BUDAPEST: A Fast and Reliable Bayesian Algorithm for TMS Threshold Estimation with an Open-Source GUI and Human Validation

This study introduces and validates BUDAPEST, a novel Bayesian adaptive algorithm with an open-source GUI that enables rapid, reliable, and user-controlled motor threshold estimation for transcranial magnetic stimulation using significantly fewer pulses than conventional methods.

The Gist

The Big Picture: Finding the "Goldilocks" Volume

Imagine you are trying to find the perfect volume setting on a radio. If the volume is too low, you can't hear the music (no muscle response). If it's too high, it's blasting and uncomfortable (too much stimulation). You need to find that "just right" spot, known in the medical world as the Motor Threshold (MT).

For doctors using Transcranial Magnetic Stimulation (TMS)—a technique that uses magnetic pulses to wake up parts of the brain—knowing this exact "volume" is crucial. It ensures the treatment works without hurting the patient.

The Problem: The Old Way is Slow and Clunky

Traditionally, finding this threshold was like playing a very slow, tedious game of "Hot and Cold."

• The Old Method (5-out-of-10): A doctor would zap the brain, check if the muscle twitched, then zap it again. They had to do this 50 to 75 times just to get a rough idea. It took a long time, was boring for the patient, and sometimes the doctor would get confused by the results, leading to a wrong guess.
• The "PEST" Method: Scientists tried to make this faster using a computer algorithm called PEST. It was quicker, but it was a bit "dumb." If it got a lucky early twitch, it might get overconfident and guess the volume was too low, then keep guessing low even when the patient stopped twitching. It was like a GPS that gets stuck in a traffic jam and refuses to reroute.

The Solution: Introducing BUDAPEST

The authors of this paper created a new, smarter algorithm called BUDAPEST (Bayesian Uncertainty Dynamic Algorithm for Parameter Estimation by Sequential Testing).

Think of BUDAPEST as a smart, cautious detective instead of a guessing game.

1. How it Works: The "Fuzzy Map" Analogy

Imagine the doctor doesn't know the exact volume. Instead of guessing a single number, BUDAPEST draws a fuzzy map of possibilities.

• Start: The map is wide and blurry. "The volume could be anywhere between 30% and 70%."
• The Test: The machine gives a small zap.
• The Update:
  • If the muscle twitches, the detective says, "Okay, it's definitely not below 40%." The blurry map shrinks and shifts up.
  • If the muscle stays still, the detective says, "Okay, it's probably not above 60%." The map shrinks and shifts down.
• The Magic: With every single zap, the map gets sharper and more focused. BUDAPEST doesn't just guess; it calculates the probability of the answer. It knows exactly how sure it is.

2. The "Stop Button" Control

The best part is that the human doctor gets to decide when to stop.

• High Precision Mode: "I need to be 99% sure." The algorithm keeps zapping until the map is razor-sharp.
• Speed Mode: "I just need a good estimate quickly." The algorithm stops as soon as the map is "good enough."
• The Result: It usually finds the answer in about 10 zaps (down from 50–75), and it rarely makes the "stuck in traffic" mistakes that the old methods did.

The Experiment: Did it Work?

The researchers tested this in two ways:

1. Virtual Simulations: They created 10,000 fake patients on a computer. BUDAPEST was incredibly accurate, finding the right "volume" with very little error, even when they started with a completely wrong guess.
2. Real Humans: They tested it on real people.
   • Resting vs. Active: They tested when the hand was relaxed (Resting) and when the person was squeezing a coin (Active).
   • Reliability: They came back the next day to test again. The "Resting" results were very consistent (like a reliable clock). The "Active" results varied a bit more (because squeezing a coin is harder to do exactly the same way twice), but the algorithm handled it perfectly.

The Toolkit: A User-Friendly Dashboard

The researchers didn't just write code; they built a Graphical User Interface (GUI).

• Imagine a dashboard on a car. As the algorithm runs, you see a graph on the screen. You can watch the "fuzzy map" shrink in real-time.
• It tells the doctor exactly when the machine is confident enough to stop.
• It even talks to the TMS machine automatically, so the doctor doesn't have to manually press buttons for every zap.

Why This Matters

• For Patients: The procedure is much shorter (saving time and reducing discomfort).
• For Doctors: It removes the guesswork and human error. It's like having a co-pilot that never gets tired or confused.
• For Science: It allows for "Motor Mapping" (drawing a map of the whole brain's motor area) to happen quickly. Instead of taking an hour to map one spot, they can map a whole grid of spots in minutes.

The Bottom Line

BUDAPEST is a smarter, faster, and more reliable way to find the perfect brain stimulation dose. It turns a tedious, error-prone guessing game into a precise, data-driven process, making TMS treatments safer and more accessible for everyone.

Technical Summary

1. Problem Statement

Transcranial Magnetic Stimulation (TMS) requires precise determination of the Motor Threshold (MT)—the minimum intensity to evoke a Motor Evoked Potential (MEP) in 50% of trials—to ensure effective and safe dosing.

