Towards Quantitative Imaging Biomarkers of Tumor Dissemination: a Multi-scale Parametric Modeling of Multiple Myeloma

The advent of medical imaging and automatic image analysis is bringing the full quantitative assessment of lesions and tumor burden at every clinical examination within reach. This opens avenues for the development and testing of functional disease models, as well as their use in the clinical practice for personalized medicine. In this paper, we introduce a Bayesian statistical framework, based on mixed-effects models, to quantitatively test and learn functional disease models at different scales, on population longitudinal data. We also derive an effective mathematical model for the crossover between initially detected lesions and tumor dissemination, based on the Iwata-Kawasaki-Shigesada model. We finally propose to leverage this descriptive disease progression model into model-aware biomarkers for personalized risk-assessment, taking all available examinations and relevant covariates into account. As a use case, we study Multiple Myeloma, a disseminated plasma cell cancer, in which proper diagnostics is essential, to differentiate frequent precursor state without end-organ damage from the rapidly developing disease requiring therapy. After learning the best biological models for local lesion growth and global tumor burden evolution on clinical data, and computing corresponding population priors, we use individual model parameters as biomarkers, and can study them systematically for correlation with external covariates, such as sex or location of the lesion. On our cohort of 63 patients with smoldering Multiple Myeloma, we show that they perform substantially better than other radiological criteria, to predict progression into symptomatic Multiple Myeloma. Our study paves the way for modeling disease progression patterns for Multiple Myeloma, but also for other metastatic and disseminated tumor growth processes, and for analyzing large longitudinal image data sets acquired in oncological imaging. It shows the unprecedented potential of model-based biomarkers for better and more personalized treatment decisions and deserves being validated on larger cohorts to establish its role in clinical decision making.

[1]  Eva Forssell-Aronsson,et al.  A new method to estimate parameters of the growth model for metastatic tumours , 2013, Theoretical Biology and Medical Modelling.

[2]  Athanassios Iliadis,et al.  Mathematical modeling of tumor growth and metastatic spreading: validation in tumor-bearing mice. , 2014, Cancer research.

[3]  Binsheng Zhao,et al.  Comparison of tumor size assessments in tumor growth inhibition-overall survival models with second-line colorectal cancer data from the VELOUR study , 2018, Cancer Chemotherapy and Pharmacology.

[4]  S Vincent Rajkumar,et al.  Multiple myeloma: 2016 update on diagnosis, risk‐stratification, and management , 2016, American journal of hematology.

[5]  H. Acquah,et al.  A bootstrap approach to evaluating the performance of Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) in selection of an asymmetric price relationship. , 2012 .

[6]  Niklas Hartung,et al.  Study of metastatic kinetics in metastatic melanoma treated with B-RAF inhibitors: Introducing mathematical modelling of kinetics into the therapeutic decision , 2017, PloS one.

[7]  Michalis Mastri,et al.  Modeling Spontaneous Metastasis following Surgery: An In Vivo-In Silico Approach. , 2016, Cancer research.

[8]  L. Schwartz,et al.  New response evaluation criteria in solid tumours: revised RECIST guideline (version 1.1). , 2009, European journal of cancer.

[9]  Hans Erik Johnsen,et al.  International Myeloma Working Group updated criteria for the diagnosis of multiple myeloma. , 2014, The Lancet. Oncology.

[10]  Caleb K. Stein,et al.  Spatial genomic heterogeneity in multiple myeloma revealed by multi-region sequencing , 2017, Nature Communications.

[11]  Thierry Colin,et al.  Computational Modelling of Metastasis Development in Renal Cell Carcinoma , 2015, PLoS Comput. Biol..

[12]  Thierry Goudon,et al.  A model describing the growth and the size distribution of multiple metastatic tumors , 2009 .

[13]  Panagiotis Angelikopoulos,et al.  Personalized Radiotherapy Design for Glioblastoma: Integrating Mathematical Tumor Models, Multimodal Scans, and Bayesian Inference , 2018, IEEE Transactions on Medical Imaging.

