Subject-specific musculoskeletal loading of the tibia: Computational load estimation.

The systematic development of subject-specific computer models for the analysis of personalized treatments is currently a reality. In fact, many advances have recently been developed for creating virtual finite element-based models. These models accurately recreate subject-specific geometries and material properties from recent techniques based on quantitative image analysis. However, to determine the subject-specific forces, we need a full gait analysis, typically in combination with an inverse dynamics simulation study. In this work, we aim to determine the subject-specific forces from the computer tomography images used to evaluate bone density. In fact, we propose a methodology that combines these images with bone remodelling simulations and artificial neural networks. To test the capability of this novel technique, we quantify the personalized forces for five subject-specific tibias using our technique and a gait analysis. We compare both results, finding that similar vertical loads are estimated by both methods and that the dominant part of the load can be reliably computed. Therefore, we can conclude that the numerical-based technique proposed in this work has great potential for estimating the main forces that define the mechanical behaviour of subject-specific bone.

Stability and rupture of bifurcation bridges in semiconductor lasers subject to optical feedback.

The bifurcation diagram of a single-mode semiconductor laser subject to a delayed optical feedback is examined by using numerical continuation methods. For this, we show how to cope with the special symmetry properties of the equations. As the feedback strength is increased, branches of modes and antimodes appear, and we have found that pairs of modes and antimodes are connected by closed branches of periodic solutions (bifurcation bridges). Such connections seem generically present as new pairs of modes and antimodes appear. We subsequently investigate the behavior of the first connection as a function of the linewidth enhancement factor and the feedback phase. Our results extend and confirm existing results and hypotheses reported in the literature. For large values of the linewidth enhancement factor (alpha=5-6), bridges break through homoclinic orbits. Changing the feedback phase unfolds the bifurcation diagram of the modes and antimodes, allowing different types of connections between modes.

Bridges of periodic solutions and tori in semiconductor lasers subject to delay.

For semiconductor lasers subject to a delayed optical feedback, branches of steady states sequentially appear as the feedback rate is increased. But branches of time-periodic solutions are connecting pairs of steady states and provide bridges between stable and unstable modes. All bridges experience a change of stability through a torus bifurcation point. Close to the bifurcation point, the torus remains localized near a specific fixed point in phase space. As the feedback rate increases, the torus envelope suddenly unfolds and its trajectory visits two or more unstable fixed points, anticipating the rich dynamics observed at larger feedback rates.

Low level viral persistence after infection with LCMV: a quantitative insight through numerical bifurcation analysis.

Many important viruses persist at very low levels in the body in the face of host immunity, and may influence the maintenance of this state of 'infection immunity'. To analyse low level viral persistence in quantitative terms, we use a mathematical model of antiviral cytotoxic T lymphocyte (CTL) response to lymphocytic choriomeningitis virus (LCMV). This model, described by a non-linear system of delay differential equations (DDEs), is studied using numerical bifurcation analysis techniques for DDEs. Domains where low level LCMV coexistence with CTL memory is possible, either as an equilibrium state or an oscillatory pattern, are identified in spaces of the model parameters characterising the interaction between virus and CTL populations. Our analysis suggests that the coexistence of replication competent virus below the conventional detection limit (of about 100 pfu per spleen) in the immune host as an equilibrium state requires the per day relative growth rate of the virus population to decrease at least 5-fold compared to the acute phase of infection. Oscillatory patterns in the dynamics of persisting LCMV and CTL memory, with virus population varying between 1 and 100 pfu per spleen, are possible within quite narrow intervals of the rates of virus growth and precursor CTL population death. Whereas the virus replication rate appears to determine the stability of the low level virus persistence, it does not affect the steady-state level of the viral population, except for very low values.

Numerical bifurcation analysis of delay differential equations arising from physiological modeling.

This paper has a dual purpose. First, we describe numerical methods for continuation and bifurcation analysis of steady state solutions and periodic solutions of systems of delay differential equations with an arbitrary number of fixed, discrete delays. Second, we demonstrate how these methods can be used to obtain insight into complex biological regulatory systems in which interactions occur with time delays: for this, we consider a system of two equations for the plasma glucose and insulin concentrations in a diabetic patient subject to a system of external assistance. The model has two delays: the technological delay of the external system, and the physiological delay of the patient's liver. We compute stability of the steady state solution as a function of two parameters, compare with analytical results and compute several branches of periodic solutions and their stability. These numerical results allow to infer two categories of diabetic patients for which the external system has different efficiency.

Interacting pairs of periodic solutions lead to tori in lasers subject to delayed feedback.

