### Abstract

The mechanism of Parkinson's disease can be investigated at the molecular level by using radio-tracers. The concentration of dopamine in the brain can be observed by using a radio-tracer, 6-[^{18}F]fluorodopa (FDOPA), with positron emission tomography (PET), and the dopamine kinetics can be described as compartmental models for tissues of the brain. The models for FDOPA kinetics are solved explicitly, but the solution shows a complicated form including several convolutions over time domain. Owing to the complicated form of the solution, graphical analyses such as Logan or Patlak analysis have been utilized as conventional methods over past decades. Because some kinetic constants for Parkinson's disease are estimated in the graphical analyses with the slope or intercept of the line obtained under various assumptions, only a limited set of parameters have approximately been estimated. We have analysed the compartmental models by using the Laplace transformation of differential equations and by algebraic computation with the aid of Gröbner base constructions. We have obtained a rigorous solution with respect to the kinetic constants over the Laplace domain. Here, we first derive a rigorous solution for the parameters, together with a discussion about the merits of the derivation. Next, we describe a procedure to determine the kinetic constants with the observed time-radioactivity curves. Last, we discuss the feasibility of our method, especially as a criterion for diagnosing Parkinson's disease.

Original language | English |
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Title of host publication | Algebraic Biology - Second International Conference, AB 2007, Proceedings |

Pages | 110-124 |

Number of pages | 15 |

Publication status | Published - Dec 1 2007 |

Event | 2nd International Conference on Algebraic Biology, AB 2007 - Castle of Hagenberg, Austria Duration: Jul 2 2007 → Jul 4 2007 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 4545 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 2nd International Conference on Algebraic Biology, AB 2007 |
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Country | Austria |

City | Castle of Hagenberg |

Period | 7/2/07 → 7/4/07 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Algebraic Biology - Second International Conference, AB 2007, Proceedings*(pp. 110-124). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4545 LNCS).

**Exact parameter determination for Parkinson's disease diagnosis with PET using an algebraic approach.** / Yoshida, Hiroshi; Nakagawa, Koji; Anai, Hirokazu; Horimoto, Katsuhisa.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Algebraic Biology - Second International Conference, AB 2007, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4545 LNCS, pp. 110-124, 2nd International Conference on Algebraic Biology, AB 2007, Castle of Hagenberg, Austria, 7/2/07.

}

TY - GEN

T1 - Exact parameter determination for Parkinson's disease diagnosis with PET using an algebraic approach

AU - Yoshida, Hiroshi

AU - Nakagawa, Koji

AU - Anai, Hirokazu

AU - Horimoto, Katsuhisa

PY - 2007/12/1

Y1 - 2007/12/1

N2 - The mechanism of Parkinson's disease can be investigated at the molecular level by using radio-tracers. The concentration of dopamine in the brain can be observed by using a radio-tracer, 6-[18F]fluorodopa (FDOPA), with positron emission tomography (PET), and the dopamine kinetics can be described as compartmental models for tissues of the brain. The models for FDOPA kinetics are solved explicitly, but the solution shows a complicated form including several convolutions over time domain. Owing to the complicated form of the solution, graphical analyses such as Logan or Patlak analysis have been utilized as conventional methods over past decades. Because some kinetic constants for Parkinson's disease are estimated in the graphical analyses with the slope or intercept of the line obtained under various assumptions, only a limited set of parameters have approximately been estimated. We have analysed the compartmental models by using the Laplace transformation of differential equations and by algebraic computation with the aid of Gröbner base constructions. We have obtained a rigorous solution with respect to the kinetic constants over the Laplace domain. Here, we first derive a rigorous solution for the parameters, together with a discussion about the merits of the derivation. Next, we describe a procedure to determine the kinetic constants with the observed time-radioactivity curves. Last, we discuss the feasibility of our method, especially as a criterion for diagnosing Parkinson's disease.

AB - The mechanism of Parkinson's disease can be investigated at the molecular level by using radio-tracers. The concentration of dopamine in the brain can be observed by using a radio-tracer, 6-[18F]fluorodopa (FDOPA), with positron emission tomography (PET), and the dopamine kinetics can be described as compartmental models for tissues of the brain. The models for FDOPA kinetics are solved explicitly, but the solution shows a complicated form including several convolutions over time domain. Owing to the complicated form of the solution, graphical analyses such as Logan or Patlak analysis have been utilized as conventional methods over past decades. Because some kinetic constants for Parkinson's disease are estimated in the graphical analyses with the slope or intercept of the line obtained under various assumptions, only a limited set of parameters have approximately been estimated. We have analysed the compartmental models by using the Laplace transformation of differential equations and by algebraic computation with the aid of Gröbner base constructions. We have obtained a rigorous solution with respect to the kinetic constants over the Laplace domain. Here, we first derive a rigorous solution for the parameters, together with a discussion about the merits of the derivation. Next, we describe a procedure to determine the kinetic constants with the observed time-radioactivity curves. Last, we discuss the feasibility of our method, especially as a criterion for diagnosing Parkinson's disease.

UR - http://www.scopus.com/inward/record.url?scp=38149119014&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38149119014&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9783540734321

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 110

EP - 124

BT - Algebraic Biology - Second International Conference, AB 2007, Proceedings

ER -