Experimental method and statistical analysis to fit tumor growth model using SPECT/CT imaging

A preclinical study

Ivan Hidrovo, Joyoni Dey, Megan E. Chesal, Dmytro Shumilov, Narayan Bhusal, James Michael Mathis

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)

Abstract

Background: Over the last decade, several theoretical tumor-models have been developed to describe tumor growth. Oncology imaging is performed using various modalities including computed tomography (CT), magnetic resonance imaging (MRI), single-photon emission computed tomography (SPECT) and fluorodeoxyglucose-positron emission tomography (FDG-PET). Our goal is to extract useful, otherwise hidden, quantitative biophysical parameters (such as growth-rate, tumor-necrotic-factor, etc.) from these serial images of tumors by fitting mathematical models to images. These biophysical features are intrinsic to the tumor types and specific to the study-subject, and expected to add valuable information on the tumor containment or spread and help treatment plans. Thus, fitting realistic but practical models and assessing parameter-errors and degree of fit is important. Methods: We implemented an existing theoretical ode-compartment model and variants and applied them for the first time, in vivo. We developed an inversion algorithm to fit the models for tumor growth for simulated as well as in vivo experimental data. Serial SPECT/CT scans of mice breast-tumors were acquired, and SPECT data was used to segment the proliferating-layers of tumors. Results: Results of noisy data simulation and inversion show that 5 out of 7 parameters were recovered to within 4.3% error. In particular, tumor growth-rate parameter was recovered to 0.07% error. For model fitting to in vivo mice-tumors, regression analysis on the P-layer volume showed R2 of 0.99 for logistic and Gompertzian while surface area model yielded R2=0.96. For the necrotic layer the R2 values were 0.95, 0.93 and 0.94 respectively for surface-area, logistic and Gompertzian. The Akaike Information Criterion (AIC) weights of the models (giving their relative probability of being the best Kullback-Leibler (K-L) model among the set of candidate models) were 0, 0.43 and 0.57 for surface-area, logistic and Gompertzian models. Conclusions: Model-fitting to mice tumor studies demonstrates feasibility of applying the models to in vivo imaging data to extract features. Akaike information criterion (AIC) evaluations show Gompertzian or logistic growth model fits in vivo breast-tumors better than surface-area based growth model.

Original languageEnglish
Pages (from-to)299-309
Number of pages11
JournalQuantitative Imaging in Medicine and Surgery
Volume7
Issue number3
DOIs
StatePublished - 1 Jun 2017

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Growth
Neoplasms
Single-Photon Emission-Computed Tomography
Single Photon Emission Computed Tomography Computed Tomography
Theoretical Models
Logistic Models
Breast Neoplasms
Feasibility Studies
Positron-Emission Tomography
Tomography
Regression Analysis
Magnetic Resonance Imaging
Weights and Measures

Keywords

  • Cancer biology
  • Mathematical tumor growth model
  • Quantification tumor growth

Cite this

Hidrovo, Ivan ; Dey, Joyoni ; Chesal, Megan E. ; Shumilov, Dmytro ; Bhusal, Narayan ; Mathis, James Michael. / Experimental method and statistical analysis to fit tumor growth model using SPECT/CT imaging : A preclinical study. In: Quantitative Imaging in Medicine and Surgery. 2017 ; Vol. 7, No. 3. pp. 299-309.
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title = "Experimental method and statistical analysis to fit tumor growth model using SPECT/CT imaging: A preclinical study",
abstract = "Background: Over the last decade, several theoretical tumor-models have been developed to describe tumor growth. Oncology imaging is performed using various modalities including computed tomography (CT), magnetic resonance imaging (MRI), single-photon emission computed tomography (SPECT) and fluorodeoxyglucose-positron emission tomography (FDG-PET). Our goal is to extract useful, otherwise hidden, quantitative biophysical parameters (such as growth-rate, tumor-necrotic-factor, etc.) from these serial images of tumors by fitting mathematical models to images. These biophysical features are intrinsic to the tumor types and specific to the study-subject, and expected to add valuable information on the tumor containment or spread and help treatment plans. Thus, fitting realistic but practical models and assessing parameter-errors and degree of fit is important. Methods: We implemented an existing theoretical ode-compartment model and variants and applied them for the first time, in vivo. We developed an inversion algorithm to fit the models for tumor growth for simulated as well as in vivo experimental data. Serial SPECT/CT scans of mice breast-tumors were acquired, and SPECT data was used to segment the proliferating-layers of tumors. Results: Results of noisy data simulation and inversion show that 5 out of 7 parameters were recovered to within 4.3{\%} error. In particular, tumor growth-rate parameter was recovered to 0.07{\%} error. For model fitting to in vivo mice-tumors, regression analysis on the P-layer volume showed R2 of 0.99 for logistic and Gompertzian while surface area model yielded R2=0.96. For the necrotic layer the R2 values were 0.95, 0.93 and 0.94 respectively for surface-area, logistic and Gompertzian. The Akaike Information Criterion (AIC) weights of the models (giving their relative probability of being the best Kullback-Leibler (K-L) model among the set of candidate models) were 0, 0.43 and 0.57 for surface-area, logistic and Gompertzian models. Conclusions: Model-fitting to mice tumor studies demonstrates feasibility of applying the models to in vivo imaging data to extract features. Akaike information criterion (AIC) evaluations show Gompertzian or logistic growth model fits in vivo breast-tumors better than surface-area based growth model.",
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Experimental method and statistical analysis to fit tumor growth model using SPECT/CT imaging : A preclinical study. / Hidrovo, Ivan; Dey, Joyoni; Chesal, Megan E.; Shumilov, Dmytro; Bhusal, Narayan; Mathis, James Michael.

