Methods for determining key components in a mathematical model for tumor–immune dynamics in multiple myeloma

Gallaher, Jill; Larripa, Kamila; Renardy, Marissa; Shtylla, Blerta; Tania, Nessy; White, David; Wood, Karen L.; Zhu, Li; Passey, Chaitali; Robbins, Michael; Bezman, Natalie; Shelat, Suresh G.; Cho, Hearn Jay; Moore, Helen M.

doi:10.1016/j.jtbi.2018.08.037

Cited by 18 publications

(28 citation statements)

References 74 publications

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“…First, we perform a structural identifiability analysis to determine whether or not it is possible to obtain a unique solution for the parameters while assuming perfect data (noise‐free and continuous in time and space) [36–40]. Obtaining the parameter identifiability for nonlinear tumor‐immune models is typically challenging [36]. In this section, we follow the approach in [36] and consider only the subset of the sensitive parameters identified in Section 3.1.…”

Section: Pretreatment Resultsmentioning

confidence: 99%

“…Using experimental data for mean tumor volume with FGFR3 mutation, our simulation showed that

α_{2}

and

γ_{T}

have a normal and a broad distribution, respectively (Figure 7C), within its range in Table 2. Hence,

α_{2}

is practically identifiable and

γ_{T}

is not practically identifiable given the available experimental data [36]. We again sample from the posterior distribution and forward simulate to generate tumor volume distributions with FGFR3 mutation, and again we see that these distributions are tightly controlled and follow the mean

\pm

SD of the corresponding data on days 14, 19, 21, and 25 (Figure 7D) indicating that the data on time points 14, 19, 21, and 25 may be ideal for estimating the identifiable parameter

α_{2}

.…”

Section: Pretreatment Resultsmentioning

confidence: 99%

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A validated mathematical model of FGFR3‐mediated tumor growth reveals pathways to harness the benefits of combination targeted therapy and immunotherapy in bladder cancer

et al. 2021

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Bladder cancer is a common malignancy with over 80,000 estimated new cases and nearly 18,000 deaths per year in the United States alone. Therapeutic options for metastatic bladder cancer had not evolved much for nearly four decades, until recently, when five immune checkpoint inhibitors were approved by the U.S. Food and Drug Administration (FDA). Despite the activity of these drugs in some patients, the objective response rate for each is less than 25%. At the same time, fibroblast growth factor receptors (FGFRs) have been attractive drug targets for a variety of cancers, and in 2019 the FDA approved the first therapy targeted against FGFR3 for bladder cancer. Given the excitement around these new receptor tyrosine kinase and immune checkpoint targeted strategies, and the challenges they each may face on their own, emerging data suggest that combining these treatment options could lead to improved therapeutic outcomes. In this paper, we develop a mathematical model for FGFR3‐mediated tumor growth and use it to investigate the impact of the combined administration of a small molecule inhibitor of FGFR3 and a monoclonal antibody against the PD‐1/PD‐L1 immune checkpoint. The model is carefully calibrated and validated with experimental data before survival benefits, and dosing schedules are explored. Predictions of the model suggest that FGFR3 mutation reduces the effectiveness of anti‐PD‐L1 therapy, that there are regions of parameter space where each monotherapy can outperform the other, and that pretreatment with anti‐PD‐L1 therapy always results in greater tumor reduction even when anti‐FGFR3 therapy is the more effective monotherapy.

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Section: Pretreatment Resultsmentioning

confidence: 99%

“…Using experimental data for mean tumor volume with FGFR3 mutation, our simulation showed that

α_{2}

and

γ_{T}

have a normal and a broad distribution, respectively (Figure 7C), within its range in Table 2. Hence,

α_{2}

is practically identifiable and

γ_{T}

\pm

SD of the corresponding data on days 14, 19, 21, and 25 (Figure 7D) indicating that the data on time points 14, 19, 21, and 25 may be ideal for estimating the identifiable parameter

α_{2}

.…”

