Mathematical Assessment of the Role of Intervention Programs for Malaria Control.

Malaria remains a global health problem despite the many attempts to control and eradicate it. There is an urgent need to understand the current transmission dynamics of malaria and to determine the interventions necessary to control malaria. In this paper, we seek to develop a fit-for-purpose mathematical model to assess the interventions needed to control malaria in an endemic setting. To achieve this, we formulate a malaria transmission model to analyse the spread of malaria in the presence of interventions. A sensitivity analysis of the model is performed to determine the relative impact of the model parameters on disease transmission. We explore how existing variations in the recruitment and management of intervention strategies affect malaria transmission. Results obtained from the study imply that the discontinuation of existing interventions has a significant effect on malaria prevalence. Thus, the maintenance of interventions is imperative for malaria elimination and eradication. In a scenario study aimed at assessing the impact of long-lasting insecticidal nets (LLINs), indoor residual spraying (IRS), and localized individual measures, our findings indicate that increased LLINs utilization and extended IRS coverage (with longer-lasting insecticides) cause a more pronounced reduction in symptomatic malaria prevalence compared to a reduced LLINs utilization and shorter IRS coverage. Additionally, our study demonstrates the impact of localized preventive measures in mitigating the spread of malaria when compared to the absence of interventions.

Free and Interfacial Boundaries in Individual-Based Models of Multicellular Biological systems.

Coordination of cell behaviour is key to a myriad of biological processes including tissue morphogenesis, wound healing, and tumour growth. As such, individual-based computational models, which explicitly describe inter-cellular interactions, are commonly used to model collective cell dynamics. However, when using individual-based models, it is unclear how descriptions of cell boundaries affect overall population dynamics. In order to investigate this we define three cell boundary descriptions of varying complexities for each of three widely used off-lattice individual-based models: overlapping spheres, Voronoi tessellation, and vertex models. We apply our models to multiple biological scenarios to investigate how cell boundary description can influence tissue-scale behaviour. We find that the Voronoi tessellation model is most sensitive to changes in the cell boundary description with basic models being inappropriate in many cases. The timescale of tissue evolution when using an overlapping spheres model is coupled to the boundary description. The vertex model is demonstrated to be the most stable to changes in boundary description, though still exhibits timescale sensitivity. When using individual-based computational models one should carefully consider how cell boundaries are defined. To inform future work, we provide an exploration of common individual-based models and cell boundary descriptions in frequently studied biological scenarios and discuss their benefits and disadvantages.

Extinction of Bistable Populations is Affected by the Shape of their Initial Spatial Distribution.

The question of whether biological populations survive or are eventually driven to extinction has long been examined using mathematical models. In this work, we study population survival or extinction using a stochastic, discrete lattice-based random walk model where individuals undergo movement, birth and death events. The discrete model is defined on a two-dimensional hexagonal lattice with periodic boundary conditions. A key feature of the discrete model is that crowding effects are introduced by specifying two different crowding functions that govern how local agent density influences movement events and birth/death events. The continuum limit description of the discrete model is a nonlinear reaction-diffusion equation, and we focus on crowding functions that lead to linear diffusion and a bistable source term that is often associated with the strong Allee effect. Using both the discrete and continuum modelling tools, we explore the complicated relationship between the long-term survival or extinction of the population and the initial spatial arrangement of the population. In particular, we study different spatial arrangements of initial distributions: (i) a well-mixed initial distribution where the initial density is independent of position in the domain; (ii) a vertical strip initial distribution where the initial density is independent of vertical position in the domain; and, (iii) several forms of two-dimensional initial distributions where the initial population is distributed in regions with different shapes. Our results indicate that the shape of the initial spatial distribution of the population affects extinction of bistable populations. All software required to solve the discrete and continuum models used in this work are available on GitHub .

A first-in-human phase I study to evaluate the MEK1/2 inhibitor, cobimetinib, administered daily in patients with advanced solid tumors.

