arXiv subjects

Guillermo Lorenzo

Publications and source records attributed to Guillermo Lorenzo.

15 recordsLinked to original sources

arXiv2026

Cahn-Hilliard phase-field modeling of tumor growth via locally adaptive isogeometric analysis with THB-splines

Predicting tumor dynamics in biological systems under physiologically relevant conditions using mathematical and computational models remains a challenging problem. Continuum models based on phase-field (diffuse-interface) formulations have proven to be an effective modeling strategy to govern tumor dynamics and interactions of multiple species. Within this framework, the present work investigates a tumor growth model based on the Cahn-Hilliard (CH) equation. The formulation involves a fourth-order differential operator that imposes higher continuity requirement on approximation spaces for a well-defined primal variational formulation. To address this challenge, we use isogeometric analysis (IGA), which inherently satisfies this requirement through spline-based basis functions and eliminates the need for mixed or auxiliary-variable approaches commonly used in standard finite element discretizations. Additionally, a locally adaptive IGA scheme with truncated hierarchical B-splines (THB-splines) is used to reduce computational cost while maintaining accuracy. The model is first evaluated on standard benchmark cases and then applied to an organ-scale, patient-specific geometric model of the breast reconstructed from magnetic resonance imaging (MRI) data. Our results show that the model reproduces known tumor morphologies, ranging from a spheroidal pattern to fingered growth. A series of numerical experiments further shows the diversity of tumor dynamics produced by different model parameter choices. Our findings demonstrate the predictive potential of the CH-based phase-field tumor growth model integrated with a locally adaptive IGA framework.

math.NA↗

arXiv2026

An MRI-informed poromechanical model for organ-scale prediction of glioma growth

Gliomas constitute one of the most aggressive and heterogeneous forms of brain tumors, posing major challenges for understanding their biology and developing effective treatments. Animal models enable the collection of rich longitudinal datasets describing tumor dynamics, which can be integrated within mathematical models to elucidate the biological mechanisms governing tumor growth. While most formulations rely on reaction-diffusion systems with limited insight on tissue deformation and fluid transport, we propose a magnetic resonance imaging (MRI)-informed, poroelastic model to describe C6 glioma growth in rats. We use data from animals (n=4) that were imaged five times after intracranial injection of cancer cells. Each MRI dataset includes (i) anatomical T1-weighted data for brain and tumor segmentation and to assign mechanical properties; (ii) diffusion-weighted MRI, which enables estimation of the fraction of each voxel that is tumor; and (iii) dynamic contrast-enhanced MRI, which informs permeability as well as vascular and liquid fraction maps. Using finite-element simulations, model calibration for each rat uses the Levenberg-Marquardt method informed by the first three MRI datasets. Tumor forecasts are validated by assessing model-data agreement on the remaining two MRI datasets. Our results show relative tumor volume errors between 0.94 percent and 11.27 percent at calibration, and prediction errors between 4.73 percent and 36.03 percent. Additionally, Dice scores ranged from 0.80 to 0.93 during calibration, and from 0.75 to 0.93 during validation. Thus, our results suggest that our poromechanical model can describe C6 glioma growth. This study provides a first step toward a patient-specific, multiscale model of the spatiotemporal poromechanics underlying glioma progression and therapeutic response.

physics.comp-ph↗

arXiv2025

Validating the predictions of mathematical models describing tumor growth and treatment response

Despite advances in methods to interrogate tumor biology, the observational and population-based approach of classical cancer research and clinical oncology does not enable anticipation of tumor outcomes to hasten the discovery of cancer mechanisms and personalize disease management. To address these limitations, individualized cancer forecasts have been shown to predict tumor growth and therapeutic response, inform treatment optimization, and guide experimental efforts. These predictions are obtained via computer simulations of mathematical models that are constrained with data from a patient's cancer and experiments. This book chapter addresses the validation of these mathematical models to forecast tumor growth and treatment response. We start with an overview of mathematical modeling frameworks, model selection techniques, and fundamental metrics. We then describe the usual strategies employed to validate cancer forecasts in preclinical and clinical scenarios. Finally, we discuss existing barriers in validating these predictions along with potential strategies to address them.

