Theoretical Biology and Medical Modelling - Latest Articles

Numerical investigation of the effect of cannula placement on thrombosis

ChiWei Ong — 2013-05-16T00:00:00Z

Despite the rapid advancement of left ventricular assist devices (LVADs), adverse events leading to deaths have been frequently reported in patients implanted with LVADs, including bleeding, infection, thromboembolism, neurological dysfunction and hemolysis.Cannulation forms an important component with regards to thrombus formation in assisted patients by varying the intraventricular flow distribution in the left ventricle (LV). To investigate the correlation between LVAD cannula placement and potential for thrombus formation, detailed analysis of the intraventricular flow field was carried out in the present study using a two way fluid structure interaction (FSI), axisymmetric model of a passive LV incorporating an inflow cannula. Three different cannula placements were simulated, with device insertion near the LV apex, penetrating one-fourth and mid-way into the LV long axis. The risk of thrombus formation is assessed by analyzing the intraventricular vorticity distribution and its associated vortex intensity, amount of stagnation flow in the ventricle as well as the level of wall shear stress. Our results show that the one-fourth placement of the cannula into the LV achieves the best performance in reducing the risk of thrombus formation. Compared to cannula placement near the apex, higher vortex intensity is achieved at the one-fourth placement, thus increasing wash out of platelets at the ventricular wall. One-fourth LV penetration produced negligible stagnation flow region near the apical wall region, helping to reduce platelet deposition on the surface of the cannula and the ventricular wall.

Using allometric procedures to substantiate the plastochrone method for eelgrass leaf growth assessments

Héctor Echavarría-Heras — 2013-05-16T00:00:00Z

Estimation of leaf productivity in eelgrass (Zostera marina L.) is crucial for evaluating the ecological role of this important seagrass species. Although leaf marking techniques are widely used to obtain estimates of leaf productivity, the accuracy of these assessments, has been questioned mainly because these fail to account for leaf growth bellow the reference mark and also because they apparently disregard the contribution of mature leaf tissues to the growth rate of leaves. On the other hand, the plastochrone method is a simpler technique that has been considered to effectively capture growth in a more realistic way, thereby providing more accurate assessments of both above- and below-ground productivities. But since the actual values of eelgrass growth rates are difficult to obtain, the worth of the plastochrone method has been largely vindicated because it produces assessments that overestimate productivity as compared to estimates obtained by leaf marking. Additionally, whenever eelgrass leaf biomass can be allometrically scaled in terms of matching leaf length in a consistent way, the associated leaf growth rates can be also projected allometrically. In this contribution, we used that approach to derive an authentication of the plastochrone method and formally demonstrate that, as has been claimed to occur for leaf marking approaches, the plastochrone method itself underestimates actual values of eelgrass leaf growth rates. We also show that this unavoidable bias is mainly due to the inadequacy of single-leaf biomass assessments in providing a proxy for the growth of all leaf tissue in a shoot over a given interval. Moreover, the derived formulae give conditions under which assessments of leaf growth rates using the plastochrone method would systematically underestimate matching values obtained by leaf marking procedures. And, assessments of leaf growth rates obtained by using the present data show that plastochrone method estimations underestimated corresponding proxies obtained allometrically (27 %), or through leaf marking (35 %). Allometric projection is recommended as a simpler and more effective procedure to reduce the bias in eelgrass leaf productivity estimations that associates to the use of plastochrone methods.

