Researchers created a mathematical model that helps transplant centers make decisions about when to move forward with a matching donor and when to wait. This work can potentially help decision making in other industries. Photo via Getty Images

To wait, or not to wait? That is the question — or at least it might be, if you need a kidney transplant.

Nearly 89,000 Americans with chronic kidney disease are on a waitlist for a new organ, and an estimated 13 people die each day while awaiting a transplant. But there are real costs to matching patients with the first donor that becomes available, just as there are equally real costs to having them wait in hopes of finding a better one.

Recently, Rice Business professor Süleyman Kerimov and colleagues at Stanford University and Northwestern University developed a mathematical model that helps clarify when it's best to match patients to donors as quickly as possible and when it's best to wait.

Their findings, which appear in two papers published in Management Science and Operations Research, respectively, could help optimize all manner of matching markets in which participants seek to connect with potential partners based on mutual compatibility — a sprawling category that encompasses everything from e-commerce platforms to labor markets that match employees with employers.

Kerimov and his colleagues focused on programs that match live kidney donors with people who need transplants. Live donors typically volunteer to give one of their kidneys to a loved one. But biological differences between a donor and their intended recipient can render the pair incompatible.

Kidney exchange programs solve this problem by swapping donors amongst different patient-donor pairs, choreographing a kind of kidney-transplant square dance aimed at finding a compatible partner for every willing donor.

In countries such as Canada and the Netherlands, kidney-matching programs perform a batch of matches every few months (called periodic policies). American programs, meanwhile, tend to perform daily matches (called greedy policies). Both models seek to produce the greatest number of high-quality transplants possible, but they each have advantages and disadvantages.

Less frequent matches in a periodic policy allow more patient-donor pairs to accumulate in the kidney exchange network, creating potential for better matches over time. But this approach risks making some patients sicker as they wait for a better match that might never appear.

Arranging feasible matches as soon as they become available in a greedy policy avoids that predicament. But it means passing up the opportunity to make a potentially better match that could represent the possibility of a longer, healthier life.

Balancing these trade-offs is tricky. There is no way of predicting precisely when a patient-donor pair with a particular set of characteristics will show up at the kidney-exchange network. And in the world of organ transplants, there are no do-overs.

Kerimov and his colleagues have constructed a mathematical model that represents a simplified version of a kidney exchange network.

Within the model, the researchers could dictate which patient-donor pairs could be matched with one another. They can also assign different values to individual matches based on the number of life years they provide. And they can establish the probability that various kinds of patient-donor pairs with particular characteristics might arrive at the network and queue up for a transplant at any given time.

Having set those parameters, the researchers applied different matching policies and compared the results. As it turns out, the answer to whether one should wait or not is: It depends.

To determine which policies generated the best outcomes — i.e., performing matches either daily or periodically — the researchers calculated the difference between the total value in life years that could possibly be generated within the network and the amount generated by a specific policy at a particular point in time. The goal was to keep that number, evocatively dubbed "all-time regret," as small as possible over both the short and long term.

In their first paper, Kerimov and his team explored a complex network in which donor kidneys could be swapped amongst three or more patient-donor pairs. When such multiway matches were possible, the cost of applying a daily-match policy turned out to be onerous. Using all available matches as quickly as possible eliminated the chance of later performing potentially higher-value matches.

Instead, the researchers found they could minimize regret by applying a periodic policy that required waiting for a certain number of patient-donor pairs to arrive before attempting to match them. The model even allowed the team to calculate precisely how long to wait between matchmaking sessions to get the best possible results.

In their second paper, however, the team looked at a simpler network in which kidneys could only be swapped between two donor-patient pairs. Here, their findings contradicted the first: Applying a daily-match policy minimized regret; a periodic matching process yielded no benefit whatsoever.

To their surprise, the researchers discovered they could design a foolproof algorithm for making two-way matches in simple networks. The algorithm employed a ranked list of possible match types; and the researchers found that no matter how many patient-donor pairs of various kinds randomly arrived at the network, the best choice was always simply to perform the highest-ranked match on the list.