[14]  Glenn F Webb,et al.  A mathematical model of bone remodeling dynamics for normal bone cell populations and myeloma bone disease , 2010, Biology Direct.

[15]  Stefan Delorme,et al.  A magnetic resonance imaging-based prognostic scoring system to predict outcome in transplant-eligible patients with multiple myeloma , 2015, Haematologica.

[16]  T Hielscher,et al.  [Focal lesions in whole-body MRI in multiple myeloma : Quantification of tumor mass and correlation with disease-related parameters and prognosis]. , 2018, Der Radiologe.

[17]  L. Fass Imaging and cancer: A review , 2008, Molecular oncology.

[18]  É. Moulines,et al.  Convergence of a stochastic approximation version of the EM algorithm , 1999 .

[19]  A. Boyer,et al.  Quantitative mathematical modeling of clinical brain metastasis dynamics in non-small cell lung cancer , 2018 .

[20]  Bjoern H. Menze,et al.  Introducing PSMA-Bone-PET-Index for quantitative assessment of osseous tumor burden in prostate cancer , 2017 .

[21]  A Orfao,et al.  Next Generation Flow for highly sensitive and standardized detection of minimal residual disease in multiple myeloma , 2017, Leukemia.

[22]  V. Savage,et al.  A Quantitative Theory of Solid Tumor Growth, Metabolic Rate and Vascularization , 2011, PloS one.

[23]  Hana M. Dobrovolny,et al.  Differences in predictions of ODE models of tumor growth: a cautionary example , 2016, BMC Cancer.

[24]  Georg Langs,et al.  Volumetry based biomarker speed of growth: Quantifying the change of total tumor volume in whole-body magnetic resonance imaging over time improves risk stratification of smoldering multiple myeloma patients , 2018, Oncotarget.

[25]  Eva Forssell-Aronsson,et al.  Analysis of inter-patient variations in tumour growth rate , 2014, Theoretical Biology and Medical Modelling.

[26]  Philip Hahnfeldt,et al.  Mathematical Modeling of Tumor-Tumor Distant Interactions Supports a Systemic Control of Tumor Growth. , 2017, Cancer research.

[27]  Irene M. Ghobrial,et al.  How I treat smoldering multiple myeloma. , 2014, Blood.

[28]  M. Jorge Cardoso,et al.  Molecular Imaging, Reconstruction and Analysis of Moving Body Organs, and Stroke Imaging and Treatment , 2017, Lecture Notes in Computer Science.

[29]  Leo Joskowicz,et al.  Medical Image Computing and Computer-Assisted Intervention – MICCAI 2016 , 2016, Lecture Notes in Computer Science.

[30]  Konstantinos Kamnitsas,et al.  DeepMedic for Brain Tumor Segmentation , 2016, BrainLes@MICCAI.

[31]  John M. L. Ebos,et al.  Classical Mathematical Models for Description and Prediction of Experimental Tumor Growth , 2014, PLoS Comput. Biol..

[32]  T Hielscher,et al.  Predictive value of longitudinal whole-body magnetic resonance imaging in patients with smoldering multiple myeloma , 2014, Leukemia.

[33]  M. Zweig,et al.  Receiver-operating characteristic (ROC) plots: a fundamental evaluation tool in clinical medicine. , 1993, Clinical chemistry.

[34]  Jian Hou,et al.  Role of magnetic resonance imaging in the management of patients with multiple myeloma: a consensus statement. , 2015, Journal of clinical oncology : official journal of the American Society of Clinical Oncology.

[35]  Hiroyuki Takamatsu,et al.  Comparison of Minimal Residual Disease Detection by Multiparameter Flow Cytometry, ASO-qPCR, Droplet Digital PCR, and Deep Sequencing in Patients with Multiple Myeloma Who Underwent Autologous Stem Cell Transplantation , 2017, Journal of clinical medicine.