Exploring haemodynamics of haemodialysis using extrema points analysis model

Mohamed Eldehni — 2013-05-16T00:00:00Z

Background: Haemodialysis is a form of renal replacement therapy used to treat patients with end stage renal failure. It is becoming more appreciated that haemodialysis patients exhibit higher rates of multiple end organ damage compared to the general population. There is also a strong emerging evidence that haemodialysis itself causes circulatory stress. We aimed at examining haemodynamic patterns during haemodialysis using a new model and test that model against a normal control. Methods: We hypothesised that blood pressures generated by each heart beat constantly vary between local peaks and troughs (local extrema), the frequency and amplitude of which is regulated to maintain optimal organ perfusion. We also hypothesised that such model could reveal multiple haemodynamic aberrations during HD. Using a non-invasive cardiac output monitoring device (Finometer(R)) we compared various haemodynamic parameters using the above model between a haemodialysis patient during a dialysis session and an exercised normal control after comparison at rest. Results: Measurements yielded 29,751 data points for each haemodynamic parameter. Extrema points frequency of mean arterial blood pressure was higher in the HD subject compared to the normal control (0.761Hz IQR 0.5-0.818 vs 0.468Hz IQR 0.223-0.872, P < 0.0001). Similarly, extrema points frequency of systolic blood pressure was significantly higher in haemodialysis compared to normal. In contrary, the frequency of extrema points for TPR was higher in the normal control compared to HD (0.947 IQR 0.520-1.512 vs 0.845 IQR 0.730-1.569, P < 0.0001) with significantly higher amplitudes. Conclusion: Haemodialysis patients potentially exhibit an aberrant haemodynamic behaviour characterised by higher extrema frequencies of mean arterial blood pressure and lower extrema frequencies of total peripheral resistance. This, in theory, could lead to higher variation in organ perfusion and may be detrimental to vulnerable vascular beds.

Computational simulation of the bone remodeling using the finite element method: an elastic-damage theory for small displacements

Ahmed Idhammad — 2013-05-13T00:00:00Z

Background: The resistance of the bone against damage by repairing itself and adapting to environmental conditions is its most important property. These adaptive changes are regulated by physiological process commonly called the bone remodeling. Better understanding this process requires that we apply the theory of elastic-damage under the hypothesis of small displacements to a bone structure and see its mechanical behavior. Results: The purpose of the present study is to simulate a two dimensional model of a proximal femur by taking into consideration elastic-damage and mechanical stimulus. Here, we present a mathematical model based on a system of nonlinear ordinary differential equations and we develop the variational formulation for the mechanical problem. Then, we implement our mathematical model into the finite element method algorithm to investigate the effect of the damage. Conclusion: The results are consistent with the existing literature which shows that the bone stiffness drops in damaged bone structure under mechanical loading.

A new method to estimate parameters of the growth model for metastatic tumours

Esmaeil Mehrara — 2013-05-09T00:00:00Z

Purpose: Knowledge of natural tumour growth is valuable for understanding tumour biology, optimising screening programs, prognostication, optimal scheduling of chemotherapy, and assessing tumour spread. However, mathematical modelling in individuals is hampered by the limited data available. We aimed to develop a method to estimate parameters of the growth model and formation rate of metastases in individual patients.Materials and methods: Data from one patient with liver metastases from a primary ileum carcinoid and one patient with lung metastases from a primary renal cell carcinoma were used to demonstrate this new method. Metastatic growth models were estimated by direct curve fitting, as well as with the new proposed method based on the relationship between tumour growth rate and tumour volume. The new model was derived from the Gompertzian growth model by eliminating the time factor (age of metastases), which made it possible to perform the calculations using data from all metastases in each patient. Finally, the formation time of each metastasis and, consecutively, the formation rate of metastases in each patient were estimated. Results: With limited measurements in clinical studies, fitting different growth curves was insufficient to estimate true tumour growth, even if patients were followed for several years. Growth of liver metastases was well described with a general growth model for all metastases. However, the lung metastases from renal cell carcinoma were better described by heterogeneous exponential growth with various growth rates. Conclusion: Analysis of the regression of tumour growth rate with the logarithm of tumour volume can be used to estimate parameters of the tumour growth model and metastasis formation rates, and therefore the number and size distribution of metastases in individuals.