In: Quantitative Imaging in Medicine and Surgery, Vol. 7, No. 3, 01.06.2017, p. 299-309.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - Experimental method and statistical analysis to fit tumor growth model using SPECT/CT imaging

T2 - A preclinical study

AU - Hidrovo, Ivan

AU - Dey, Joyoni

AU - Chesal, Megan E.

AU - Shumilov, Dmytro

AU - Bhusal, Narayan

AU - Mathis, James Michael

PY - 2017/6/1

Y1 - 2017/6/1

N2 - Background: Over the last decade, several theoretical tumor-models have been developed to describe tumor growth. Oncology imaging is performed using various modalities including computed tomography (CT), magnetic resonance imaging (MRI), single-photon emission computed tomography (SPECT) and fluorodeoxyglucose-positron emission tomography (FDG-PET). Our goal is to extract useful, otherwise hidden, quantitative biophysical parameters (such as growth-rate, tumor-necrotic-factor, etc.) from these serial images of tumors by fitting mathematical models to images. These biophysical features are intrinsic to the tumor types and specific to the study-subject, and expected to add valuable information on the tumor containment or spread and help treatment plans. Thus, fitting realistic but practical models and assessing parameter-errors and degree of fit is important. Methods: We implemented an existing theoretical ode-compartment model and variants and applied them for the first time, in vivo. We developed an inversion algorithm to fit the models for tumor growth for simulated as well as in vivo experimental data. Serial SPECT/CT scans of mice breast-tumors were acquired, and SPECT data was used to segment the proliferating-layers of tumors. Results: Results of noisy data simulation and inversion show that 5 out of 7 parameters were recovered to within 4.3% error. In particular, tumor growth-rate parameter was recovered to 0.07% error. For model fitting to in vivo mice-tumors, regression analysis on the P-layer volume showed R2 of 0.99 for logistic and Gompertzian while surface area model yielded R2=0.96. For the necrotic layer the R2 values were 0.95, 0.93 and 0.94 respectively for surface-area, logistic and Gompertzian. The Akaike Information Criterion (AIC) weights of the models (giving their relative probability of being the best Kullback-Leibler (K-L) model among the set of candidate models) were 0, 0.43 and 0.57 for surface-area, logistic and Gompertzian models. Conclusions: Model-fitting to mice tumor studies demonstrates feasibility of applying the models to in vivo imaging data to extract features. Akaike information criterion (AIC) evaluations show Gompertzian or logistic growth model fits in vivo breast-tumors better than surface-area based growth model.

AB - Background: Over the last decade, several theoretical tumor-models have been developed to describe tumor growth. Oncology imaging is performed using various modalities including computed tomography (CT), magnetic resonance imaging (MRI), single-photon emission computed tomography (SPECT) and fluorodeoxyglucose-positron emission tomography (FDG-PET). Our goal is to extract useful, otherwise hidden, quantitative biophysical parameters (such as growth-rate, tumor-necrotic-factor, etc.) from these serial images of tumors by fitting mathematical models to images. These biophysical features are intrinsic to the tumor types and specific to the study-subject, and expected to add valuable information on the tumor containment or spread and help treatment plans. Thus, fitting realistic but practical models and assessing parameter-errors and degree of fit is important. Methods: We implemented an existing theoretical ode-compartment model and variants and applied them for the first time, in vivo. We developed an inversion algorithm to fit the models for tumor growth for simulated as well as in vivo experimental data. Serial SPECT/CT scans of mice breast-tumors were acquired, and SPECT data was used to segment the proliferating-layers of tumors. Results: Results of noisy data simulation and inversion show that 5 out of 7 parameters were recovered to within 4.3% error. In particular, tumor growth-rate parameter was recovered to 0.07% error. For model fitting to in vivo mice-tumors, regression analysis on the P-layer volume showed R2 of 0.99 for logistic and Gompertzian while surface area model yielded R2=0.96. For the necrotic layer the R2 values were 0.95, 0.93 and 0.94 respectively for surface-area, logistic and Gompertzian. The Akaike Information Criterion (AIC) weights of the models (giving their relative probability of being the best Kullback-Leibler (K-L) model among the set of candidate models) were 0, 0.43 and 0.57 for surface-area, logistic and Gompertzian models. Conclusions: Model-fitting to mice tumor studies demonstrates feasibility of applying the models to in vivo imaging data to extract features. Akaike information criterion (AIC) evaluations show Gompertzian or logistic growth model fits in vivo breast-tumors better than surface-area based growth model.

KW - Cancer biology

KW - Mathematical tumor growth model

KW - Quantification tumor growth

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