• Limitations of Current Methods:
  • Standard Protocols (e.g., "5-out-of-10"): Accurate but inefficient, requiring 50–75 pulses, leading to prolonged session times and participant discomfort.
  • Adaptive Methods (e.g., PEST): Faster (~14–16 pulses) but prone to severe misestimation (underestimation) if early responses are noisy or contradictory, lacking robust convergence guarantees.
  • Stochastic Methods (e.g., SAMT): Show promise but lack explicit, trial-by-trial quantification of uncertainty, making it difficult to define principled stopping criteria for specific clinical or research needs.
• Core Challenge: There is a need for an algorithm that balances speed and accuracy while providing user-controlled uncertainty quantification to allow experimenters to trade off procedure duration against precision dynamically.

2. Methodology: The BUDAPEST Algorithm

The authors introduced BUDAPEST (Bayesian Uncertainty Dynamic Algorithm for Parameter Estimation by Sequential Testing), a Bayesian active-learning framework.

• Statistical Framework:
  • Model: Treats MT as a statistical parameter $\theta$ with a prior probability distribution (Gaussian).
  • Likelihood: Assumes binary MEP responses (1 = present, 0 = absent) follow a sigmoid (logistic) function relative to the stimulation intensity $I$ and threshold $\theta$.
  • Update Rule: Uses Bayes' rule to iteratively update the posterior distribution $P(\theta|r)$ after every trial based on the observed binary response.
  • Next Step Selection: The next stimulation intensity is selected as the posterior mean, representing the most probable threshold given accumulated evidence.
• Uncertainty-Based Stopping Criterion:
  • Unlike fixed-trial methods, BUDAPEST terminates when the posterior standard deviation (uncertainty) falls below a user-defined threshold (e.g., 2% MSO).
  • This allows users to explicitly control the trade-off between estimation precision and the number of pulses delivered.
• Implementation:
  • Developed in MATLAB with an open-source Graphical User Interface (GUI).
  • Features real-time visualization of the posterior distribution and uncertainty.
  • Includes serial port communication for automated control of MagVenture TMS stimulators.

3. Key Contributions

1. Algorithmic Innovation: A principled Bayesian approach that explicitly models and reduces uncertainty, avoiding the "overshooting" or persistent underestimation seen in PEST.
2. User-Centric Design: The open-source GUI allows researchers to set custom uncertainty thresholds, making the tool adaptable to diverse experimental constraints (e.g., high-throughput screening vs. high-precision clinical dosing).
3. Comprehensive Validation: Rigorous testing across 10,000 virtual simulations and human subjects (resting and active MT), including session-to-session reliability and spatial mapping.
4. Automation Readiness: The system is designed for integration into closed-loop frameworks, including potential future automation of MEP detection and robotic coil positioning.

4. Results

A. Simulation Performance (Virtual Subjects)

• Accuracy: With a 2% uncertainty criterion, BUDAPEST achieved a Mean Absolute Error (MAE) of 1.93% MSO with a 95% error interval of -6.0% to +5.0%.
• Efficiency: Converged in an average of 10.2 trials (range 8–12).
• Robustness: Showed no tendency toward persistent underestimation, a common failure mode of PEST.
• Trade-offs:
  • 1% Criterion: Higher accuracy (MAE 1.27%) but slower (26.4 trials).
  • 5% Criterion: Fastest (3.6 trials) but lower precision (MAE 3.84%).

B. Human Validation

• Accuracy: MT estimates were accurate within ±4% MSO of the ground truth (determined by the "5-out-of-10" method).
• Initialization Robustness: The algorithm successfully converged to accurate estimates even when starting intensities were intentionally offset by ±10% to ±15% from the true MT.
• Reliability:
  • Resting MT (rMT): Strong session-to-session reliability ($r = 0.78$).
  • Active MT (aMT): Lower reliability ($r = 0.49$), attributed to physiological variability in voluntary muscle contraction rather than algorithmic error.
• Spatial Mapping: Successfully mapped a 3×5 grid, revealing coherent excitability gradients centered on the hotspot, with MT increasing as distance from the hotspot increased.

5. Significance and Future Directions

• Clinical & Research Impact: BUDAPEST significantly reduces participant burden and session time (estimating MT in ~1 minute per site with ~10 pulses) without sacrificing accuracy. This facilitates high-throughput TMS applications and standardized clinical dosing.
• Standardization: By providing a quantitative, uncertainty-controlled stopping rule, it reduces operator bias and variability in MT determination.
• Future Integration: The authors propose integrating BUDAPEST with:
  • Automated MEP Detection: Using machine learning to classify responses, removing the need for manual visual inspection.
  • Robotic Coil Positioning: Enabling fully automated, multi-site motor mapping (e.g., a 15-site map in ~15 minutes).
  • Multi-Muscle Inference: Extending the Bayesian framework to estimate thresholds for multiple muscles simultaneously from a single pulse stream.

In conclusion, BUDAPEST represents a significant advancement in TMS methodology, offering a fast, reliable, and flexible tool that bridges the gap between theoretical Bayesian estimation and practical clinical application.