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**Harvard**

Larsson, J. (2019) *Solving the Fisher Equation to Capture Tumour Behaviour for Patients with Low Grade Glioma*.

** BibTeX **

@mastersthesis{

Larsson2019,

author={Larsson, Julia},

title={Solving the Fisher Equation to Capture Tumour Behaviour for Patients with Low Grade Glioma},

abstract={Low Grade Glioma is a slow growing brain tumour, whose size is estimated using Magnetic Resonance Imaging and is treated with a combination of surgery, radiation and chemotherapy. However, cancer cells often remain after surgery leading to recurrence of the tumour and eventually death. To address this problem the Fisher equation has been considered, a partial diﬀerential equation describing how the cancer cell density changes over space and time. The Fisher equation can thus be ﬁtted to patient data by comparing the tumour growth rate and the slope of the tumour interface, properties that is hypothesized to aﬀect the survival time of the patients. The aim of this project is to simulate tumour growth to give additional informationaboutLowGradeGliomathatcannotbeestimateddirectlyfromMagnetic Resonance images, but requires mathematical modelling. To do this, tumour propertieshavebeenestimatedfromdataandstatisticallytestedtoinvestigatetheir potential eﬀect on survival. Also, we have compared diﬀerent methods of solving the Fisher equation and ﬁtted the equation to data through parameter estimation techniques. The results show that two out of three investigated tumour properties have a signiﬁcant eﬀect on survival. The parameter estimation was successful and the diﬀerent numerical methods for solving the Fisher equation yielded similar results for most cases. Additional information about the tumour was estimated from the Fisher equation, but the reliability of these results could be questioned. The main caveat is the simplicity of the Fisher equation and the small size of the patient data set. One solution could be to include the eﬀect of surrounding tissue in the Fisher equation, but this requires accurate data containing many measurements for all patients. A second approach could therefore be to create a model using Non Linear Mixed Eﬀect modelling, with the Fisher equation as the framework, in order to make the model more accurately capture the variation among patients.
},

year={2019},

}

** RefWorks **

RT Generic

SR Electronic

ID 256760

A1 Larsson, Julia

T1 Solving the Fisher Equation to Capture Tumour Behaviour for Patients with Low Grade Glioma

YR 2019

AB Low Grade Glioma is a slow growing brain tumour, whose size is estimated using Magnetic Resonance Imaging and is treated with a combination of surgery, radiation and chemotherapy. However, cancer cells often remain after surgery leading to recurrence of the tumour and eventually death. To address this problem the Fisher equation has been considered, a partial diﬀerential equation describing how the cancer cell density changes over space and time. The Fisher equation can thus be ﬁtted to patient data by comparing the tumour growth rate and the slope of the tumour interface, properties that is hypothesized to aﬀect the survival time of the patients. The aim of this project is to simulate tumour growth to give additional informationaboutLowGradeGliomathatcannotbeestimateddirectlyfromMagnetic Resonance images, but requires mathematical modelling. To do this, tumour propertieshavebeenestimatedfromdataandstatisticallytestedtoinvestigatetheir potential eﬀect on survival. Also, we have compared diﬀerent methods of solving the Fisher equation and ﬁtted the equation to data through parameter estimation techniques. The results show that two out of three investigated tumour properties have a signiﬁcant eﬀect on survival. The parameter estimation was successful and the diﬀerent numerical methods for solving the Fisher equation yielded similar results for most cases. Additional information about the tumour was estimated from the Fisher equation, but the reliability of these results could be questioned. The main caveat is the simplicity of the Fisher equation and the small size of the patient data set. One solution could be to include the eﬀect of surrounding tissue in the Fisher equation, but this requires accurate data containing many measurements for all patients. A second approach could therefore be to create a model using Non Linear Mixed Eﬀect modelling, with the Fisher equation as the framework, in order to make the model more accurately capture the variation among patients.

LA eng

LK http://publications.lib.chalmers.se/records/fulltext/256760/256760.pdf

OL 30