruption, and this estimate can be used as a digital biomarker to predict depression symptoms. >
The results of this study, in which Professor Dae Wook Kim of the Department of Brain and Cognitive Sciences at KAIST participated as the joint first author and corresponding author, were published in the online version of the international academic journal npj Digital Medicine on December 5, 2024. (Paper title: The real-world association between digital markers of circadian disruption and mental health risks) DOI: 10.1038/s41746-024-01348-6
This study was conducted with the support of the KAIST's Research Support Program for New Faculty Members, the US National Science Foundation, the US National Institutes of Health, and the US Army Research Institute MURI Program.
2025.01.20 View 3250 -
Scientists re-writes FDA-recommended equation to improve estimation of drug-drug interaction
Drugs absorbed into the body are metabolized and thus removed by enzymes from several organs like the liver. How fast a drug is cleared out of the system can be affected by other drugs that are taken together because added substance can increase the amount of enzyme secretion in the body. This dramatically decreases the concentration of a drug, reducing its efficacy, often leading to the failure of having any effect at all. Therefore, accurately predicting the clearance rate in the presence of drug-drug interaction* is critical in the process of drug prescription and development of a new drug in order to ensure its efficacy and/or to avoid unwanted side-effects.
*Drug-drug interaction: In terms of metabolism, drug-drug interaction is a phenomenon in which one drug changes the metabolism of another drug to promote or inhibit its excretion from the body when two or more drugs are taken together. As a result, it increases the toxicity of medicines or causes loss of efficacy.
Since it is practically impossible to evaluate all interactions between new drug candidates and all marketed drugs during the development process, the FDA recommends indirect evaluation of drug interactions using a formula suggested in their guidance, first published in 1997, revised in January of 2020, in order to evaluate drug interactions and minimize side effects of having to use more than one type of drugs at once.
The formula relies on the 110-year-old Michaelis-Menten (MM) model, which has a fundamental limit of making a very broad and groundless assumption on the part of the presence of the enzymes that metabolizes the drug. While MM equation has been one of the most widely known equations in biochemistry used in more than 220,000 published papers, the MM equation is accurate only when the concentration of the enzyme that metabolizes the drug is almost non-existent, causing the accuracy of the equation highly unsatisfactory – only 38 percent of the predictions had less than two-fold errors.
“To make up for the gap, researcher resorted to plugging in scientifically unjustified constants into the equation,” Professor Jung-woo Chae of Chungnam National University College of Pharmacy said. “This is comparable to having to have the epicyclic orbits introduced to explain the motion of the planets back in the days in order to explain the now-defunct Ptolemaic theory, because it was 'THE' theory back then.”
< (From left) Ph.D. student Yun Min Song (KAIST, co-first authors), Professor Sang Kyum Kim (Chungnam National University, co-corresponding author), Jae Kyoung Kim, CI (KAIST, co-corresponding author), Professor Jung-woo Chae (Chungnam National University, co-corresponding author), Ph.D. students Quyen Thi Tran and Ngoc-Anh Thi Vu (Chungnam National University, co-first authors) >
A joint research team composed of mathematicians from the Biomedical Mathematics Group within the Institute for Basic Science (IBS) and the Korea Advanced Institute of Science and Technology (KAIST) and pharmacological scientists from the Chungnam National University reported that they identified the major causes of the FDA-recommended equation’s inaccuracies and presented a solution.
When estimating the gut bioavailability (Fg), which is the key parameter of the equation, the fraction absorbed from the gut lumen (Fa) is usually assumed to be 1. However, many experiments have shown that Fa is less than 1, obviously since it can’t be expected that all of the orally taken drugs to be completely absorbed by the intestines. To solve this problem, the research team used an “estimated Fa” value based on factors such as the drug’s transit time, intestine radius, and permeability values and used it to re-calculate Fg.
Also, taking a different approach from the MM equation, the team used an alternative model they derived in a previous study back in 2020, which can more accurately predict the drug metabolism rate regardless of the enzyme concentration. Combining these changes, the modified equation with re-calculated Fg had a dramatically increased accuracy of the resulting estimate. The existing FDA formula predicted drug interactions within a 2-fold margin of error at the rate of 38%, whereas the accuracy rate of the revised formula reached 80%.