Objective Cobimetinib, a MEK1/2 inhibitor, was administered to patients with advanced solid tumors to assess safety, pharmacokinetics, pharmacodynamics, and anti-tumor activity. Methods For dose-escalation, a 3 + 3 design was used. Oral cobimetinib was administered once daily on a 21-day on/7-day off (21/7) or a 14-day on/14-day off (14/14) schedule. Serial plasma samples were collected for pharmacokinetic (PK) analysis on Day 1 and at steady state. In expansion stages, patients with RAS or RAF mutant tumors were treated at the maximum tolerated dose (MTD) of the 21/7 or 14/14 schedule. Results Ninety-seven patients received cobimetinib. In the 21/7 dose escalation, 36 patients enrolled in 8 cohorts (0.05 mg/kg-80 mg). Dose-limiting toxicities (DLTs) were Grade 4 hepatic encephalopathy, Grade 3 diarrhea, and Grade 3 rash. In the 14/14 dose escalation, 20 patients enrolled in 4 cohorts (60-125 mg). DLTs were Grade 3 rash and Grade 3 blurred vision associated with presence of reversible subretinal fluid. The MTD was 60 mg on 21/7 schedule and 100 mg on 14/14 schedule. Cobimetinib PK showed dose-proportional increases in exposure. The most frequent adverse events attributed to cobimetinib were diarrhea, rash, fatigue, edema, nausea, and vomiting. In patients treated at the 60-mg (21/7) or 100-mg (14/14) dose, one unconfirmed complete response and 6 confirmed partial responses were observed. All responses occurred in melanoma patients; 6 harbored the BRAF(V600E) mutation. Conclusions Cobimetinib is generally well tolerated and durable responses were observed in BRAF(V600E) mutant melanoma patients. Evaluation of cobimetinib in combination with other therapies is ongoing.

Quantifying the effect of experimental design choices for in vitro scratch assays.

Scratch assays are often used to investigate potential drug treatments for chronic wounds and cancer. Interpreting these experiments with a mathematical model allows us to estimate the cell diffusivity, D, and the cell proliferation rate, λ. However, the influence of the experimental design on the estimates of D and λ is unclear. Here we apply an approximate Bayesian computation (ABC) parameter inference method, which produces a posterior distribution of D and λ, to new sets of synthetic data, generated from an idealised mathematical model, and experimental data for a non-adhesive mesenchymal population of fibroblast cells. The posterior distribution allows us to quantify the amount of information obtained about D and λ. We investigate two types of scratch assay, as well as varying the number and timing of the experimental observations captured. Our results show that a scrape assay, involving one cell front, provides more precise estimates of D and λ, and is more computationally efficient to interpret than a wound assay, with two opposingly directed cell fronts. We find that recording two observations, after making the initial observation, is sufficient to estimate D and λ, and that the final observation time should correspond to the time taken for the cell front to move across the field of view. These results provide guidance for estimating D and λ, while simultaneously minimising the time and cost associated with performing and interpreting the experiment.

Phase I study of XL281 (BMS-908662), a potent oral RAF kinase inhibitor, in patients with advanced solid tumors.

Background XL281 is a potent and selective inhibitor of wild-type and mutant RAF kinases with anti-tumor activity in multiple xenograft models. Mutations in KRAS or BRAF can activate the RAF/MEK/ERK pathway in human tumors and may confer sensitivity to RAF kinase inhibitors. Methods We performed a phase I study of XL281 in patients with advanced solid tumors. Patients were enrolled in successive cohorts of XL281 orally once daily in 28-day cycles. Twice daily dosing, different formulations, and the effect of food and famotidine were also studied. At the MTD expanded cohorts with defined mutations were treated. Results In total, 160 patients were treated. The MTD on the QD schedule was 150 mg. The most common toxicities were diarrhea, nausea, and fatigue. Plasma Cmax and AUC increased with dose. Famotidine resulted in lower AUC while food had no effect. Two patients had partial responses by RECIST: One with papillary thyroid cancer with NRAS mutation and one with uveal melanoma. Another nine patients had tumor decrease of >10% but did not meet RECIST criteria for PR. Matched tumors pairs from 33 patients showed evidence of RAF inhibition with significant decreases in pERK, pMEK and pAKT. Conclusions XL281 was generally well tolerated and the MTD was established at 150 mg/day. Partial responses and clinical benefit were observed in several patients. Tumor biopsies demonstrated effective target inhibition.

Modelling the movement of interacting cell populations: a moment dynamics approach.

Mathematical models describing the movement of multiple interacting subpopulations are relevant to many biological and ecological processes. Standard mean-field partial differential equation descriptions of these processes suffer from the limitation that they implicitly neglect to incorporate the impact of spatial correlations and clustering. To overcome this, we derive a moment dynamics description of a discrete stochastic process which describes the spreading of distinct interacting subpopulations. In particular, we motivate our model by mimicking the geometry of two typical cell biology experiments. Comparing the performance of the moment dynamics model with a traditional mean-field model confirms that the moment dynamics approach always outperforms the traditional mean-field approach. To provide more general insight we summarise the performance of the moment dynamics model and the traditional mean-field model over a wide range of parameter regimes. These results help distinguish between those situations where spatial correlation effects are sufficiently strong, such that a moment dynamics model is required, from other situations where spatial correlation effects are sufficiently weak, such that a traditional mean-field model is adequate.

