Corina Drapaca - Academia.edu (original) (raw)
Papers by Corina Drapaca
Bulletin of Mathematical Biology
Fractional calculus has recently been applied to the mathematical modelling of tumour growth, but... more Fractional calculus has recently been applied to the mathematical modelling of tumour growth, but its use introduces complexities that may not be warranted. Mathematical modelling with differential equations is a standard approach to study and predict treatment outcomes for population-level and patient-specific responses. Here, we use patient data of radiation-treated tumours to discuss the benefits and limitations of introducing fractional derivatives into three standard models of tumour growth. The fractional derivative introduces a history-dependence into the growth function, which requires a continuous death-rate term for radiation treatment. This newly proposed radiation-induced death-rate term improves computational efficiency in both ordinary and fractional derivative models. This computational speed-up will benefit common simulation tasks such as model parameterization and the construction and running of virtual clinical trials.
Fractal and Fractional
Action potentials in myelinated neurons happen only at specialized locations of the axons known a... more Action potentials in myelinated neurons happen only at specialized locations of the axons known as the nodes of Ranvier. The shapes, timings, and propagation speeds of these action potentials are controlled by biochemical interactions among neurons, glial cells, and the extracellular space. The complexity of brain structure and processes suggests that anomalous diffusion could affect the propagation of action potentials. In this paper, a spatio-temporal fractional cable equation for action potentials propagation in myelinated neurons is proposed. The impact of the ionic anomalous diffusion on the distribution of the membrane potential is investigated using numerical simulations. The results show spatially narrower action potentials at the nodes of Ranvier when using spatial derivatives of the fractional order only and delayed or lack of action potentials when adding a temporal derivative of the fractional order. These findings could reveal the pathological patterns of brain diseases...
Frontiers in Physiology
Nitric oxide (NO) is a small gaseous molecule that is involved in some critical biochemical proce... more Nitric oxide (NO) is a small gaseous molecule that is involved in some critical biochemical processes in the body such as the regulation of cerebral blood flow and pressure. Infection and inflammatory processes such as those caused by COVID-19 produce a disequilibrium in the NO bioavailability and/or a delay in the interactions of NO with other molecules contributing to the onset and evolution of cardiocerebrovascular diseases. A link between the SARS-CoV-2 virus and NO is introduced. Recent experimental observations of intracellular transport of metabolites in the brain and the NO trapping inside endothelial microparticles (EMPs) suggest the possibility of anomalous diffusion of NO, which may be enhanced by disease processes. A novel space-fractional reaction-diffusion equation to model NO biotransport in the brain is further proposed. The model incorporates the production of NO by synthesis in neurons and by mechanotransduction in the endothelial cells, and the loss of NO due to i...
Fractal and Fractional
Alzheimer’s disease (AD) is an age-related degenerative disorder of the cerebral neuro-glial-vasc... more Alzheimer’s disease (AD) is an age-related degenerative disorder of the cerebral neuro-glial-vascular units. Not only are post-menopausal females, especially those who carry the APOE4 gene, at a higher risk of AD than males, but also AD in females appears to progress faster than in aged-matched male patients. Currently, there is no cure for AD. Mathematical models can help us to understand mechanisms of AD onset, progression, and therapies. However, existing models of AD do not account for sex differences. In this paper a mathematical model of AD is proposed that uses variable-order fractional temporal derivatives to describe the temporal evolutions of some relevant cells’ populations and aggregation-prone amyloid-β fibrils. The approach generalizes the model of Puri and Li. The variable fractional order describes variable fading memory due to neuroprotection loss caused by AD progression with age which, in the case of post-menopausal females, is more aggressive because of fast estr...
arXiv (Cornell University), Aug 24, 2018
Mathematical models that accurately predict the mechanical behavior of blood can contribute to th... more Mathematical models that accurately predict the mechanical behavior of blood can contribute to the development of biomedical devices and medications which are relevant in clinical applications. The models existing in the literature are complex enough in order to agree with various in vitro experimental observations. Latest technological advancements opened the possibility of studying blood flow in vivo which could play an important role in the creation of biocompatible implants for health monitoring and treatment purposes. However, most of existing models may fail to predict blood behavior in vivo because they require many parameters which are difficult to find in vivo and they do not incorporate pertinent coupled chemo-mechanical dynamics specific to blood flow in a living body. Recently, we used the fractional model of continuum mechanics proposed by Drapaca and Sivaloganathan [J. Elast.,107: 105-123, 2012] to study blood circulation. In this mathematical formulation the spatial derivatives of the rate of deformation tensor are expressed using Caputo fractional derivatives. The aim of this paper is to compare the Poiseuille flows of blood through an axi-symmetric circular rigid and impermeable pipe where the blood is described by the above mentioned fractional model, the Casson's model, and the power law model. Although the velocity profiles of these three models look similar, the fractional model provides a better fitting to published experimental data.