How to interpret the transmissibility of novel influenza A(H7N9): an analysis of initial epidemiological data of human cases from China

Hiroshi Nishiura — 2013-05-04T00:00:00Z

Background: As the human infections with novel influenza A(H7N9) virus have been reported from several different provinces in China, the pandemic potential of the virus has been questioned. The presence of human-to-human transmission has not been demonstrated, but the absence of demonstration does not guarantee that there is no such transmission. Methods: A mathematical model of cluster size distribution is devised without imposing an assumption of subcriticality of the reproduction number and accounting for right censoring of new clusters. The proportion of cases with a history of bird contact is analytically derived, permitting us to fit the model to the observed data of confirmed cases. Using contact history with bird among confirmed cases (n = 129), we estimate the reproduction number of the novel influenza A(H7N9) from human to human. Results: Analysing twenty confirmed cases with known exposure, the reproduction number for human-to-human transmission was estimated at 0.28 (95% CI: 0.11, 0.45). Sensitivity analysis indicated that the reproduction number is substantially below unity. Conclusions: It is unlikely to observe an immediate pandemic of novel influenza A(H7N9) virus with human to human transmission. Continued monitoring of cases and animals would be the key to elucidate additional epidemiological characteristics of the virus.

Determination of the optimal tubulin isotype target as a method for the development of individualized cancer chemotherapy

Siamak Ravanbakhsh — 2013-05-01T00:00:00Z

Background: As microtubules are essential for cell growth and division, its constituent protein β-tubulin has been a popular target for various treatments, including cancer chemotherapy. There are several isotypes of human β-tubulin and each type of cell expresses its characteristic distribution of these isotypes. Moreover, each tubulin-binding drug has its own distribution of binding affinities over the various isotypes, which further complicates identifying the optimal drug selection. An ideal drug would preferentially bind only the tubulin isotypes expressed abundantly by the cancer cells, but not those in the healthy cells. Unfortunately, as the distributions of the tubulin isotypes in cancer cells overlap with those of healthy cells, this ideal scenario is clearly not possible. We can, however, seek a drug that interferes significantly with the isotype distribution of the cancer cell, but has only minor interactions with those of the healthy cells. Methods: We describe a quantitative methodology for identifying this optimal tubulin isotype profile for an ideal cancer drug, given the isotype distribution of a specific cancer type, as well as the isotype distributions in various healthy tissues, and the physiological importance of each such tissue. Results: We report the optimal isotype profiles for different types of cancer with various routes of delivery. Conclusions: Our algorithm, which defines the best profile for each type of cancer (given the drug delivery route and some specified patient characteristics), will help to personalize the design of pharmaceuticals for individual patients. This paper is an attempt to explicitly consider the effects of the tubulin isotype distributions in both cancer and normal cell types, for rational chemotherapy design aimed at optimizing the drug’s efficacy with minimal side effects.

Development of a three-dimensional model of the human respiratory system for dosimetric use

Jacky Rosati Rowe — 2013-05-01T00:00:00Z

Background: Determining the fate of inhaled contaminants in the human respiratory system has challenged scientists for years. Human and animal studies have provided some data, but there is a paucity of data for toxic contaminants and sensitive populations (such as children, elderly, diseased). Methods: Three-dimensional modeling programs and publicly available human physiology data have been used to develop a comprehensive model of the human respiratory system. Results: The in silico human respiratory system model, which includes the extrathoracic region (nasal, oral, pharyngeal, and laryngeal passages), the upper airways (trachea and main bronchi), the tracheobronchial tree, and branching networks through alveolar region, allows for virtually any variation of airway geometries and disease states. The model allows for parameterization of variables that define the subject's airways by integrating morphological changes created by disease, age, etc. with a dynamic morphology. Conclusions: The model can be used for studies of sensitive populations and the homeland security community, in cases where inhalation studies on humans cannot be conducted with toxic contaminants of interest.