“Such drastic improvement in drug-drug interaction prediction accuracy is expected to make great contribution to increasing the success rate of new drug development and drug efficacy in clinical trials. As the results of this study were published in one of the top clinical pharmacology journal, it is expected that the FDA guidance will be revised according to the results of this study.” said Professor Sang Kyum Kim from Chungnam National University College of Pharmacy.
Furthermore, this study highlights the importance of collaborative research between research groups in vastly different disciplines, in a field that is as dynamic as drug interactions.
“Thanks to the collaborative research between mathematics and pharmacy, we were able to recify the formula that we have accepted to be the right answer for so long to finally grasp on the leads toward healthier life for mankind.,” said Professor Jae Kyung Kim. He continued, “I hope seeing a ‘K-formula’ entered into the US FDA guidance one day.”
The results of this study were published in the online edition of Clinical Pharmacology and Therapeutics (IF 7.051), an authoritative journal in the field of clinical pharmacology, on December 15, 2022 (Korean time).
Thesis Title: Beyond the Michaelis-Menten: Accurate Prediction of Drug Interactions through Cytochrome P450 3A4 Induction (doi: 10.1002/cpt.2824)
< Figure 1. The formula proposed by the FDA guidance for predicting drug-drug interactions (top) and the formula newly derived by the researchers (bottom). AUCR (the ratio of substrate area under the plasma concentration-time curve) represents the rate of change in drug concentration due to drug interactions. The research team more than doubled the accuracy of drug interaction prediction compared to the existing formula. >
< Figure 2. Existing FDA formulas tend to underestimate the extent of drug-drug interactions (gray dots) than the actual measured values. On the other hand, the newly derived equation (red dot) has a prediction rate that is within the error range of 2 times (0.5 to 2 times) of the measured value, and is more than twice as high as the existing equation. The solid line in the figure represents the predicted value that matches the measured value. The dotted line represents the predicted value with an error of 0.5 to 2 times. >
For further information or to request media assistance, please contact Jae Kyoung Kim at Biomedical Mathematics Group, Institute for Basic Science (IBS) (jaekkim@ibs.re.kr) or William I. Suh at the IBS Communications Team (willisuh@ibs.re.kr).
- About the Institute for Basic Science (IBS)
IBS was founded in 2011 by the government of the Republic of Korea with the sole purpose of driving forward the development of basic science in South Korea. IBS has 4 research institutes and 33 research centers as of January 2023. There are eleven physics, three mathematics, five chemistry, nine life science, two earth science, and three interdisciplinary research centers.
2023.01.18 View 11769 -
Mathematicians Identify a Key Source of Cell-to-Cell Variability in Cell Signaling
Systematic inferences identify a major source of heterogeneity in cell signaling dynamics
Why do genetically identical cells respond differently to the same external stimuli, such as antibiotics? This long-standing mystery has been solved by KAIST and IBS mathematicians who have developed a new framework for analyzing cell responses to some stimuli. The team found that the cell-to-cell variability in antibiotic stress response increases as the effective length of the cell signaling pathway (i.e., the number of rate-limiting steps) increases. This finding could identify more effective chemotherapies to overcome the fractional killing of cancer cells caused by cell-to-cell variability.
Cells in the human body contain signal transduction systems that respond to various external stimuli such as antibiotics and changes in osmotic pressure. When an external stimulus is detected, various biochemical reactions occur sequentially. This leads to the expression of relevant genes, allowing the cells to respond to the perturbed external environment. Furthermore, signal transduction leads to a drug response (e.g., antibiotic resistance genes are expressed when antibiotic drugs are given).
However, even when the same external stimuli are detected, the responses of individual cells are greatly heterogeneous. This leads to the emergence of persister cells that are highly resistant to drugs. To identify potential sources of this cell-to cell variability, many studies have been conducted. However, most of the intermediate signal transduction reactions are unobservable with current experimental techniques.