The physicochemical properties of legume protein isolates and their ability to stabilize oil-in-water emulsions with and without genipin.

The physicochemical and emulsifying properties of legume protein isolates prepared from chickpea (CPI), faba bean (FPI), lentil (LPI) and soy (SPI) were investigated in the presence and absence of genipin. Solubility was highest for CPI (~94 %), followed by LPI (~90 %), FPI (~85 %) and SPI (~50 %). Surface characteristics revealed similar zeta potentials (~ - 47 mV) for CPI, LPI and FPI, but lower for SPI (~ - 44 mV). Contrastingly, surface hydrophobicity was greatest for CPI (~137 arbitrary units, AU), followed by SPI/LPI (~70 AU) and FPI (~24 AU). A significant (from 16.73 to ~8.42 mN/m) reduction in interfacial tension was observed in canola oil-water mixtures in the presence of non-crosslinked legume protein isolates. The extent of legume protein isolate-genipin crosslinking was found to be similar for all isolates. Overall, creaming stability increased in the presence of genipin, with maximum stability observed for SPI (65 %), followed by FPI (61 %), LPI (56 %) and finally CPI (50 %).

Avoidance, confusion or solitude? Modelling how noise pollution affects whale migration.

Many baleen whales are renowned for their acoustic communication. Under pristine conditions, this communication can plausibly occur across hundreds of kilometres. Frequent vocalisations may allow a dispersed migrating group to maintain contact, and therefore benefit from improved navigation via the "wisdom of the crowd". Human activities have considerably inflated ocean noise levels. Here we develop a data-driven mathematical model to investigate how ambient noise levels may inhibit whale migration. Mathematical models allow us to simultaneously simulate collective whale migration behaviour, auditory cue detection, and noise propagation. Rising ambient noise levels are hypothesised to influence navigation through three mechanisms: (i) diminished communication space; (ii) reduced ability to hear external sound cues and; (iii) triggering noise avoidance behaviour. Comparing pristine and current soundscapes, we observe navigation impairment that ranges from mild (increased journey time) to extreme (failed navigation). Notably, the three mechanisms induce qualitatively different impacts on migration behaviour. We demonstrate the model's potential predictive power, exploring the extent to which migration may be altered under future shipping and construction scenarios.

TRPV4 is expressed by enteric glia and muscularis macrophages of the colon but does not play a prominent role in colonic motility.

Background: Mechanosensation is an important trigger of physiological processes in the gastrointestinal tract. Aberrant responses to mechanical input are associated with digestive disorders, including visceral hypersensitivity. Transient Receptor Potential Vanilloid 4 (TRPV4) is a mechanosensory ion channel with proposed roles in visceral afferent signaling, intestinal inflammation, and gut motility. While TRPV4 is a potential therapeutic target for digestive disease, current mechanistic understanding of how TRPV4 may influence gut function is limited by inconsistent reports of TRPV4 expression and distribution. Methods: In this study we profiled functional expression of TRPV4 using Ca2+ imaging of wholemount preparations of the mouse, monkey, and human intestine in combination with immunofluorescent labeling for established cellular markers. The involvement of TRPV4 in colonic motility was assessed in vitro using videomapping and contraction assays. Results: The TRPV4 agonist GSK1016790A evoked Ca2+ signaling in muscularis macrophages, enteric glia, and endothelial cells. TRPV4 specificity was confirmed using TRPV4 KO mouse tissue or antagonist pre-treatment. Calcium responses were not detected in other cell types required for neuromuscular signaling including enteric neurons, interstitial cells of Cajal, PDGFRα+ cells, and intestinal smooth muscle. TRPV4 activation led to rapid Ca2+ responses by a subpopulation of glial cells, followed by sustained Ca2+ signaling throughout the enteric glial network. Propagation of these waves was suppressed by inhibition of gap junctions or Ca2+ release from intracellular stores. Coordinated glial signaling in response to GSK1016790A was also disrupted in acute TNBS colitis. The involvement of TRPV4 in the initiation and propagation of colonic motility patterns was examined in vitro. Conclusions: We reveal a previously unappreciated role for TRPV4 in the initiation of distension-evoked colonic motility. These observations provide new insights into the functional role of TRPV4 activation in the gut, with important implications for how TRPV4 may influence critical processes including inflammatory signaling and motility.

