Topological stability through tame retractions

A smooth map is said to be stable if small perturbations of the map only differ from the original one by a smooth change of coordinates. Smoothly stable maps are generic among the proper maps between given source and target manifolds when the source and target dimensions belong to the so-called nice dimensions, but outside this range of dimensions, smooth maps cannot generally be approximated by stable maps. This leads to the definition of topologically stable maps, where the smooth coordinate changes are replaced with homeomorphisms. The topologically stable maps are generic among proper maps for any dimensions of source and target. The purpose of this thesis is to investigate methods for proving topological stability by constructing extremely tame (E-tame) retractions onto the map in question from one of its smoothly stable unfoldings. In particular, we investigate how to use E-tame retractions from stable unfoldings to find topologically ministable unfoldings for certain weighted homogeneous maps or germs. Our first results are concerned with the construction of E-tame retractions and their relation to topological stability. We study how to construct the E-tame retractions from partial or local information, and these results form our toolbox for the main constructions. In the next chapter we study the group of right-left equivalences leaving a given multigerm f invariant, and show that when the multigerm is finitely determined, the group has a maximal compact subgroup and that the corresponding quotient is contractible. This means, essentially, that the group can be replaced with a compact Lie group of symmetries without much loss of information. We also show how to split the group into a product whose components only depend on the monogerm components of f. In the final chapter we investigate representatives of the E- and Z-series of singularities, discuss their instability and use our tools to construct E-tame retractions for some of them. The construction is based on describing the geometry of the set of points where the map is not smoothly stable, discovering that by using induction and our constructional tools, we already know how to construct local E-tame retractions along the set. The local solutions can then be glued together using our knowledge about the symmetry group of the local germs. We also discuss how to generalize our method to the whole E- and Z- series.

External signal-activated liposomal drug delivery systems

Modern drug discovery gives rise to a great number of potential new therapeutic agents, but in some cases the efficient treatment of patient may not be achieved because the delivery of active compounds to the target site is insufficient. Thus, drug delivery is one of the major challenges in current pharmaceutical research. Numerous nanoparticle-based drug carriers, e.g. liposomes, have been developed for enhanced drug delivery and targeting. Drug targeting may enhance the efficiency of the treatment and, importantly, reduce unwanted side effects by decreasing drug distribution to non-target tissues. Liposomes are biocompatible lipid-based carriers that have been studied for drug delivery during the last 40 years. They can be functionalized with targeting ligands and sensing materials for triggered activation. In this study, various external signal-assisted liposomal delivery systems were developed. Signals can be used to modulate drug permeation or release from the liposome formulation, and they provide accurate control of time, place and rate of activation. The study involved three types of signals that were used to trigger drug permeation and release: electricity, heat and light. Electrical stimulus was utilized to enhance the permeation of liposomal DNA across the skin. Liposome/DNA complex-mediated transfections were performed in tight rat epidermal cell model. Various transfection media and current intensities were tested, and transfection efficiency was evaluated non-invasively by monitoring the concentration of secreted reporter protein in cell culture medium. Liposome/DNA complexes produced gene expression, but electrical stimulus did not enhance the transfection efficiency significantly. Heat-sensitive liposomal drug delivery system was developed by coating liposomes with biodegradable and thermosensitive poly(N-(2-hydroxypropyl) methacrylamide-mono/dilactate polymer. Temperature-triggered liposome aggregation and contents release from liposomes were evaluated. The cloud point temperature (CP) of the polymer was set to 42 °C. Polymer-coated liposome aggregation and contents release were observed above CP of the polymer, while non-coated liposomes remained intact. Polymer precipitates above its CP and interacts with liposomal bilayers. It is likely that this induces permeabilization of the liposomal membrane and contents release. Light-sensitivity was introduced to liposomes by incorporation of small (< 5 nm) gold nanoparticles. Hydrophobic and hydrophilic gold nanoparticles were embedded in thermosensitive liposomes, and contents release was investigated upon UV light exposure. UV light-induced lipid phase transitions were examined with small angle X-ray scattering, and light-triggered contents release was shown also in human retinal pigment epithelial cell line. Gold nanoparticles absorb light energy and transfer it into heat, which induces phase transitions in liposomes and triggers the contents release. In conclusion, external signal-activated liposomes offer an advanced platform for numerous applications in drug delivery, particularly in the localized drug delivery. Drug release may be localized to the target site with triggering stimulus that results in better therapeutic response and less adverse effects. Triggering signal and mechanism of activation can be selected according to a specific application.