A group of researchers including Dae Wook Kim and Hyukpyo Hong and led by Professor Jae Kyoung Kim from the KAIST Department of Mathematical Sciences and IBS Biomedical Mathematics Group solved the mystery by exploiting queueing theory and Bayesian inference methodology. They proposed a queueing process that describes the signal transduction system in cells. Based on this, they developed Bayesian inference computational software using MBI (the Moment-based Bayesian Inference method). This enables the analysis of the signal transduction system without a direct observation of the intermediate steps. This study was published in Science Advances.
By analyzing experimental data from Escherichia coli using MBI, the research team found that cell-to-cell variability increases as the number of rate-limiting steps in the signaling pathway increases.
The rate-limiting steps denote the slowest steps (i.e., bottlenecks) in sequential biochemical reaction steps composing cell signaling pathways and thus dominates most of the signaling time. As the number of the rate-limiting steps increases, the intensity of the transduced signal becomes greatly heterogeneous even in a population of genetically identical cells. This finding is expected to provide a new paradigm for studying the heterogeneous antibiotic resistance of cells, which is a big challenge in cancer medicine.
Professor Kim said, “As a mathematician, I am excited to help advance the understanding of cell-to-cell variability in response to external stimuli. I hope this finding facilitates the development of more effective chemotherapies.”
This work was supported by the Samsung Science and Technology Foundation, the National Research Foundation of Korea, and the Institute for Basic Science.
-Publication:Dae Wook Kim, Hyukpyo Hong, and Jae Kyoung Kim (2022) “Systematic inference identifies a major source of heterogeneity in cell signaling dynamics: the rate-limiting step number,”Science Advances March 18, 2022 (DOI: 10.1126/sciadv.abl4598)
-Profile:Professor Jae Kyoung Kimhttp://mathsci.kaist.ac.kr/~jaekkim
jaekkim@kaist.ac.kr@umichkim on TwitterDepartment of Mathematical SciencesKAIST
2022.03.29 View 9133 -
Professor Jae Kyoung Kim to Lead a New Mathematical Biology Research Group at IBS
Professor Jae Kyoung Kim from the KAIST Department of Mathematical Sciences was appointed as the third Chief Investigator (CI) of the Pioneer Research Center (PRC) for Mathematical and Computational Sciences at the Institute for Basic Science (IBS). Professor Kim will launch and lead a new research group that will be devoted to resolving various biological conundrums from a mathematical perspective. His appointment began on March 1, 2021.
Professor Kim, a rising researcher in the field of mathematical biology, has received attention from both the mathematical and biological communities at the international level. Professor Kim puts novel and unremitting efforts into understanding biological systems such as cell-to-cell interactions mathematically and designing mathematical models for identifying causes of diseases and developing therapeutic medicines.
Through active joint research with biologists, mathematician Kim has addressed many challenges that have remained unsolved in biology and published papers in a number of leading international journals in related fields. His notable works based on mathematical modelling include having designed a biological circuit that can maintain a stable circadian rhythm (Science, 2015) and unveiling the principles of how the biological clock in the body maintains a steady speed for the first time in over 60 years (Molecular Cell, 2015). Recently, through a joint research project with Pfizer, Professor Kim identified what causes the differences between animal and clinical test results during drug development explaining why drugs have different efficacies in different people (Molecular Systems Biology, 2019).
The new IBS biomedical mathematics research group led by Professor Kim will further investigate the causes of unstable circadian rhythms and sleeping patterns. The team will aim to present a new paradigm in treatments for sleep disorders.
Professor Kim said, “We are all so familiar with sleep behaviors, but the exact mechanisms behind how such behaviors occur are still unknown. Through cooperation with biomedical scientists, our group will do its best to discover the complicated, fundamental mechanisms of sleep, and investigate the causes and cures of sleep disorders.”
Every year, the IBS selects young and promising researchers and appoints them as CIs. A maximum of five selected CIs can form each independent research group within the IBS PRC, and receive research funds of 1 billion to 1.5 billion KRW over five years.
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2021.03.18 View 9397 -
Professor Baik Awarded Sangsan Young Mathematician Prize
(Professor Hyungryul Baik)
Professor Hyungryul Baik from the Department of Mathematical Sciences was honored as the recipient of the 2018 Sangsan Prize for Young Mathematicians by the Korean Mathematical Society (KMS).