Mathematical models for the Notch and Wnt signaling pathways and the crosstalk between them during somitogenesis

Hong-yan Wang — 2013-04-20T00:00:00Z

Background: Somitogenesis is a fundamental characteristic feature of development in various animal embryos. Molecular evidence has proved that the Notch and Wnt pathways play important roles in regulating the process of somitogenesis and there is crosstalk between these two pathways. However, it is difficult to investigate the detailed mechanism of these two pathways and their interactions in somitogenesis through biological experiments. In recent years some mathematical models have been proposed for the purpose of studying the dynamics of the Notch and Wnt pathways in somitogenesis. Unfortunately, only a few of these models have explored the interactions between them. Results: In this study, we have proposed three mathematical models for the Notch signalling pathway alone, the Wnt signalling pathway alone, and the interactions between them. These models can simulate the dynamics of the Notch and Wnt pathways in somitogenesis, and are capable of reproducing the observations derived from wet experiments. They were used to investigate the molecular mechanisms of the Notch and Wnt pathways and their crosstalk in somitogenesis through the model simulations. Conclusions: Three mathematical models are proposed for the Notch and Wnt pathways and their interaction during somitogenesis. The simulations demonstrate that the extracellular Notch and Wnt signals are essential for the oscillating expressions of both Notch and Wnt target genes. Moreover, the internal negative feedback loops and the three levels of crosstalk between these pathways play important but distinct roles in maintaining the system oscillation. In addition, the results of the parameter sensitivity analysis of the models indicate that the Notch pathway is more sensitive to perturbation in somitogenesis.

Structural mimicry between SLA/LP and Rickettsia surface antigens as a driver of autoimmune hepatitis: insights from an in silico study

Alessandro Paiardini — 2013-04-10T00:00:00Z

Background: Autoimmune hepatitis (AIH) is a chronic, progressive liver disease, characterized by continuing hepatocellular inflammation and necrosis. A subgroup of AIH patients presents specific autoantibodies to soluble liver antigen/liver-pancreas (SLA/LP) protein, which is regarded as a highly specific diagnostic marker. Autoantigenic SLA/LP peptides are targeted by CD4+ T cells, and restricted by the allele HLA-DRB1*03:01, which confers disease susceptibility in Europeans and Americans. A positively charged residue at position 71 has been indicated as critical for AIH susceptibility in all of the HLA alleles identified to date. Though the exact molecular mechanisms underlying pathogenesis of AIH are not clear, molecular mimicry between SLA/LP and viral/bacterial antigens has been invoked. Methods: The immunodominant region of SLA/LP was used as query in databank searches to identify statistically significant similarities with viral/bacterial peptides. Homology modeling and docking was used to investigate the potential interaction of HLA-DRB1*03:01 with the identified peptides. By molecular mechanics means, the interactions and energy of binding at the HLA binding site was also scrutinized. Results: A statistically significant structural similarity between the immunodominant regions of SLA/LP and a region of the surface antigen PS 120 from Rickettsia spp. has been detected. The interaction of the SLA/LP autoepitope and the corresponding Rickettsia sequence with the allele HLA-DRB1*03:01 has been simulated. The obtained results predict for both peptides a similar binding mode and affinity to HLA-DRB1*03:01. A “hot spot” of interaction between HLA-DRB1*03:01 and PS 120 is located at the P4 binding pocket, and is represented by a salt bridge involving Lys at position 71 of the HLA protein, and Glu 795 of PS120 peptide. Conclusions: These findings strongly support the notion that a molecular mimicry mechanism can trigger AIH onset. CD4+ T cells recognizing peptides of SLA/LP could indeed cross-react with foreign Rickettsia spp. antigens. Finally, the same analysis suggests a molecular explanation for the importance of position 71 in conferring the susceptibility of the allele HLA-DRB1*03:01 to AIH. The lack of a positive charge at such position could prevent HLA alleles from binding the foreign peptides and triggering the molecular mimicry event.