Bioabsorbable materials for osteosynthesis and small joint arthroplasty in the hand

Fractures and arthritic joint destruction are common in the hand. A reliable and stable fracture fixation can be achieved by metal implants, which however, become unnecessary or even harmful after consolidation. The silicone implant arthroplasty is the current method of choice for reconstruction of metacarpophalangeal joints in rheumatoid patients. However, the outcome tends to worsen with long-term follow-up and implant-related complications become frequent. To address these problems, bioabsorbable implants were designed for the hand area. Aims of the studies were: 1) to evaluate the biomechanical stabilities provided by self- reinforced (SR) bioabsorbable implants in a transverse and an oblique osteotomy of small tubular bones and to compare them with those provided by metal implants; 2) to evaluate the SR poly-L/DL-lactide 70/30 plate for osteosynthesis in a proof-of-principle type of experiment in three cases of hand injuries; and 3) to evaluate the poly-L/D-lactide (PLA) 96/4 joint scaffold, a composite joint implant with a supplementary intramedullary Polyactive® stem and Swanson silicone implant in an experimental small joint arthroplasty model. Methods used were: 1) 112 fresh frozen human cadaver and 160 pig metacarpal bones osteotomised transversally or obliquely, respectively, and tested ex vivo in three point bending and in torsion; 2) three patient cases of complex hand injuries; and 3) the fifth metacarpophalangeal joints reconstructed in 18 skeletally-mature minipigs and studied radiologically and histologically. The initial fixation stabilities provided by bioabsorbable implants in the tubular bones of the hand were comparable with currently-employed metal fixation techniques, and were sufficient for fracture stabilisation in three preliminary cases in the hand. However, in torsion the stabilities provided by bioabsorbable implants were lower than that provided by metal counterparts. The bioabsorbable plate enhanced the bending stability for the bioabsorbable fixation construct. PLA 96/4 joint scaffolds demonstrated good biocompatibility and enabled fibrous tissue in-growth in situ. After scaffold degradation, a functional, stable pseudarthrosis with dense fibrous connective tissue was formed. However, the supplementary Polyactive® stem caused a deleterious tissue reaction and therefore the stem can not be applied to the composite joint implant. The bioabsorbable implants have potential for use in clinical hand surgery, but have to await validation in clinical patient series and controlled trials.

Peritoneal dialysis and neurological outcome in infants and small children

Although improved outcomes for children on peritoneal dialysis (PD) have been seen in recent years, the youngest patients continue to demonstrate inferior growth, more frequent infections, more neurological sequelae, and higher mortality compared to older children. Also, maintain-ing normal intravascular volume status, especially in anuric patients, has proven difficult. This study was designed to treat and monitor these youngest PD patients, which are relatively many due to the high prevalence of congenital nephrotic syndrome of the Finnish type (CNF, NPHS1) in Finland, with a strict protocol, to evaluate the results and to improve metabolic balance, growth, and development. A retrospective analysis of 23 children under two years of age at onset of PD, treated between 1995 and 2000, was performed to obtain a control population for our prospective PD study. Respectively, 21 patients less than two years of age at the beginning of PD were enrolled in prospective studies between 2001 and 2005. Medication for uremia and nutrition were care-fully adjusted during PD. Laboratory parameters and intravascular volume status were regu-larly analyzed. Growth was analyzed and compared with midparental height. In a prospective neurological study, the risk factors for development and the neurological development was determined. Brain images were surveyed. Hearing was tested. In a retrospective neurological study, the data of six NPHS1 patients with a congruent neurological syndrome was analyzed. All these patients had a serious dyskinetic cerebral palsy-like syndrome with muscular dysto-nia and athetosis (MDA). They also had a hearing defect. Metabolic control was mainly good in both PD patient groups. Hospitalization time shortened clearly. The peritonitis rate diminished. Hypertension was a common problem. Left ventricular hypertrophy decreased during the prospective study period. None of the patients in either PD group had pulmonary edema or dialysis-related seizures. Growth was good and catch-up growth was documented in most patients in both patient groups during PD. Mortality was low (5% in prospective and 9% in retrospective PD patients). In the prospective PD patient group 11 patients (52%) had some risk factor for their neuro-development originating from the predialysis period. The neurological problems, detected be-fore PD, did not worsen during PD and none of the patients developed new neurological com-plications during PD. Brain infarcts were detected in four (19%) and other ischemic lesions in three patients (14%). At the end of this study, 29% of the prospectively followed patients had a major impairment of their neurodevelopment and 43% only minor impairment. In the NPHS1+MDA patients, no clear explanation for the neurological syndrome was found. The brain MRI showed increased signal intensity in the globus pallidus area. Kernic-terus was contemplated to be causative in the hypoproteinemic newborns but it could not be proven. Mortality was as high as 67%. Our results for young PD patients were promising. Metabolic control was acceptable and growth was good. However, the children were significantly smaller when compared to their midparental height. Although many patients were found to have neurological impairment at the end of our follow-up period, PD was a safe treatment whereby the neurodevelopment did not worsen during PD.

Tuning and stability of a singly resonant continuous-wave optical parametric oscillator close to degeneracy

Wavelength tuning and stability characteristics of a singly resonant continuous-wave optical parametric oscillator (cw OPO) in the proximity of signal-idler degeneracy have been studied. The OPO is made singly resonant by using a Bragg grating as a spectral filter in the OPO cavity. The signal-idler frequency difference can be tuned from 0.5 to 7 THz, which makes the OPO suitable for cw THz generation by optical heterodyning. The operation of the OPO within this singly-resonant regime is characterized by a strong self-stabilization effect. A gradual transition to an unstable, doubly-resonant regime is observed for a signal-idler detuning smaller than ~ 0.5 THz.