The Sangsan Prize recognizes young mathematicians who finished their degree within the previous five years and have begun an outstanding research career. Professor Baik was recognized for his studies in the fields of low-dimensional topology, geophysical mathematics, and geometric theory. In particular, his Ph.D. dissertation presented a new criterion that completely identifies the hyperbolic surface group, making an inference about the nature of the hyperbolic manifold group.
Recently, Professor Baik co-published a paper entitled Spaces of Invariant Circular Orders of Groups with Professor Eric Samperton at the University of California Santa Barbara in the renowned academic journal Groups, Geometry, and Dynamics in 2018.
Professor Baik earned his BS at KAIST and finished his MS and Ph.D. in mathematics in 2014 at Cornell University. He joined KAIST as a faculty member last year.
2018.10.30 View 6351 -
Partnership with École Centrale Paris
Courtesy of École Centrale Paris News: http://www.ecp.fr/lang/en/home/news?actuID=48892
Strengthening of the partnership betwenn CentraleSupélec and KAIST University, South Korea
The two institutions signed a new agreement.
Hervé Biausser (left in the picture), Director of CentraleSupélec, has met Sung-Mo Steve Kang (right in the picture), the President of the Korea Advanced Institute of Science and Technology (KAIST). They signed an agreement aiming to strengthen the partnership between the two institutions concerning research and higher education.
CentraleSupélec and KAIST have cooperated since 2010 on research projects in the context of the Erasmus Mundus BEAM and EASED programs, which are coordinated by CentraleSupélec.
The next step is now the application of graduate academic mobility in the common fields of excellency of the institutions: energy, electronic, physics and mathematics.
2015.11.02 View 5702 -
Graduate School of Culture and Technology Begins Mobile Science Classroom
KAIST Graduate School of Culture and Technology plans visits to elementary schools without the facilities to facilitate hands on science education.
The Graduate School of Culture and Technology planned the ‘STEAM Creative Camp’ involving three elementary schools during the summer holidays.
The ‘STEAM Creative Camp’ involves increasing interest and artistic sensitivity through experience based science education.
The program is composed of two separate programs in consideration to the level of participating students.
The beginner level program includes: code making, writing secret letters, sticker decorating program and the moderate level program includes: making wipers using complex pulley system, catapult design using elasticity, and puppet show using joints to animate.
The programs will be taught by masters and doctorate program candidates from the KAIST Youth Culture and Technology Experience Center.
*STEAM: And integrated education system including Science, Technology, Engineering, Arts, and Mathematics.
2012.07.26 View 8970 -
KAIST Ph.D Mihyun Jang Employed as Professor at Technische Universitat Graz
A Ph.D purely from Korea has been employed as a professor at Technische Universitat Graz.
This is the news of Prof.Mihyun Kang (39) who has graduated from KAIST’s mathematics department. Prof.Kang has transferred on January 2012.
KAIST explained that “it’s the first time for a mathematics Ph.D from Korea has been employed abroad.”
Technische Universitat Graz of Australia is ranked the top third university within the country. It is a global university with 1,700 students from 78 different countries out of its 11,000 students.
Prof. Kang researched mainly theories of combination including random graphing theories, analytical combination theories, and probabilistic combination theories. She has been employed as a lifetime professor through open recruitment where she competed with others through academic debates and interviews.
Technische Universitat Graz valued Prof. Kang’s research highly made her the department head of the ‘Optimization and Discrete Mathematics department’ to create an environment where she could continuously research.
Prof. Kang graduated from Jeju university majoring math educations and did her graduate studies in KAIST. She is a purely ‘Korean’ Ph.D. After her studies, she worked for Germany’s Humboldt University and Freie Universitat Berlin. In 2007, she was able to be employed as a professor in Germany, and in 2008, she was chosen as a Heisenberg fellow.
Prof. Kang who had her research achievements recognized in Germany and Austria was also offered seat as professor in Ludwig Masximilan University of Germany and Alpenadria University in Austria, but chose Technische Universitat Graz.
2012.01.31 View 11202