Capturing and Quantifying Particle Transcytosis with Microphysiological Intestine-on-Chip Models.

Understanding the intestinal transport of particles is critical in several fields ranging from optimizing drug delivery systems to capturing health risks from the increased presence of nano- and micro-sized particles in human environment. While Caco-2 cell monolayers grown on permeable supports are the traditional in vitro model used to probe intestinal absorption of dissolved molecules, they fail to recapitulate the transcytotic activity of polarized enterocytes. Here, an intestine-on-chip model is combined with in silico modeling to demonstrate that the rate of particle transcytosis is ≈350× higher across Caco-2 cell monolayers exposed to fluid shear stress compared to Caco-2 cells in standard "static" configuration. This relates to profound phenotypical alterations and highly polarized state of cells grown under mechanical stimulation and it is shown that transcytosis in the microphysiological model is energy-dependent and involves both clathrin and macropinocytosis mediated endocytic pathways. Finally, it is demonstrated that the increased rate of transcytosis through cells exposed to flow is explained by a higher rate of internal particle transport (i.e., vesicular cellular trafficking and basolateral exocytosis), rather than a change in apical uptake (i.e., binding and endocytosis). Taken together, the findings have important implications for addressing research questions concerning intestinal transport of engineered and environmental particles.

IP3R activity increases propensity of RyR-mediated sparks by elevating dyadic [Ca2＋].

Calcium (Ca2＋) plays a critical role in the excitation contraction coupling (ECC) process that mediates the contraction of cardiomyocytes during each heartbeat. While ryanodine receptors (RyRs) are the primary Ca2＋ channels responsible for generating the cell-wide Ca2＋ transients during ECC, Ca2＋ release, via inositol 1,4,5-trisphosphate (IP3) receptors (IP3Rs) are also reported in cardiomyocytes to elicit ECC-modulating effects. Recent studies suggest that the localization of IP3Rs at dyads grant their ability to modify the occurrence of Ca2＋ sparks (elementary Ca2＋ release events that constitute cell wide Ca2＋ releases associated with ECC) which may underlie their modulatory influence on ECC. Here, we aim to uncover the mechanism by which dyad-localized IP3Rs influence Ca2＋ spark dynamics. To this end, we developed a mathematical model of the dyad that incorporates the behaviour of IP3Rs, in addition to RyRs, to reveal the impact of their activity on local Ca2＋ handling and consequent Ca2＋ spark occurrence and its properties. Consistent with published experimental data, our model predicts that the propensity for Ca2＋ spark formation increases in the presence of IP3R activity. Our simulations support the hypothesis that IP3Rs elevate Ca2＋ in the dyad, sensitizing proximal RyRs towards activation and hence Ca2＋ spark formation. The stochasticity of IP3R gating is an important aspect of this mechanism. However, dyadic IP3R activity lowers the Ca2＋ available in the junctional sarcoplasmic reticulum (JSR) for release, thus resulting in Ca2＋ sparks with similar durations but lower amplitudes.

Mathematical assessment of the role of intervention programs for malaria control.

Malaria remains a global health problem despite the many attempts to control and eradicate it. There is an urgent need to understand the current transmission dynamics of malaria and to determine the interventions necessary to control malaria. In this paper, we seek to develop a fit-for-purpose mathematical model to assess the interventions needed to control malaria in an endemic setting. To achieve this, we formulate a malaria transmission model to analyse the spread of malaria in the presence of interventions. A sensitivity analysis of the model is performed to determine the relative impact of the model parameters on disease transmission. We explore how existing variations in the recruitment and management of intervention strategies affect malaria transmission. Results obtained from the study imply that the discontinuation of existing interventions has a significant effect on malaria prevalence. Thus, the maintenance of interventions is imperative for malaria elimination and eradication. In a scenario study aimed at assessing the impact of long-lasting insecticidal nets (LLINs), indoor residual spraying (IRS), and localized individual measures, our findings indicate that increased LLINs utilization and extended IRS coverage (with longer-lasting insecticides) cause a more pronounced reduction in symptomatic malaria prevalence compared to a reduced LLINs utilization and shorter IRS coverage. Additionally, our study demonstrates the impact of localized preventive measures in mitigating the spread of malaria when compared to the absence of interventions.

Identification of clinical isolates of α-hemolytic streptococci by 16S rRNA gene sequencing, matrix-assisted laser desorption ionization-time of flight mass spectrometry using MALDI Biotyper, and conventional phenotypic methods: a comparison.