[36]  Yu Zhao,et al.  W-Net for Whole-Body Bone Lesion Detection on ^68 Ga-Pentixafor PET/CT Imaging of Multiple Myeloma Patients , 2017, CMMI/RAMBO/SWITCH@MICCAI.

[37]  M. Pike,et al.  Design and analysis of randomized clinical trials requiring prolonged observation of each patient. II. analysis and examples. , 1977, British Journal of Cancer.

[38]  Johan Pallud,et al.  A Tumor Growth Inhibition Model for Low-Grade Glioma Treated with Chemotherapy or Radiotherapy , 2012, Clinical Cancer Research.

[39]  France Mentré,et al.  The SAEM algorithm for group comparison tests in longitudinal data analysis based on non‐linear mixed‐effects model , 2007, Statistics in medicine.

[40]  B. Sola,et al.  Molecular Cancer BioMed Central Review , 2007 .

[41]  I. Ghobrial,et al.  Myeloma as a model for the process of metastasis: implications for therapy. , 2012, Blood.

[42]  T Bastogne,et al.  Phenomenological modeling of tumor diameter growth based on a mixed effects model. , 2010, Journal of theoretical biology.

[43]  N. Shigesada,et al.  A dynamical model for the growth and size distribution of multiple metastatic tumors. , 2000, Journal of theoretical biology.

[44]  E. Kuhn,et al.  Coupling a stochastic approximation version of EM with an MCMC procedure , 2004 .

[45]  Tobias Bäuerle,et al.  Prognostic significance of focal lesions in whole-body magnetic resonance imaging in patients with asymptomatic multiple myeloma. , 2010, Journal of clinical oncology : official journal of the American Society of Clinical Oncology.

[46]  Marc Lavielle,et al.  Maximum likelihood estimation in nonlinear mixed effects models , 2005, Comput. Stat. Data Anal..

[47]  Hervé Delingette,et al.  Image Guided Personalization of Reaction-Diffusion Type Tumor Growth Models Using Modified Anisotropic Eikonal Equations , 2010, IEEE Transactions on Medical Imaging.

[48]  Philip Gerlee,et al.  The model muddle: in search of tumor growth laws. , 2012, Cancer research.

[49]  C. Mercier,et al.  Modélisation du risque d’évolution métastatique chez les patients supposés avoir une maladie localisée , 2011, Oncologie.

[50]  France Mentré,et al.  Evaluation of bootstrap methods for estimating uncertainty of parameters in nonlinear mixed-effects models: a simulation study in population pharmacokinetics , 2014, Journal of Pharmacokinetics and Pharmacodynamics.

[51]  Neha Korde,et al.  Dilemmas in treating smoldering multiple myeloma. , 2015, Journal of Clinical Oncology.

[52]  Paolo Magni,et al.  Predictive Pharmacokinetic-Pharmacodynamic Modeling of Tumor Growth Kinetics in Xenograft Models after Administration of Anticancer Agents , 2004, Cancer Research.

[53]  T. Mutis,et al.  Diagnosis, risk stratification and management of monoclonal gammopathy of undetermined significance and smoldering multiple myeloma , 2016, International journal of laboratory hematology.

[54]  Anthony C. Davison,et al.  Bootstrap Methods and Their Application , 1998 .

[55]  E. Kaplan,et al.  Nonparametric Estimation from Incomplete Observations , 1958 .

[56]  Seyed-Ahmad Ahmadi,et al.  Automatic Liver and Lesion Segmentation in CT Using Cascaded Fully Convolutional Neural Networks and 3D Conditional Random Fields , 2016, MICCAI.

[57]  Kenneth C. Anderson,et al.  Criteria for the classification of monoclonal gammopathies, multiple myeloma and related disorders: a report of the International Myeloma Working Group , 2003, British journal of haematology.