It is well known that the mechanical behavior of arterial walls plays an important role in the pa... more It is well known that the mechanical behavior of arterial walls plays an important role in the pathogenesis of vascular diseases. Most studies existing in the literature focus on the mechanical interactions between the blood flow and wall’s deformations. However, in the brain, the smaller vessels experience not only oscillatory forces due to the pulsatile blood flow but also structural and morphological changes controlled by the surrounding brain cells. In this study, the mechanical deformation of the cerebral arterial wall caused by the pulsatile blood flow and the dynamics of the neuronal nitric oxide (NO) is investigated. NO is a small diffusive gaseous molecule produced by the endothelial cells and neurons, which is involved in the regulation of cerebral blood flow and pressure. The cerebral vessel is assumed to be a hollow axial symmetric cylinder whose wall thickness is much smaller than the cylinder’s radius and longitudinal length is much less than the propagating wavelength...
Emerging Science Journal, 2020
Myelinated neurons are characterized by the presence of myelin, a multilaminated wrapping around ... more Myelinated neurons are characterized by the presence of myelin, a multilaminated wrapping around the axons formed by specialized neuroglial cells. Myelin acts as an electrical insulator and therefore, in myelinated neurons, the action potentials do not propagate within the axons but happen only at the nodes of Ranvier which are gaps in the axonal myelination. Recent advancements in brain science have shown that the shapes, timings, and propagation speeds of these so-called saltatory action potentials are controlled by various biochemical interactions among neurons, glial cells and the extracellular space. Given the complexity of brain’s structure and processes, the work hypothesis made in this paper is that non-local effects are involved in the optimal propagation of action potentials. A non- local model of the action potentials propagation in myelinated neurons is proposed that involves spatial derivatives of fractional order. The effects of non- locality on the distribution of the...
Science Advances, 2020
Aspiration-assisted bioprinting enables precise positioning of viscoelastic spheroids in both sca... more Aspiration-assisted bioprinting enables precise positioning of viscoelastic spheroids in both scaffold-based and free manner.
Fractal and Fractional, 2018
International Journal of Non-Linear Mechanics, 2019
Emerging Science Journal, 2018
Brain tissue is a complex material made of interconnected neural, glial, and vascular networks. W... more Brain tissue is a complex material made of interconnected neural, glial, and vascular networks. While the physics and biochemistry of brain’s cell types and their interactions within their networks have been studied extensively, only recently the interactions of and feedback among the networks have started to capture the attention of the research community. Thus, a good understanding of the coupled mechano-electrochemical processes that either provide or diminish brain’s functions is still lacking. One way to increase the knowledge on how the brain yields its functions is by developing a robust controlled feedback engineering system that uses fundamental science concepts to guide and interpret experiments investigating brain’s response to various stimuli, aging, trauma, diseases, treatment and recovery processes. Recently, a mathematical model for an implantable neuro-glial-vascular unit, named brain-on-a-chip, was proposed that can be optimized to perform some fundamental cellular ...