Models of class-B lasers subject to either an optoelectronic or an optical feedback are investigated analytically and numerically. We derive slow time amplitude equations from the laser delay differential equations and find multiple bifurcating and isolated branches of periodic solutions. We then show that secondary bifurcations to tori result from the interaction of pairs of Hopf bifurcations. The branches emerging from these bifurcations are followed numerically using a continuation method developed for delay differential equations.

Impaired autoregulation of cerebral blood flow in an experimental model of traumatic brain injury.

In order to study the pathophysiology and the intracranial hemodynamics of traumatic brain injury, we have developed a modified closed-head injury model of impact-acceleration that expresses several features of severe head injury in humans, including acute and long-lasting intracranial hypertension, diffuse axonal injury, neuronal necrosis, bleeding, and edema. In view of the clinical relevance of impaired autoregulation of cerebral blood flow after traumatic brain injury, and aiming at further characterization of the model, we investigated the autoregulation efficiency 24 h after experimental closed-head injury. Cortical blood flow was continuously monitored with a laser-Doppler flowmeter, and the mean arterial blood pressure was progressively decreased by controlled hemorrhage. Relative laser-Doppler flow was plotted against the corresponding mean arterial blood pressure, and a two-line segmented model was applied to determine the break point and slopes of the autoregulation curves. The slope of the curve at the right hand of the break point was significantly increased in the closed head injury group (0.751 +/- 0.966%/mm Hg versus -0.104 +/- 0.425%/mm Hg,p = 0.028). The break point tended towards higher values in the closed head injury group (62.2 +/- 20.8 mm Hg versus 46.9 +/- 12.7 mm Hg; mean +/- SD, p = 0.198). It is concluded that cerebral autoregulation in this modified closed head injury model is impaired 24 h after traumatic brain injury. This finding, in addition to other characteristic features of severe head injury established earlier in this model, significantly contributes to its clinical relevance.

Temporal changes in intracranial pressure in a modified experimental model of closed head injury.

OBJECT: The authors describe an experimental model of closed head injury in rodents that was modified from one developed by Marmarou and colleagues. This modification allows dual control of the dynamic process of impact compared with impulse loading that occurs at the moment of primary brain injury. The principal element in this weight-drop model is an adjustable table that supports the rat at the moment of impact from weights positioned at different heights (accelerations). The aim was to obtain reproducible pathological intracranial pressure (ICPs) while maximally reducing the incidence of mortality and skull fractures. METHODS: Intracranial pressure was investigated in different experimental settings, including two different rat strains and various impact-acceleration conditions and posttrauma survival times. Identical impact-acceleration injuries produced a considerably higher mortality rate in Wistar rats than in Sprague-Dawley rats (50% and 0%, respectively). Gradually increasing severity of impact-acceleration conditions resulted in findings of a significant correlation between the degree of traumatic challenge and increased ICP at 4 hours (p < 0.001, R2=0.73). When the impact-acceleration ratio was changed to result in a more severe head injury, the ICP at 4, 24, and 72 hours was significantly elevated in comparison with that seen in sham-injured rats (4 hours: 19.7+/-2.8 mm Hg, p=0.004; 24 hours: 21.8+/-1.1 mm Hg, p=0.002; 72 hours: 11.9+/-2.5 mm Hg, p=0.009). Comparison of the rise in ICP between moderate and severe impact-acceleration injury at 4 and 24 hours revealed a significantly higher value after severe injury (4 hours: p=0.008; 24 hours: p=0.004). Continuous recordings showed that ICP mounted very rapidly to peak values, which declined gradually toward a pathological level dependent on the severity of the primary insult. Histological examination after severe trauma revealed evidence of irreversible neuronal necrosis, diffuse axonal injury, petechial bleeding, glial swelling, and perivascular edema. CONCLUSIONS: This modified closed head injury model mimics several clinical features of traumatic injury and produces reliable, predictable, and reproducible ICP elevations with concomitant morphological alterations.

Intracranial pressure in a modified experimental model of closed head injury.

Intracranial pressure (ICP) was studied in a modified experimental model of closed head injury, in which the dynamic process of impact versus impulse loading was separately controlled. In this model, mortality of Wistar rats was considerably higher as compared to Sprague-Dawley rats subjected to similar traumatic conditions. Therefore Sprague-Dawley rats were used for all further experiments. Twenty-four rats, divided into 4 groups, underwent either sham or gradually increasing impact-acceleration trauma. Four hours after closed head injury, ICP measurements showed a significant correlation between the severity of the traumatic challenge and the resultant pressure rise (r2 = 0.731; p < 0.001). At the moment of impact there was a momentary blood pressure peak immediately followed by a transient period of hypotension. ICP measurements following directly to an impact-acceleration trauma, revealed an abrupt rise in ICP reaching pathological levels within 5 minutes. In conclusion, this modified model of closed head injury produces a predictable and reproducible pathologic ICP in Sprague-Dawley rats.