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Targeted Drug Delivery: Algorithmic Methods for Collecting a Swarm of Particles with Uniform External Forces

Aaron T. Becker, Sándor P. Fekete, Li Huang, Phillip Keldenich, Linda Kleist, Dominik Krupke, Christian Rieck, Arne Schmidt

TL;DR

The paper studies the problem of gathering a large swarm of microrobotic particles to a target region under a uniform external force in maze-like vascular environments. It proves NP-completeness of Min-Gathering (even for thin polyominoes) via a 3-SAT reduction and shows related hardness for Tilt Robot Localization, then provides algorithmic approaches that achieve strong worst-case guarantees such as $O(kD^2)$ steps in general and $O(kD)$ in hole-free environments, along with a rectangle-decomposition based strategy for simple polyominoes. The work also explores deep-learning aided search to find short command sequences and validates performance through extensive simulations. These results offer principled bounds and practical planning methods for targeted drug delivery applications where a single, global actuation affects all particles similarly.

Abstract

We investigate algorithmic approaches for targeted drug delivery in a complex, maze-like environment, such as a vascular system. The basic scenario is given by a large swarm of micro-scale particles (''agents'') and a particular target region (''tumor'') within a system of passageways. Agents are too small to contain on-board power or computation and are instead controlled by a global external force that acts uniformly on all particles, such as an applied fluidic flow or electromagnetic field. The challenge is to deliver all agents to the target region with a minimum number of actuation steps. We provide a number of results for this challenge. We show that the underlying problem is NP-complete, which explains why previous work did not provide provably efficient algorithms. We also develop several algorithmic approaches that greatly improve the worst-case guarantees for the number of required actuation steps. We evaluate our algorithmic approaches by numerous simulations, both for deterministic algorithms and searches supported by deep learning, which show that the performance is practically promising.

Targeted Drug Delivery: Algorithmic Methods for Collecting a Swarm of Particles with Uniform External Forces

TL;DR

The paper studies the problem of gathering a large swarm of microrobotic particles to a target region under a uniform external force in maze-like vascular environments. It proves NP-completeness of Min-Gathering (even for thin polyominoes) via a 3-SAT reduction and shows related hardness for Tilt Robot Localization, then provides algorithmic approaches that achieve strong worst-case guarantees such as steps in general and in hole-free environments, along with a rectangle-decomposition based strategy for simple polyominoes. The work also explores deep-learning aided search to find short command sequences and validates performance through extensive simulations. These results offer principled bounds and practical planning methods for targeted drug delivery applications where a single, global actuation affects all particles similarly.

Abstract

We investigate algorithmic approaches for targeted drug delivery in a complex, maze-like environment, such as a vascular system. The basic scenario is given by a large swarm of micro-scale particles (''agents'') and a particular target region (''tumor'') within a system of passageways. Agents are too small to contain on-board power or computation and are instead controlled by a global external force that acts uniformly on all particles, such as an applied fluidic flow or electromagnetic field. The challenge is to deliver all agents to the target region with a minimum number of actuation steps. We provide a number of results for this challenge. We show that the underlying problem is NP-complete, which explains why previous work did not provide provably efficient algorithms. We also develop several algorithmic approaches that greatly improve the worst-case guarantees for the number of required actuation steps. We evaluate our algorithmic approaches by numerous simulations, both for deterministic algorithms and searches supported by deep learning, which show that the performance is practically promising.
Paper Structure (6 sections, 4 theorems, 1 figure)

This paper contains 6 sections, 4 theorems, 1 figure.

Table of Contents

  1. Introduction
  2. Related work.
  3. Preliminaries.
  4. Our Contribution.
  5. -completeness for thin polyominoes
  6. Algorithmic approaches

Key Result

Theorem 1

Min-Gathering is -complete, even for thin polyominoes.

Figures (1)

  • Figure 1: (Left) An MRI image of a brain tumor (marked by the red circle), located in the cerebellum. (Right) How can the particles (indicated by yellow dots) be delivered to the target region?

Theorems & Definitions (4)

  • Theorem 1
  • Corollary 2
  • Corollary 3
  • Theorem 4