q-bio.TO↗

arXiv2024

Iterative algorithms for the reconstruction of early states of prostate cancer growth

The development of mathematical models of cancer informed by time-resolved measurements has enabled personalised predictions of tumour growth and treatment response. However, frequent cancer monitoring is rare, and many tumours are treated soon after diagnosis with limited data. To improve the predictive capabilities of cancer models, we investigate the problem of recovering earlier tumour states from a single spatial measurement at a later time. Focusing on prostate cancer, we describe tumour dynamics using a phase-field model coupled with two reaction-diffusion equations for a nutrient and the local prostate-specific antigen. We generate synthetic data using a discretisation based on Isogeometric Analysis. Then, building on our previous analytical work (Beretta et al., SIAP (2024)), we propose an iterative reconstruction algorithm based on the Landweber scheme, showing local convergence with quantitative rates and exploring an adaptive step size that leads to faster reconstruction algorithms. Finally, we run simulations demonstrating high-quality reconstructions even with long time horizons and noisy data.

math.AP↗

arXiv2024

Mathematical analysis of a model-constrained inverse problem for the reconstruction of early states of prostate cancer growth

The availability of cancer measurements over time enables the personalised assessment of tumour growth and therapeutic response dynamics. However, many tumours are treated after diagnosis without collecting longitudinal data, and cancer monitoring protocols may include infrequent measurements. To facilitate the estimation of disease dynamics and better guide ensuing clinical decisions, we investigate an inverse problem enabling the reconstruction of earlier tumour states by using a single spatial tumour dataset and a biomathematical model describing disease dynamics. We focus on prostate cancer, since aggressive cases of this disease are usually treated after diagnosis. We describe tumour dynamics with a phase-field model driven by a generic nutrient ruled by reaction-diffusion dynamics. The model is completed with another reaction-diffusion equation for the local production of prostate-specific antigen, which is a key prostate cancer biomarker. We first improve previous well-posedness results by further showing that the solution operator is continuously Fréchet differentiable. We then analyse the backward inverse problem concerning the reconstruction of earlier tumour states starting from measurements of the model variables at the final time. Since this problem is severely ill-posed, only very weak conditional stability of logarithmic type can be recovered from the terminal data. However, by restricting the unknowns to a compact subset of a finite-dimensional subspace, we can derive an optimal Lipschitz stability estimate.

math.AP↗

arXiv2023

Patient-specific computational forecasting of prostate cancer growth during active surveillance using an imaging-informed biomechanistic model

Active surveillance (AS) is a suitable management option for newly-diagnosed prostate cancer (PCa), which usually presents low to intermediate clinical risk. Patients enrolled in AS have their tumor closely monitored via longitudinal multiparametric magnetic resonance imaging (mpMRI), serum prostate-specific antigen tests, and biopsies. Hence, the patient is prescribed treatment when these tests identify progression to higher-risk PCa. However, current AS protocols rely on detecting tumor progression through direct observation according to standardized monitoring strategies. This approach limits the design of patient-specific AS plans and may lead to the late detection and treatment of tumor progression. Here, we propose to address these issues by leveraging personalized computational predictions of PCa growth. Our forecasts are obtained with a spatiotemporal biomechanistic model informed by patient-specific longitudinal mpMRI data. Our results show that our predictive technology can represent and forecast the global tumor burden for individual patients, achieving concordance correlation coefficients ranging from 0.93 to 0.99 across our cohort (n=7). Additionally, we identify a model-based biomarker of higher-risk PCa: the mean proliferation activity of the tumor (p=0.041). Using logistic regression, we construct a PCa risk classifier based on this biomarker that achieves an area under the receiver operating characteristic curve of 0.83. We further show that coupling our tumor forecasts with this PCa risk classifier enables the early identification of PCa progression to higher-risk disease by more than one year. Thus, we posit that our predictive technology constitutes a promising clinical decision-making tool to design personalized AS plans for PCa patients.

q-bio.TO↗

arXiv2023

Patient-specific, mechanistic models of tumor growth incorporating artificial intelligence and big data