Theoretical Biology and Medical Modelling, 2017
Conference Proceedings of the Society for Experimental Mechanics Series, 2011
The aim of this paper is to formulate a novel mathematical model that will be able to differentia... more The aim of this paper is to formulate a novel mathematical model that will be able to differentiate not only between normal and abnormal tissues, but, more importantly, between benign and malignant tumors. We present some very promising preliminary results of a multiscale triphasic model for biological tissues that couple the electro-chemical processes that take place in tissue’s microstructure and
Lecture Notes in Computational Vision and Biomechanics, 2013
Lecture Notes in Computer Science, 2012
Mechanics of Biological Systems and Materials, Volume 4, 2013
ASME 2013 2nd Global Congress on NanoEngineering for Medicine and Biology, 2013
Hydrocephalus is a brain disease characterized by abnormalities in the cerebrospinal fluid (CSF) ... more Hydrocephalus is a brain disease characterized by abnormalities in the cerebrospinal fluid (CSF) circulation. The treatment is surgical in nature and continues to suffer of poor outcomes. The first mathematical model for studying the CSF pressure-volume relationship in hydrocephalus was proposed by Marmarou in the 1970s. However, the model fails to fully capture the complex CSF dynamics controlled by CSF-brain tissue interactions. In this paper we use fractional calculus to introduce multiscaling effects in Marmarou’s model. We solve our fractional order non-linear differential equation analytically using a modified Adomian decomposition method.
Frontiers in Cellular Neuroscience, 2015
Journal of neurosurgery. Pediatrics, 2010
Hydrocephalus has traditionally been quantified by linear measures of ventricular size, with adju... more Hydrocephalus has traditionally been quantified by linear measures of ventricular size, with adjunct use of cortical mantle thickness. However, clinical outcome depends on cognitive function, which is more directly related to brain volume than these previous measures. The authors sought to quantify the dynamics of brain and ventricular volume growth in normal compared with hydrocephalic mice. Hydrocephalus was induced in 14-day-old C57BL/6 mice by percutaneous injection of kaolin into the cisterna magna. Nine hydrocephalic and 6 normal mice were serially imaged from age 2-12 weeks with a 14.1-T MR imaging unit. Total brain and ventricle volumes were calculated, and linear discriminant analysis was applied. Two very different patterns of response were seen in hydrocephalic mice compared with mice with normative growth. In one pattern (3 mice) brain growth was normal despite accumulation of CSF, and in the second pattern (6 mice) abnormal brain enlargement was accompanied by increased...
SPIE Proceedings, 2004
This paper focuses on the problem of accurately extracting the CSF-tissue boundary, particularly ... more This paper focuses on the problem of accurately extracting the CSF-tissue boundary, particularly around the ventricular surface, from serial structural MRI of the brain acquired in imaging studies of aging and dementia. This is a challenging problem because of the common occurrence ...
Bulletin of Mathematical Biology
Fractional calculus has recently been applied to the mathematical modelling of tumour growth, but... more Fractional calculus has recently been applied to the mathematical modelling of tumour growth, but its use introduces complexities that may not be warranted. Mathematical modelling with differential equations is a standard approach to study and predict treatment outcomes for population-level and patient-specific responses. Here, we use patient data of radiation-treated tumours to discuss the benefits and limitations of introducing fractional derivatives into three standard models of tumour growth. The fractional derivative introduces a history-dependence into the growth function, which requires a continuous death-rate term for radiation treatment. This newly proposed radiation-induced death-rate term improves computational efficiency in both ordinary and fractional derivative models. This computational speed-up will benefit common simulation tasks such as model parameterization and the construction and running of virtual clinical trials.
Fractal and Fractional
Action potentials in myelinated neurons happen only at specialized locations of the axons known a... more Action potentials in myelinated neurons happen only at specialized locations of the axons known as the nodes of Ranvier. The shapes, timings, and propagation speeds of these action potentials are controlled by biochemical interactions among neurons, glial cells, and the extracellular space. The complexity of brain structure and processes suggests that anomalous diffusion could affect the propagation of action potentials. In this paper, a spatio-temporal fractional cable equation for action potentials propagation in myelinated neurons is proposed. The impact of the ionic anomalous diffusion on the distribution of the membrane potential is investigated using numerical simulations. The results show spatially narrower action potentials at the nodes of Ranvier when using spatial derivatives of the fractional order only and delayed or lack of action potentials when adding a temporal derivative of the fractional order. These findings could reveal the pathological patterns of brain diseases...
