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Distributed and Lumped Parameter Models for the Characterization of High Throughput Bioreactors

View Article: PubMed Central - PubMed

ABSTRACT

Next generation bioreactors are being developed to generate multiple human cell-based tissue analogs within the same fluidic system, to better recapitulate the complexity and interconnection of human physiology [1, 2]. The effective development of these devices requires a solid understanding of their interconnected fluidics, to predict the transport of nutrients and waste through the constructs and improve the design accordingly. In this work, we focus on a specific model of bioreactor, with multiple input/outputs, aimed at generating osteochondral constructs, i.e., a biphasic construct in which one side is cartilaginous in nature, while the other is osseous. We next develop a general computational approach to model the microfluidics of a multi-chamber, interconnected system that may be applied to human-on-chip devices. This objective requires overcoming several challenges at the level of computational modeling. The main one consists of addressing the multi-physics nature of the problem that combines free flow in channels with hindered flow in porous media. Fluid dynamics is also coupled with advection-diffusion-reaction equations that model the transport of biomolecules throughout the system and their interaction with living tissues and C constructs. Ultimately, we aim at providing a predictive approach useful for the general organ-on-chip community. To this end, we have developed a lumped parameter approach that allows us to analyze the behavior of multi-unit bioreactor systems with modest computational effort, provided that the behavior of a single unit can be fully characterized.

No MeSH data available.


Variation of the outlet concentration of oxygen with respect to the number of units (unit #0 denotes the inlet value) for the mass transport model without cell metabolism (dashed line), with linear consumption rate (dotted line) and with Michaelis-Menten consumption model (solid line).Data calculated using the full 3D model are reported in red.
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pone.0162774.g009: Variation of the outlet concentration of oxygen with respect to the number of units (unit #0 denotes the inlet value) for the mass transport model without cell metabolism (dashed line), with linear consumption rate (dotted line) and with Michaelis-Menten consumption model (solid line).Data calculated using the full 3D model are reported in red.

Mentions: The inspection of the matrices D,Dl,Dmm informs about the characteristics of the different consumption models compared here. We observe that the diagonal entries of Dl are the smallest, confirming that the linear model is the one with the highest oxygen consumption rate. The extra-diagonal coefficients correspond to the oxygen exchange between the upper and lower chambers. Their magnitude is similar in all cases, because they depend on the diffusion parameters solely. For the linear case, the theory at the basis of the LPM derivation is satisfied, while it does not rigorously hold true for the Michaelis-Menten model, because the mass transport equation becomes nonlinear. Once again, numerical simulations based on the full model applied to the 8-unit array confirm that the LPM model with linear consumption rate, namely Dl, predicts outlet concentrations with less than 1% error. The corresponding results are reported in Table 10 and visualized in Fig 9. In Table 11 we report the error of the LPM based on the Michaelis-Menten nonlinear consumption rate. Despite the nonlinear nature of the problem, in conflict with the principles at the basis of the LPM derivation, the LPM model is fairly accurate in predicting the concentration split and decay at the outlet also with a Michaelis-Menten consumption rate, with a maximum error of about 10% for an array of 4-units, located on the bottom outlet of the bioreactor.


Distributed and Lumped Parameter Models for the Characterization of High Throughput Bioreactors
Variation of the outlet concentration of oxygen with respect to the number of units (unit #0 denotes the inlet value) for the mass transport model without cell metabolism (dashed line), with linear consumption rate (dotted line) and with Michaelis-Menten consumption model (solid line).Data calculated using the full 3D model are reported in red.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5036894&req=5

pone.0162774.g009: Variation of the outlet concentration of oxygen with respect to the number of units (unit #0 denotes the inlet value) for the mass transport model without cell metabolism (dashed line), with linear consumption rate (dotted line) and with Michaelis-Menten consumption model (solid line).Data calculated using the full 3D model are reported in red.
Mentions: The inspection of the matrices D,Dl,Dmm informs about the characteristics of the different consumption models compared here. We observe that the diagonal entries of Dl are the smallest, confirming that the linear model is the one with the highest oxygen consumption rate. The extra-diagonal coefficients correspond to the oxygen exchange between the upper and lower chambers. Their magnitude is similar in all cases, because they depend on the diffusion parameters solely. For the linear case, the theory at the basis of the LPM derivation is satisfied, while it does not rigorously hold true for the Michaelis-Menten model, because the mass transport equation becomes nonlinear. Once again, numerical simulations based on the full model applied to the 8-unit array confirm that the LPM model with linear consumption rate, namely Dl, predicts outlet concentrations with less than 1% error. The corresponding results are reported in Table 10 and visualized in Fig 9. In Table 11 we report the error of the LPM based on the Michaelis-Menten nonlinear consumption rate. Despite the nonlinear nature of the problem, in conflict with the principles at the basis of the LPM derivation, the LPM model is fairly accurate in predicting the concentration split and decay at the outlet also with a Michaelis-Menten consumption rate, with a maximum error of about 10% for an array of 4-units, located on the bottom outlet of the bioreactor.

View Article: PubMed Central - PubMed

ABSTRACT

Next generation bioreactors are being developed to generate multiple human cell-based tissue analogs within the same fluidic system, to better recapitulate the complexity and interconnection of human physiology [1, 2]. The effective development of these devices requires a solid understanding of their interconnected fluidics, to predict the transport of nutrients and waste through the constructs and improve the design accordingly. In this work, we focus on a specific model of bioreactor, with multiple input/outputs, aimed at generating osteochondral constructs, i.e., a biphasic construct in which one side is cartilaginous in nature, while the other is osseous. We next develop a general computational approach to model the microfluidics of a multi-chamber, interconnected system that may be applied to human-on-chip devices. This objective requires overcoming several challenges at the level of computational modeling. The main one consists of addressing the multi-physics nature of the problem that combines free flow in channels with hindered flow in porous media. Fluid dynamics is also coupled with advection-diffusion-reaction equations that model the transport of biomolecules throughout the system and their interaction with living tissues and C constructs. Ultimately, we aim at providing a predictive approach useful for the general organ-on-chip community. To this end, we have developed a lumped parameter approach that allows us to analyze the behavior of multi-unit bioreactor systems with modest computational effort, provided that the behavior of a single unit can be fully characterized.

No MeSH data available.