Section: Pretreatment Resultsmentioning

confidence: 99%

A validated mathematical model of FGFR3‐mediated tumor growth reveals pathways to harness the benefits of combination targeted therapy and immunotherapy in bladder cancer

et al. 2021

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“…In the model (2.1), out of 12 parameters, namely r L α β γ s α σ β Q θ μ , , , , , , , , , , , , 1 1 2 2 0 sensitive parameters of the model system are to be identified. For this, due to nonavailability and uncertainty of real data, global sensitivity analysis is being performed for all the 12 parameters by calculating partial rank correlation coefficients (PRCCs) with Latin hypercube sampling The numerical simulations used in sensitivity analysis are executed using the code developed in MATLAB software (Gallaher et al 2018). Under LHS analysis, 1,000 parameter sets for all the 12 parameters are obtained with parameter ranges as defined in Table 2.…”

Section: Sensitivity Analysismentioning

confidence: 99%

“…For this, due to nonavailability and uncertainty of real data, global sensitivity analysis is being performed for all the 12 parameters by calculating partial rank correlation coefficients (PRCCs) with Latin hypercube sampling (LHS) (Blower & Dowlatabadi 1994; Gomero 2012; Wu, Dhingra, Gambhir, & Remais 2013). The numerical simulations used in sensitivity analysis are executed using the code developed in MATLAB software (Gallaher et al 2018).…”

Section: Quantitative Analysismentioning

confidence: 99%

“…With these values, using the statistical technique described in research studies (Gallaher et al 2018; Iman 2008), LHS is performed with the partitioning of each parameter range into 2,000 equiprobable subintervals, considering uniform probability distributions of the parameters in their ranges. Here, 1,000 random samples are produced with the sampling of each subinterval only once for each of the 12 model parameters.…”

Section: Quantitative Analysismentioning

confidence: 99%

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Dynamical behavior of tribal‐forest system in the presence of development activities: Leslie–Gower‐based nonlinear modeling study

Tandon

2020

Natural Resource Modeling

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A nonlinear dynamical system is developed in the proposed study to gain insight into the tribal-forest system in the presence of unplanned development activities. Here, the system is comprised of densities of forest resources, tribal population, and development activities as dynamic variables. The realistic dynamics between the tribal population and forest resources is considered to be of modified Leslie-Gower consumerresource type. The qualitative properties of the system are obtained by establishing the equilibrium points and their stabilities. However, permanence is derived to prove the system's viability in the long run. The model is also quantitatively examined using global sensitivity and bifurcation analyses. Through these analyses, sensitivity to different parameters and their thresholds for qualitative behavioral change are determined. The mathematical analyses prove that excessive overexploitation of forest resources and uncontrollable development activities can put the system in a state of destabilization and impermanence. Recommendations for Resource Managers• A harmonious tribal-forest system can be established by devising proper schemes to check unprecedented and unplanned development activities in the tribal region. For this, development projects should be thoroughly evaluated by the government agencies, before their approval.• Measures to increase the density of forest resources should be practised to cover up the loss incurred due to their utilization in development activities. This can be achieved by increasing the forest cover with enhanced plantation in and around forests and through effective protection schemes. • Initiatives to retain and employ tribal people in forests should be adopted for the protection and expansion of forests. The extraordinary knowledge inherited in tribal people about flora and fauna of forest system can be productively utilized for the conservation of biodiversity.

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Evaluation framework for systems models

Braakman

Pathmanathan

Moore

2022

CPT Pharmacom & Syst Pharma

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As decisions in drug development increasingly rely on predictions from mechanistic systems models, assessing the predictive capability of such models is becoming more important. Several frameworks for the development of quantitative systems pharmacology (QSP) models have been proposed. In this paper, we add to this body of work with a framework that focuses on the appropriate use of qualitative and quantitative model evaluation methods. We provide details and references for those wishing to apply these methods, which include sensitivity and identifiability analyses, as well as concepts such as validation and uncertainty quantification. Many of these methods have been used successfully in other fields, but are not as common in QSP modeling. We illustrate how to apply these methods to evaluate QSP models, and propose methods to use in two case studies. We also share examples of misleading results when inappropriate analyses are used.

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Methods for determining key components in a mathematical model for tumor–immune dynamics in multiple myeloma

Cited by 18 publications

References 74 publications

A validated mathematical model of FGFR3‐mediated tumor growth reveals pathways to harness the benefits of combination targeted therapy and immunotherapy in bladder cancer

A validated mathematical model of FGFR3‐mediated tumor growth reveals pathways to harness the benefits of combination targeted therapy and immunotherapy in bladder cancer

Dynamical behavior of tribal‐forest system in the presence of development activities: Leslie–Gower‐based nonlinear modeling study

Evaluation framework for systems models

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