Frontiers in Physiology
Nitric oxide (NO) is a small gaseous molecule that is involved in some critical biochemical proce... more Nitric oxide (NO) is a small gaseous molecule that is involved in some critical biochemical processes in the body such as the regulation of cerebral blood flow and pressure. Infection and inflammatory processes such as those caused by COVID-19 produce a disequilibrium in the NO bioavailability and/or a delay in the interactions of NO with other molecules contributing to the onset and evolution of cardiocerebrovascular diseases. A link between the SARS-CoV-2 virus and NO is introduced. Recent experimental observations of intracellular transport of metabolites in the brain and the NO trapping inside endothelial microparticles (EMPs) suggest the possibility of anomalous diffusion of NO, which may be enhanced by disease processes. A novel space-fractional reaction-diffusion equation to model NO biotransport in the brain is further proposed. The model incorporates the production of NO by synthesis in neurons and by mechanotransduction in the endothelial cells, and the loss of NO due to i...
Fractal and Fractional
Alzheimer’s disease (AD) is an age-related degenerative disorder of the cerebral neuro-glial-vasc... more Alzheimer’s disease (AD) is an age-related degenerative disorder of the cerebral neuro-glial-vascular units. Not only are post-menopausal females, especially those who carry the APOE4 gene, at a higher risk of AD than males, but also AD in females appears to progress faster than in aged-matched male patients. Currently, there is no cure for AD. Mathematical models can help us to understand mechanisms of AD onset, progression, and therapies. However, existing models of AD do not account for sex differences. In this paper a mathematical model of AD is proposed that uses variable-order fractional temporal derivatives to describe the temporal evolutions of some relevant cells’ populations and aggregation-prone amyloid-β fibrils. The approach generalizes the model of Puri and Li. The variable fractional order describes variable fading memory due to neuroprotection loss caused by AD progression with age which, in the case of post-menopausal females, is more aggressive because of fast estr...
arXiv (Cornell University), Aug 24, 2018
Mathematical models that accurately predict the mechanical behavior of blood can contribute to th... more Mathematical models that accurately predict the mechanical behavior of blood can contribute to the development of biomedical devices and medications which are relevant in clinical applications. The models existing in the literature are complex enough in order to agree with various in vitro experimental observations. Latest technological advancements opened the possibility of studying blood flow in vivo which could play an important role in the creation of biocompatible implants for health monitoring and treatment purposes. However, most of existing models may fail to predict blood behavior in vivo because they require many parameters which are difficult to find in vivo and they do not incorporate pertinent coupled chemo-mechanical dynamics specific to blood flow in a living body. Recently, we used the fractional model of continuum mechanics proposed by Drapaca and Sivaloganathan [J. Elast.,107: 105-123, 2012] to study blood circulation. In this mathematical formulation the spatial derivatives of the rate of deformation tensor are expressed using Caputo fractional derivatives. The aim of this paper is to compare the Poiseuille flows of blood through an axi-symmetric circular rigid and impermeable pipe where the blood is described by the above mentioned fractional model, the Casson's model, and the power law model. Although the velocity profiles of these three models look similar, the fractional model provides a better fitting to published experimental data.
It is well known that the mechanical behavior of arterial walls plays an important role in the pa... more It is well known that the mechanical behavior of arterial walls plays an important role in the pathogenesis of vascular diseases. Most studies existing in the literature focus on the mechanical interactions between the blood flow and wall’s deformations. However, in the brain, the smaller vessels experience not only oscillatory forces due to the pulsatile blood flow but also structural and morphological changes controlled by the surrounding brain cells. In this study, the mechanical deformation of the cerebral arterial wall caused by the pulsatile blood flow and the dynamics of the neuronal nitric oxide (NO) is investigated. NO is a small diffusive gaseous molecule produced by the endothelial cells and neurons, which is involved in the regulation of cerebral blood flow and pressure. The cerebral vessel is assumed to be a hollow axial symmetric cylinder whose wall thickness is much smaller than the cylinder’s radius and longitudinal length is much less than the propagating wavelength...
Emerging Science Journal, 2020
Myelinated neurons are characterized by the presence of myelin, a multilaminated wrapping around ... more Myelinated neurons are characterized by the presence of myelin, a multilaminated wrapping around the axons formed by specialized neuroglial cells. Myelin acts as an electrical insulator and therefore, in myelinated neurons, the action potentials do not propagate within the axons but happen only at the nodes of Ranvier which are gaps in the axonal myelination. Recent advancements in brain science have shown that the shapes, timings, and propagation speeds of these so-called saltatory action potentials are controlled by various biochemical interactions among neurons, glial cells and the extracellular space. Given the complexity of brain’s structure and processes, the work hypothesis made in this paper is that non-local effects are involved in the optimal propagation of action potentials. A non- local model of the action potentials propagation in myelinated neurons is proposed that involves spatial derivatives of fractional order. The effects of non- locality on the distribution of the...