Despite the remarkable advances in cancer diagnosis, treatment, and management that have occurred over the past decade, malignant tumors remain a major public health problem. Further progress in combating cancer may be enabled by personalizing the delivery of therapies according to the predicted response for each individual patient. The design of personalized therapies requires patient-specific information integrated into an appropriate mathematical model of tumor response. A fundamental barrier to realizing this paradigm is the current lack of a rigorous, yet practical, mathematical theory of tumor initiation, development, invasion, and response to therapy. In this review, we begin by providing an overview of different approaches to modeling tumor growth and treatment, including mechanistic as well as data-driven models based on ``big data" and artificial intelligence. Next, we present illustrative examples of mathematical models manifesting their utility and discussing the limitations of stand-alone mechanistic and data-driven models. We further discuss the potential of mechanistic models for not only predicting, but also optimizing response to therapy on a patient-specific basis. We then discuss current efforts and future possibilities to integrate mechanistic and data-driven models. We conclude by proposing five fundamental challenges that must be addressed to fully realize personalized care for cancer patients driven by computational models.

physics.med-ph↗

arXiv2023

Predictive Digital Twin for Optimizing Patient-Specific Radiotherapy Regimens under Uncertainty in High-Grade Gliomas

We develop a methodology to create data-driven predictive digital twins for optimal risk-aware clinical decision-making. We illustrate the methodology as an enabler for an anticipatory personalized treatment that accounts for uncertainties in the underlying tumor biology in high-grade gliomas, where heterogeneity in the response to standard-of-care (SOC) radiotherapy contributes to sub-optimal patient outcomes. The digital twin is initialized through prior distributions derived from population-level clinical data in the literature for a mechanistic model's parameters. Then the digital twin is personalized using Bayesian model calibration for assimilating patient-specific magnetic resonance imaging data and used to propose optimal radiotherapy treatment regimens by solving a multi-objective risk-based optimization under uncertainty problem. The solution leads to a suite of patient-specific optimal radiotherapy treatment regimens exhibiting varying levels of trade-off between the two competing clinical objectives: (i) maximizing tumor control (characterized by minimizing the risk of tumor volume growth) and (ii) minimizing the toxicity from radiotherapy. The proposed digital twin framework is illustrated by generating an in silico cohort of 100 patients with high-grade glioma growth and response properties typically observed in the literature. For the same total radiation dose as the SOC, the personalized treatment regimens lead to median increase in tumor time to progression of around six days. Alternatively, for the same level of tumor control as the SOC, the digital twin provides optimal treatment options that lead to a median reduction in radiation dose by 16.7% (10 Gy) compared to SOC total dose of 60 Gy. The range of optimal solutions also provide options with increased doses for patients with aggressive cancer, where SOC does not lead to sufficient tumor control.

cs.CE↗

arXiv2022

Identifying mechanisms driving the early response of triple negative breast cancer patients to neoadjuvant chemotherapy using a mechanistic model integrating in vitro and in vivo imaging data

Neoadjuvant chemotherapy (NAC) is a standard-of-care treatment for locally advanced triple negative breast cancer (TNBC) before surgery. The early assessment of TNBC response to NAC would enable an oncologist to adapt the therapeutic plan of a non-responding patient, thereby improving treatment outcomes while preventing unnecessary toxicities. To this end, a promising approach consists of obtaining \textsl{in silico} personalized forecasts of tumor response to NAC \textsl{via} computer simulation of mechanistic models constrained with patient-specific magnetic resonance imaging (MRI) data acquired early during NAC. Here, we present a model featuring the essential mechanisms of TNBC growth and response to NAC, including an explicit description of drug pharmacodynamics and pharmacokinetics. As longitudinal \textsl{in vivo} MRI data for model calibration is limited, we perform a sensitivity analysis to identify the model mechanisms driving the response to two NAC drug combinations: doxorubicin with cyclophosphamide, and paclitaxel with carboplatin. The model parameter space is constructed by combining patient-specific MRI-based \textsl{in silico} parameter estimates and \textit{in vitro} measurements of pharmacodynamic parameters obtained using time-resolved microscopy assays of several TNBC lines. The sensitivity analysis is run in two MRI-based scenarios corresponding to a well-perfused and a poorly-perfused tumor. Out of the 15 parameters considered herein, only the baseline tumor cell net proliferation rate along with the maximum concentrations and effects of doxorubicin, carboplatin, and paclitaxel exhibit a relevant impact on model forecasts (total effect index, $S_T>$0.1). These results dramatically limit the number of parameters that require \textsl{in vivo} MRI-constrained calibration, thereby facilitating the clinical application of our model.