In future research, Kerimov hopes to refine the model by feeding it data on real patient-donor pairs that have participated in actual kidney exchange programs. This would allow him to create a more realistic network, more accurately calculate the likelihood that particular kinds of patient-donor pairs will show up, and assign values to matches based not only on life years but also on rarity and difficulty. (Certain blood types and antibody profiles, for example, are rarer or more difficult to match than others.)

But Kerimov already suspects that in a real-world situation, the wisest course of action will be to alternate between periodic and greedy policies as circumstances dictate. In a simple region within a kidney exchange network that only allows for two-way matches, pursuing a greedy policy that involves taking the first match that appears on a fixed menu of options would be the best choice. In a more complex region that allows three-way matches, however, pursuing a periodic matching policy that involves waiting to make rarer and more difficult matches would ultimately offer more patients more years of healthy life.

The benefits of choosing flexibly between greedy and periodic policies should hold for any kind of matching market that can be represented by a network with simpler and more complex regions, such as a logistics system that matches online orders to delivery trucks or a carpooling system that matches passengers with drivers across different parts of a city.

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This article originally ran on Rice Business Wisdom and was based on research from Süleyman Kerimov, an assistant professor of management – operations management in the Jones Graduate School of Business at Rice University.

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CultureMap Emails are Awesome

Houston founder on shaping the future of medicine through biotechnology and resilience

Guest Column

Living with chronic disease has shaped my life in profound ways. My journey began in 5th grade when I was diagnosed with Scheuermann’s disease, a degenerative disc condition that kept me sidelined for an entire year. Later, I was diagnosed with hereditary neuropathy with liability to pressure palsies (HNPP), a condition that significantly impacts nerve recovery. These experiences didn’t just challenge me physically, they reshaped my perspective on healthcare — and ultimately set me on my path to entrepreneurship. What started as personal health struggles evolved into a mission to transform patient care through innovative biotechnology.

A defining part of living with these conditions was the diagnostic process. I underwent nerve tests that involved electrical shocks to my hands and arms — without anesthesia — to measure nerve activity. The pain was intense, and each test left me thinking: There has to be a better way. Even in those difficult moments, I found myself thinking about how to improve the tools and processes used in healthcare.

HNPP, in particular, has been a frustrating condition. For most people, sleeping on an arm might cause temporary numbness that disappears in an hour. For me, that same numbness can last six months. Even more debilitating is the loss of strength and fine motor skills. Living with this reality forced me to take an active role in understanding my health and seeking solutions, a mindset that would later shape my approach to leadership.

Growing up in Houston, I was surrounded by innovation. My grandfather, a pioneering urologist, was among the first to introduce kidney dialysis in the city in the 1950s. His dedication to advancing patient care initially inspired me to pursue medicine. Though my path eventually led me to healthcare administration and eventually biotech, his influence instilled in me a lifelong commitment to medicine and making a difference.

Houston’s thriving medical and entrepreneurial ecosystems played a critical role in my journey. The city’s culture of innovation and collaboration provided opportunities to explore solutions to unmet medical needs. When I transitioned from healthcare administration to founding biotech companies, I drew on the same resilience I had developed while managing my own health challenges.

My experience with chronic disease also shaped my leadership philosophy. Rather than accepting diagnoses passively, I took a proactive approach questioning assumptions, collaborating with experts, and seeking new solutions. These same principles now guide decision-making at FibroBiologics, where we are committed to developing groundbreaking therapies that go beyond symptom management to address the root causes of disease.

The resilience I built through my health struggles has been invaluable in navigating business challenges. While my early career in healthcare administration provided industry insights, launching and leading companies required the same determination I had relied on in my personal health journey.