Science Advances, 2020
Aspiration-assisted bioprinting enables precise positioning of viscoelastic spheroids in both sca... more Aspiration-assisted bioprinting enables precise positioning of viscoelastic spheroids in both scaffold-based and free manner.
Fractal and Fractional, 2018
International Journal of Non-Linear Mechanics, 2019
Emerging Science Journal, 2018
Brain tissue is a complex material made of interconnected neural, glial, and vascular networks. W... more Brain tissue is a complex material made of interconnected neural, glial, and vascular networks. While the physics and biochemistry of brain’s cell types and their interactions within their networks have been studied extensively, only recently the interactions of and feedback among the networks have started to capture the attention of the research community. Thus, a good understanding of the coupled mechano-electrochemical processes that either provide or diminish brain’s functions is still lacking. One way to increase the knowledge on how the brain yields its functions is by developing a robust controlled feedback engineering system that uses fundamental science concepts to guide and interpret experiments investigating brain’s response to various stimuli, aging, trauma, diseases, treatment and recovery processes. Recently, a mathematical model for an implantable neuro-glial-vascular unit, named brain-on-a-chip, was proposed that can be optimized to perform some fundamental cellular ...
Theoretical Biology and Medical Modelling, 2017
Conference Proceedings of the Society for Experimental Mechanics Series, 2011
The aim of this paper is to formulate a novel mathematical model that will be able to differentia... more The aim of this paper is to formulate a novel mathematical model that will be able to differentiate not only between normal and abnormal tissues, but, more importantly, between benign and malignant tumors. We present some very promising preliminary results of a multiscale triphasic model for biological tissues that couple the electro-chemical processes that take place in tissue’s microstructure and
Lecture Notes in Computational Vision and Biomechanics, 2013
Lecture Notes in Computer Science, 2012
Mechanics of Biological Systems and Materials, Volume 4, 2013
ASME 2013 2nd Global Congress on NanoEngineering for Medicine and Biology, 2013
Hydrocephalus is a brain disease characterized by abnormalities in the cerebrospinal fluid (CSF) ... more Hydrocephalus is a brain disease characterized by abnormalities in the cerebrospinal fluid (CSF) circulation. The treatment is surgical in nature and continues to suffer of poor outcomes. The first mathematical model for studying the CSF pressure-volume relationship in hydrocephalus was proposed by Marmarou in the 1970s. However, the model fails to fully capture the complex CSF dynamics controlled by CSF-brain tissue interactions. In this paper we use fractional calculus to introduce multiscaling effects in Marmarou’s model. We solve our fractional order non-linear differential equation analytically using a modified Adomian decomposition method.
Frontiers in Cellular Neuroscience, 2015
Journal of neurosurgery. Pediatrics, 2010
Hydrocephalus has traditionally been quantified by linear measures of ventricular size, with adju... more Hydrocephalus has traditionally been quantified by linear measures of ventricular size, with adjunct use of cortical mantle thickness. However, clinical outcome depends on cognitive function, which is more directly related to brain volume than these previous measures. The authors sought to quantify the dynamics of brain and ventricular volume growth in normal compared with hydrocephalic mice. Hydrocephalus was induced in 14-day-old C57BL/6 mice by percutaneous injection of kaolin into the cisterna magna. Nine hydrocephalic and 6 normal mice were serially imaged from age 2-12 weeks with a 14.1-T MR imaging unit. Total brain and ventricle volumes were calculated, and linear discriminant analysis was applied. Two very different patterns of response were seen in hydrocephalic mice compared with mice with normative growth. In one pattern (3 mice) brain growth was normal despite accumulation of CSF, and in the second pattern (6 mice) abnormal brain enlargement was accompanied by increased...
SPIE Proceedings, 2004
This paper focuses on the problem of accurately extracting the CSF-tissue boundary, particularly ... more This paper focuses on the problem of accurately extracting the CSF-tissue boundary, particularly around the ventricular surface, from serial structural MRI of the brain acquired in imaging studies of aging and dementia. This is a challenging problem because of the common occurrence ...