q-bio.TO↗

arXiv2022

Oncology and mechanics: landmark studies and promising clinical applications

Clinical management of cancer has continuously evolved for several decades. Biochemical, molecular and genomics approaches have brought and still bring numerous insights into cancerous diseases. It is now accepted that some phenomena, allowed by favorable biological conditions, emerge via mechanical signaling at the cellular scale and via mechanical forces at the macroscale. Mechanical phenomena in cancer have been studied in-depth over the last decades, and their clinical applications are starting to be understood. If numerous models and experimental setups have been proposed, only a few have led to clinical applications. The objective of this contribution is to propose to review a large scope of mechanical findings which have consequences on the clinical management of cancer. This review is mainly addressed to doctoral candidates in mechanics and applied mathematics who are faced with the challenge of the mechanics-based modeling of cancer with the aim of clinical applications. We show that the collaboration of the biological and mechanical approaches has led to promising advances in terms of modeling, experimental design and therapeutic targets. Additionally, a specific focus is brought on imaging-informed mechanics-based models, which we believe can further the development of new therapeutic targets and the advent of personalized medicine. We study in detail several successful workflows on patient-specific targeted therapies based on mechanistic modeling.

q-bio.TO↗

arXiv2022

Data-driven simulation of Fisher-Kolmogorov tumor growth models using Dynamic Mode Decomposition

The computer simulation of organ-scale biomechanistic models of cancer personalized via routinely collected clinical and imaging data enables to obtain patient-specific predictions of tumor growth and treatment response over the anatomy of the patient's affected organ. These patient-specific computational forecasts have been regarded as a promising approach to personalize the clinical management of cancer and derive optimal treatment plans for individual patients, which constitute timely and critical needs in clinical oncology. However, the computer simulation of the underlying spatiotemporal models can entail a prohibitive computational cost, which constitutes a barrier to the successful development of clinically-actionable computational technologies for personalized tumor forecasting. To address this issue, here we propose to utilize Dynamic-Mode Decomposition (DMD) to construct a low-dimensional representation of cancer models and accelerate their simulation. DMD is an unsupervised machine learning method based on the singular value decomposition that has proven useful in many applications as both a predictive and a diagnostic tool. We show that DMD may be applied to Fisher-Kolmogorov models, which constitute an established formulation to represent untreated solid tumor growth that can further accommodate other relevant cancer phenomena. Our results show that a DMD implementation of this model over a clinically-relevant parameter space can yield impressive predictions, with short to medium-term errors remaining under 1% and long-term errors remaining under 20%, despite very short training periods. We posit that this data-driven approach has the potential to greatly reduce the computational overhead of personalized simulations of cancer models, thereby facilitating tumor forecasting, parameter identification, uncertainty quantification, and treatment optimization.

physics.bio-ph↗

arXiv2021

Quantitative in vivo imaging to enable tumor forecasting and treatment optimization

Current clinical decision-making in oncology relies on averages of large patient populations to both assess tumor status and treatment outcomes. However, cancers exhibit an inherent evolving heterogeneity that requires an individual approach based on rigorous and precise predictions of cancer growth and treatment response. To this end, we advocate the use of quantitative in vivo imaging data to calibrate mathematical models for the personalized forecasting of tumor development. In this chapter, we summarize the main data types available from both common and emerging in vivo medical imaging technologies, and how these data can be used to obtain patient-specific parameters for common mathematical models of cancer. We then outline computational methods designed to solve these models, thereby enabling their use for producing personalized tumor forecasts in silico, which, ultimately, can be used to not only predict response, but also optimize treatment. Finally, we discuss the main barriers to making the above paradigm a clinical reality.

q-bio.TO↗

arXiv2020

Optimal control of cytotoxic and antiangiogenic therapies on prostate cancer growth