Fifty-six α-hemolytic streptococcal isolates were identified using MALDI Biotyper MS (Bruker Daltonics), API 20 Strep (bioMérieux), and BD Phoenix (Becton, Dickinson). The gold standard for identification was 16S rRNA gene sequence analysis with 16S-23S rRNA intergenic spacer sequencing. The following percentages of isolates were correctly identified to the species level: MALDI Biotyper, 46%; BD Phoenix, 35%; and API 20 Strep, 26%.

Preclinical disposition of GDC-0973 and prospective and retrospective analysis of human dose and efficacy predictions.

[3,4-Difluoro-2-(2-fluoro-4-iodo-phenylamino)-phenyl]-((S)-3-hydroxy-3-piperidin-2-yl-azetidin-1-yl)-methanone (GDC-0973) is a potent and highly selective inhibitor of mitogen-activated protein kinase(MAPK)/extracellular signal-regulated kinase (ERK) 1/2 (MEK1/2), a MAPK kinase that activates ERK1/2. The objectives of these studies were to characterize the disposition of GDC-0973 in preclinical species and to determine the relationship of GDC-0973 plasma concentrations to efficacy in Colo205 mouse xenograft models. The clearance (CL) of GDC-0973 was moderate in mouse (33.5 ml · min(-1) · kg(-1)), rat (37.9 ± 7.2 ml · min(-1) · kg(-1)), and monkey (29.6 ± 8.5 ml · min(-1) · kg(-1)). CL in dog was low (5.5 ± 0.3 ml · min(-1) · kg(-1)). The volume of distribution across species was large, 6-fold to 15-fold body water; half-lives ranged from 4 to 13 h. Protein binding in mouse, rat, dog, monkey, and human was high, with percentage unbound, 1 to 6%. GDC-0973-related radioactivity was rapidly and extensively distributed to tissues; however, low concentrations were observed in the brain. In rats and dogs, [(14)C]GDC-0973 was well absorbed (fraction absorbed, 70-80%). The majority of [(14)C]GDC-0973-related radioactivity was recovered in the bile of rat (74-81%) and dog (65%). The CL and volume of distribution of GDC-0973 in human, predicted by allometry, was 2.9 ml · min(-1) · kg(-1) and 9.9 l/kg, respectively. The predicted half-life was 39 h. To characterize the relationship between plasma concentration of GDC-0973 and tumor growth inhibition, pharmacokinetic-pharmacodynamic modeling was applied using an indirect response model. The KC(50) value for tumor growth inhibition in Colo205 xenografts was estimated to be 0.389 µM, and the predicted clinical efficacious dose was ∼10 mg. Taken together, these data are useful in assessing the disposition of GDC-0973, and where available, comparisons with human data were made.

The design, synthesis, and biological evaluation of PIM kinase inhibitors.

A series of substituted benzofuropyrimidinones with pan-PIM activities and excellent selectivity against a panel of diverse kinases is described. Initial exploration identified aryl benzofuropyrimidinones that were potent, but had cell permeability limitation. Using X-ray crystal structures of the bound PIM-1 complexes with 3, 5m, and 6d, we were able to guide the SAR and identify the alkyl benzofuropyrimidinone (6l) with good PIM potencies, permeability, and oral exposure.

Equation learning to identify nano-engineered particle-cell interactions: an interpretable machine learning approach.

Designing nano-engineered particles capable of the delivery of therapeutic and diagnostic agents to a specific target remains a significant challenge. Understanding how interactions between particles and cells are impacted by the physicochemical properties of the particle will help inform rational design choices. Mathematical and computational techniques allow for details regarding particle-cell interactions to be isolated from the interwoven set of biological, chemical, and physical phenomena involved in the particle delivery process. Here we present a machine learning framework capable of elucidating particle-cell interactions from experimental data. This framework employs a data-driven modelling approach, augmented by established biological knowledge. Crucially, the model of particle-cell interactions learned by the framework can be interpreted and analysed, in contrast to the 'black box' models inherent to other machine learning approaches. We apply the framework to association data for thirty different particle-cell pairs. This library of data contains both adherent and suspension cell lines, as well as a diverse collection of particles. We consider hyperbranched polymer and poly(methacrylic acid) particles, from 6 nm to 1032 nm in diameter, with small molecule, monoclonal antibody, and peptide surface functionalisations. Despite the diverse nature of the experiments, the learned models of particle-cell interactions for each particle-cell pair are remarkably consistent: out of 2048 potential models, only four unique models are learned. The models reveal that nonlinear saturation effects are a key feature governing particle-cell interactions. Further, the framework provides robust estimates of particle performance, which facilitates quantitative evaluation of particle design choices.

