# The Simplified Reference Tissue Model

### Description

The simplified reference tissue model (SRTM) estimates the binding potential from an observed time activity curve without the need for aterial sampling. It assumes a one-tissue compartment model to describe the influx and efflux in the tissue region of interest and the reference region.

### Usage

1 2 3 | ```
simplifiedReferenceTissueModel(tac, ref, time, SRTM2 = TRUE, k2prime = NULL,
guess = c(R1 = 0.5, k2 = 0.01),
control = minpack.lm::nls.lm.control())
``` |

### Arguments

`tac` |
a vector corresponding to the time activity curve from the tissue (in Bq/mL). |

`ref` |
a vector corresponding to the time activity curve from the reference region (in Bq/mL). |

`time` |
a vector of average frame times (in minutes). |

`SRTM2` |
a logical value that selects the three-parameter model (SRTM) or the two-parameter model (SRTM2), where k2prime is fixed. |

`k2prime` |
the value of k2prime that has been fixed. |

`guess` |
values for the inital parameter estimates for R1 and k2. |

`control` |
a list of parameters used by |

### Details

See the references.

The model has been parameterized in the manner of Wu and Carson (2002). That is, the nonlinear regression estimates R1, k2 and k'2 for the three-parameter model (SRTM) and R1 and k2 for the two-parameter model (SRTM2).

The convolution is performed after interpolating the time activity curves, both for the tissue and the reference region, to one-second resolution then downsampling them back to the original sampling rate.

### Value

`BP` |
Binding potential |

`R1` |
Ratio of the volumes of distrubution for the tissue and reference region |

`k2` |
Clearance rate constant from the tissue to plasma |

`BP.error` |
Approximate standard error of the binding potential |

`R1.error` |
Approximate standard error for the ratio |

`k2.error` |
Approximate standard error for k2 |

### Author(s)

Brandon Whitcher b.whitcher@gmail.com

### References

Lammertsma, A.A. and Hume, S.P. (1996) Simplified reference tissue
model for PET receptor studies, *NeuroImage*, **4**, 153-158.

Wu, Y. and Carson, R.E. (2002) Noise reduction in the simplified
reference tissue model for neuroreceptor functional imaging,
*Journal of Cerebral Blood Flow \& Metabolism*, **22**,
1440-1452.

### See Also

`deltamethod`

, `expConv`

,
`nls.lm`