Prostate cancer can be lethal in advanced stages, for which chemotherapy may become the only viable therapeutic option. While there is no clear clinical management strategy fitting all patients, cytotoxic chemotherapy with docetaxel is currently regarded as the gold standard. However, tumors may regain activity after treatment conclusion and become resistant to docetaxel. This situation calls for new delivery strategies and drug compounds enabling an improved therapeutic outcome. Combination of docetaxel with antiangiogenic therapy has been considered a promising strategy. Bevacizumab is the most common antiangiogenic drug, but clinical studies have not revealed a clear benefit from its combination with docetaxel. Here, we capitalize on our prior work on mathematical modeling of prostate cancer growth subjected to combined cytotoxic and antiangiogenic therapies, and propose an optimal control framework to robustly compute the drug-independent cytotoxic and antiangiogenic effects enabling an optimal therapeutic control of tumor dynamics. We describe the formulation of the optimal control problem, for which we prove the existence of at least a solution and determine the necessary first order optimality conditions. We then present numerical algorithms based on isogeometric analysis to run a preliminary simulation study over a single cycle of combined therapy. Our results suggest that only cytotoxic chemotherapy is required to optimize therapeutic performance and we show that our framework can produce superior solutions to combined therapy with docetaxel and bevacizumab. We also illustrate how the optimal drug-naïve cytotoxic effects computed in these simulations may be successfully leveraged to guide drug production and delivery strategies by running a nonlinear least-square fit of protocols involving docetaxel and a new design drug.

math.OC↗

arXiv2020

Simulating the spread of COVID-19 via spatially-resolved susceptible-exposed-infected-recovered-deceased (SEIRD) model with heterogeneous diffusion

We present an early version of a Susceptible-Exposed-Infected-Recovered-Deceased (SEIRD) mathematical model based on partial differential equations coupled with a heterogeneous diffusion model. The model describes the spatio-temporal spread of the COVID-19 pandemic, and aims to capture dynamics also based on human habits and geographical features. To test the model, we compare the outputs generated by a finite-element solver with measured data over the Italian region of Lombardy, which has been heavily impacted by this crisis between February and April 2020. Our results show a strong qualitative agreement between the simulated forecast of the spatio-temporal COVID-19 spread in Lombardy and epidemiological data collected at the municipality level. Additional simulations exploring alternative scenarios for the relaxation of lockdown restrictions suggest that reopening strategies should account for local population densities and the specific dynamics of the contagion. Thus, we argue that data-driven simulations of our model could ultimately inform health authorities to design effective pandemic-arresting measures and anticipate the geographical allocation of crucial medical resources.

q-bio.PE↗

arXiv2019

Mathematical analysis and simulation study of a phase-field model of prostate cancer growth with chemotherapy and antiangiogenic therapy effects

Cytotoxic chemotherapy is a common treatment for advanced prostate cancer. These tumors are also known to rely on angiogenesis, i.e., the growth of local microvasculature via chemical signaling produced by the tumor. Thus, several clinical studies have been investigating antiangiogenic therapy for advanced prostate cancer, either as monotherapy or combined with standard cytotoxic protocols. However, the complex genetic alterations promoting prostate cancer growth complicate the selection of the best chemotherapeutic approach for each patient's tumor. Here, we present a mathematical model of prostate cancer growth and chemotherapy that may enable physicians to test and design personalized chemotherapeutic protocols in silico. We use the phase-field method to describe tumor growth, which we assume to be driven by a generic nutrient following reaction-diffusion dynamics. Tumor proliferation and apoptosis (i.e., programmed cell death) can be parameterized with experimentally-determined values. Cytotoxic chemotherapy is included as a term downregulating tumor net proliferation, while antiangiogenic therapy is modeled as a reduction in intratumoral nutrient supply. Another equation couples the tumor phase field with the production of prostate-specific antigen, which is an extensively used prostate cancer biomarker. We prove the well-posedness of our model and we run a series of representative simulations using an isogeometric method to explore untreated tumor growth as well as the effects of cytotoxic chemotherapy and antiangiogenic therapy, both alone and combined. Our simulations show that our model captures the growth morphologies of prostate cancer as well as common outcomes of cytotoxic and antiangiogenic mono and combined therapy. Our model also reproduces the usual temporal trends in tumor volume and prostate-specific antigen evolution observed in previous studies.

math.AP↗