On predicting heterogeneity in nanoparticle dosage.

Nanoparticles are increasingly employed as a vehicle for the targeted delivery of therapeutics to specific cell types. However, much remains to be discovered about the fundamental biology that dictates the interactions between nanoparticles and cells. Accordingly, few nanoparticle-based targeted therapeutics have succeeded in clinical trials. One element that hinders our understanding of nanoparticle-cell interactions is the presence of heterogeneity in nanoparticle dosage data obtained from standard experiments. It is difficult to distinguish between heterogeneity that arises from stochasticity in nanoparticle-cell interactions, and that which arises from heterogeneity in the cell population. Mathematical investigations have revealed that both sources of heterogeneity contribute meaningfully to the heterogeneity in nanoparticle dosage. However, these investigations have relied on simplified models of nanoparticle internalisation. Here we present a stochastic mathematical model of nanoparticle internalisation that incorporates a suite of relevant biological phenomena such as multistage internalisation, cell division, asymmetric nanoparticle inheritance and nanoparticle saturation. Critically, our model provides information about nanoparticle dosage at an individual cell level. We perform model simulations to examine the influence of specific biological phenomena on the heterogeneity in nanoparticle dosage in the absence of heterogeneity in the cell population. Under certain modelling assumptions, we derive analytic approximations of the nanoparticle dosage distribution. We demonstrate that the analytic approximations are accurate, and show that nanoparticle dosage can be described by a Poisson mixture distribution with rate parameters that are a function of Beta-distributed random variables. We discuss the implications of the analytic results with respect to parameter estimation and model identifiability from standard experimental data. Finally, we highlight extensions and directions for future research.

Modelling realistic 3D deformations of simple epithelia in dynamic homeostasis.

The maintenance of tissue and organ structures during dynamic homeostasis is often not well understood. In order for a system to be stable, cell renewal, cell migration and cell death must be finely balanced. Moreover, a tissue's shape must remain relatively unchanged. Simple epithelial tissues occur in various structures throughout the body, such as the endothelium, mesothelium, linings of the lungs, saliva and thyroid glands, and gastrointestinal tract. Despite the prevalence of simple epithelial tissues, there are few models which accurately describe how these tissues maintain a stable structure. Here, we present a novel, 3D, deformable, multilayer, cell-centre model of a simple epithelium. Cell movement is governed by the minimisation of a bending potential across the epithelium, cell-cell adhesion, and viscous effects. We show that the model is capable of maintaining a consistent tissue structure while undergoing self renewal. We also demonstrate the model's robustness under tissue renewal, cell migration and cell removal. The model presented here is a valuable advancement towards the modelling of tissues and organs with complex and generalised structures.

Spatio-temporal analysis of nanoparticles in live tumor spheroids impacted by cell origin and density.

Nanoparticles hold great preclinical promise in cancer therapy but continue to suffer attrition through clinical trials. Advanced, three dimensional (3D) cellular models such as tumor spheroids can recapitulate elements of the tumor environment and are considered the superior model to evaluate nanoparticle designs. However, there is an important need to better understand nanoparticle penetration kinetics and determine how different cell characteristics may influence this nanoparticle uptake. A key challenge with current approaches for measuring nanoparticle accumulation in spheroids is that they are often static, losing spatial and temporal information which may be necessary for effective nanoparticle evaluation in 3D cell models. To overcome this challenge, we developed an analysis platform, termed the Determination of Nanoparticle Uptake in Tumor Spheroids (DONUTS), which retains spatial and temporal information during quantification, enabling evaluation of nanoparticle uptake in 3D tumor spheroids. Outperforming linear profiling methods, DONUTS was able to measure silica nanoparticle uptake to 10 µm accuracy in both isotropic and irregularly shaped cancer cell spheroids. This was then extended to determine penetration kinetics, first by a forward-in-time, center-in-space model, and then by mathematical modelling, which enabled the direct evaluation of nanoparticle penetration kinetics in different spheroid models. Nanoparticle uptake was shown to inversely relate to particle size and varied depending on the cell type, cell stiffness and density of the spheroid model. The automated analysis method we have developed can be applied to live spheroids in situ, for the advanced evaluation of nanoparticles as delivery agents in cancer therapy.