I believe the future of healthcare lies in curative treatments, not just symptom management. Fibroblast cells hold the promise of engaging the body’s own healing processes — the most powerful cure for chronic diseases. Cell therapy represents both a scientific breakthrough and a significant business opportunity, one that has the potential to improve patient outcomes while reducing long-term healthcare costs.

Innovation in medicine isn’t just about technology; it’s about reimagining what’s possible. The future of healthcare is being written today. At FibroBiologics, our mission is driven by more than just financial success. We are focused on making a meaningful impact on patients’ lives, and this purpose-driven approach helps attract talent, engage stakeholders, and differentiate in the marketplace. Aligning business goals with patient needs isn’t just the right thing to do, it’s a powerful model for sustainable growth and lasting innovation in biotech.

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Pete O’Heeron is the CEO and founder of FibroBiologics, a Houston-based regenerative medicine company.


Houston researchers make headway on affordable, sustainable sodium-ion battery

Energy Solutions

A new study by researchers from Rice University’s Department of Materials Science and NanoEngineering, Baylor University and the Indian Institute of Science Education and Research Thiruvananthapuram has introduced a solution that could help develop more affordable and sustainable sodium-ion batteries.

The findings were recently published in the journal Advanced Functional Materials.

The team worked with tiny cone- and disc-shaped carbon materials from oil and gas industry byproducts with a pure graphitic structure. The forms allow for more efficient energy storage with larger sodium and potassium ions, which is a challenge for anodes in battery research. Sodium and potassium are more widely available and cheaper than lithium.

“For years, we’ve known that sodium and potassium are attractive alternatives to lithium,” Pulickel Ajayan, the Benjamin M. and Mary Greenwood Anderson Professor of Engineering at Rice, said in a news release. “But the challenge has always been finding carbon-based anode materials that can store these larger ions efficiently.”

Lithium-ion batteries traditionally rely on graphite as an anode material. However, traditional graphite structures cannot efficiently store sodium or potassium energy, since the atoms are too big and interactions become too complex to slide in and out of graphite’s layers. The cone and disc structures “offer curvature and spacing that welcome sodium and potassium ions without the need for chemical doping (the process of intentionally adding small amounts of specific atoms or molecules to change its properties) or other artificial modifications,” according to the study.

“This is one of the first clear demonstrations of sodium-ion intercalation in pure graphitic materials with such stability,” Atin Pramanik, first author of the study and a postdoctoral associate in Ajayan’s lab, said in the release. “It challenges the belief that pure graphite can’t work with sodium.”

In lab tests, the carbon cones and discs stored about 230 milliamp-hours of charge per gram (mAh/g) by using sodium ions. They still held 151 mAh/g even after 2,000 fast charging cycles. They also worked with potassium-ion batteries.

“We believe this discovery opens up a new design space for battery anodes,” Ajayan added in the release. “Instead of changing the chemistry, we’re changing the shape, and that’s proving to be just as interesting.”

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This story originally appeared on EnergyCapitalHTX.com.

FAA demands investigation into SpaceX's out-of-control Starship flight

Out of this world

The Federal Aviation Administration is demanding an accident investigation into the out-of-control Starship flight by SpaceX on May 27.

Tuesday's test flight from Texas lasted longer than the previous two failed demos of the world's biggest and most powerful rocket, which ended in flames over the Atlantic. The latest spacecraft made it halfway around the world to the Indian Ocean, but not before going into a spin and breaking apart.

The FAA said Friday that no injuries or public damage were reported.

The first-stage booster — recycled from an earlier flight — also burst apart while descending over the Gulf of Mexico. But that was the result of deliberately extreme testing approved by the FAA in advance.

All wreckage from both sections of the 403-foot (123-meter) rocket came down within the designated hazard zones, according to the FAA.

The FAA will oversee SpaceX's investigation, which is required before another Starship can launch.

CEO Elon Musk said he wants to pick up the pace of Starship test flights, with the ultimate goal of launching them to Mars. NASA needs Starship as the means of landing astronauts on the moon in the next few years.